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-   Aliquot Sequences (https://www.mersenneforum.org/forumdisplay.php?f=90)
-   -   Aliquot sequences that start on the integer powers n^i (https://www.mersenneforum.org/showthread.php?t=23612)

 EdH 2022-09-03 14:19

Thanks Jean-Luc! I'll do another update for the other thread a bit later. Are you interested in the frequency of primes <300 throughout the tables? Maybe I can resurrect some of my work from last year(s) and see if we match. It may be a while before I do, though.

I've been thinking about the genealogy thread from back long ago and wondered what might be found trying to tie some of the terminated sequences together. I'm kind of wondering for how many iterations prior to termination most of the sequences are merged , but it's just a fleeting thought ATM. I have some ideas as to how to approach finding them, but haven't programmed anything yet. There are limited ways that a certain prime can be "Aliqueitly" arrived at via previous composite terms. It may be interesting to trace some backwards. Perhaps you've already worked there?

 garambois 2022-09-04 10:10

2 Attachment(s)
[SIZE=-1]It is time for me to explain in more detail what I am doing.[/SIZE]
[SIZE=-1]It's the same work as explained in post [URL="https://www.mersenneforum.org/showpost.php?p=592117&postcount=1360"]#1360[/URL], but with much more data and many more primes.[/SIZE]
[SIZE=-1] I have also developed a list of "things to look at".
After the Big Scan, one of my programs gave me the following lines in a few hours :

[/SIZE][CODE][2, [2, 1]]
[3, [2, 2], [2, 4], [2, 55], [2, 164], [2, 305], [2, 317], [3, 1], [3, 2], [3, 5], [3, 247], [5, 38], [6, 152], [7, 4], [7, 77], [10, 124], [11, 2], [11, 15], [12, 1], [12, 2], [13, 15], [14, 76], [14, 80], [15, 1], [19, 15], [20, 2], [20, 8], [21, 21], [21, 55], [22, 80], [23, 3], [23, 109], [26, 1], [29, 2], [29, 69], [30, 1], [30, 82], [30, 92], [31, 79], [33, 1], [35, 49], [37, 11], [38, 11], [38, 30], [40, 14], [41, 2], [42, 1], [43, 15], [44, 58], [45, 1], [45, 34], [46, 1], [47, 13], [50, 73], [52, 1], [52, 34], [53, 2], [53, 27], [53, 30], [54, 1], [54, 10], [55, 53], [58, 18], [59, 49], [60, 86], [66, 1], [70, 70], [71, 2], [72, 1], [74, 6], [74, 20], [74, 78], [75, 45], [77, 5], [77, 19], [78, 1], [79, 97], [83, 43], [84, 30], [86, 1], [87, 1], [87, 17], [89, 2], [90, 1], [93, 49], [95, 5], [96, 42], [98, 45], [99, 3], [99, 71], [101, 2], [102, 1], [104, 58], [105, 1], [107, 11], [109, 13], [113, 2], [131, 57], [137, 3], [139, 33], [157, 5], [167, 63], [167, 79], [173, 2], [197, 2], [197, 23], [197, 27], [211, 2], [220, 16], [239, 3], [242, 41], [251, 33], [257, 2], [269, 2], [277, 9], [288, 1], [288, 3], [293, 11], [293, 23], [306, 17], [338, 2], [338, 13], [396, 11], [450, 1], [450, 19], [564, 2], [648, 1], [648, 56], [722, 37], [800, 21], [828, 24], [882, 5], [966, 6], [966, 34], [968, 8], [996, 12], [1058, 31], [1250, 10], [1352, 1], [2310, 36], [14288, 12], [223092870, 20]]
[5, [5, 1]]
[7, [2, 3], [2, 10], [2, 12], [2, 141], [2, 278], [2, 387], [2, 421], [3, 6], [3, 8], [3, 118], [3, 198], [3, 305], [7, 1], [7, 2], [7, 8], [7, 127], [10, 1], [11, 5], [12, 21], [13, 2], [13, 87], [14, 1], [14, 19], [14, 21], [14, 130], [15, 10], [17, 24], [17, 91], [18, 13], [18, 52], [18, 70], [18, 134], [19, 2], [20, 1], [21, 8], [21, 17], [22, 1], [22, 19], [23, 11], [26, 3], [26, 19], [26, 50], [26, 80], [28, 9], [28, 47], [30, 52], [30, 70], [34, 1], [34, 7], [34, 9], [35, 11], [37, 2], [38, 1], [38, 13], [40, 2], [41, 49], [42, 2], [43, 20], [45, 4], [45, 55], [46, 33], [47, 8], [47, 42], [48, 61], [50, 17], [53, 8], [56, 38], [58, 5], [58, 27], [61, 2], [62, 1], [66, 5], [66, 31], [68, 10], [70, 48], [72, 25], [74, 11], [75, 1], [75, 63], [76, 39], [77, 2], [77, 16], [78, 23], [79, 7], [80, 28], [84, 31], [92, 32], [93, 29], [94, 22], [96, 3], [96, 7], [97, 5], [99, 19], [102, 2], [105, 2], [151, 2], [163, 4], [193, 3], [200, 24], [200, 56], [211, 65], [220, 15], [223, 4], [227, 10], [229, 4], [242, 39], [271, 3], [271, 34], [277, 25], [293, 55], [338, 39], [385, 57], [450, 12], [450, 17], [496, 31], [564, 21], [648, 40], [696, 7], [722, 51], [800, 51], [888, 5], [968, 60], [8128, 38], [14264, 7], [15015, 35], [15472, 3], [19116, 15], [131071, 8], [131071, 25]]
[11, [2, 60], [2, 316], [2, 480], [2, 499], [3, 15], [3, 189], [3, 303], [5, 15], [7, 143], [10, 20], [11, 1], [11, 137], [13, 31], [14, 14], [14, 28], [17, 2], [18, 1], [18, 55], [18, 76], [21, 1], [21, 47], [24, 2], [26, 36], [35, 83], [37, 50], [47, 47], [51, 1], [53, 15], [53, 67], [58, 2], [58, 24], [59, 81], [63, 85], [65, 2], [65, 33], [67, 3], [70, 2], [71, 61], [72, 4], [72, 58], [72, 63], [73, 3], [76, 28], [77, 15], [79, 3], [80, 3], [82, 2], [82, 54], [88, 54], [91, 1], [92, 30], [95, 63], [98, 2], [99, 13], [109, 15], [109, 75], [139, 5], [162, 70], [193, 57], [210, 58], [242, 25], [271, 23], [283, 27], [284, 19], [288, 4], [564, 30], [578, 50], [648, 41], [648, 42], [800, 54], [882, 50], [888, 26], [968, 32], [14288, 2], [14288, 4], [14288, 9], [31704, 16], [223092870, 4]]
[13, [2, 358], [3, 3], [3, 31], [3 formes polynĂ´miales de degrĂ© 3 , 67], [5, 9], [11, 3], [11, 27], [13, 1], [20, 72], [23, 49], [23, 77], [24, 70], [35, 1], [38, 86], [39, 91], [43, 3], [43, 17], [50, 62], [50, 99], [56, 8], [62, 2], [69, 1], [70, 34], [73, 11], [75, 13], [79, 23], [93, 1], [94, 12], [96, 6], [103, 5], [104, 24], [104, 64], [131, 9], [167, 17], [173, 69], [179, 25], [181, 23], [197, 3], [229, 21], [263, 7], [263, 15], [271, 4], [392, 48], [392, 54], [648, 7], [770, 28], [968, 1], [1058, 7], [8191, 17], [15015, 9], [15015, 33], [6469693230, 2]]
[17, [3, 63], [6, 2], [7, 55], [13, 21], [15, 79], [17, 1], [19, 97], [23, 2], [24, 1], [24, 4], [38, 42], [39, 1], [45, 5], [46, 10], [51, 31], [55, 1], [58, 70], [60, 28], [78, 52], [84, 78], [85, 63], [92, 4], [96, 34], [99, 23], [119, 79], [131, 15], [157, 65], [162, 39], [271, 21], [396, 6], [1152, 31]]
[19, [2, 39], [2, 76], [2, 190], [2, 219], [2, 505], [3, 275], [3, 327], [5, 233], [10, 2], [10, 12], [10, 44], [12, 4], [12, 150], [13, 3], [13, 141], [15, 21], [19, 1], [22, 32], [34, 96], [40, 6], [41, 7], [41, 68], [42, 10], [42, 22], [45, 15], [55, 29], [59, 85], [60, 30], [65, 1], [70, 28], [71, 21], [72, 74], [76, 66], [77, 1], [79, 13], [88, 62], [89, 9], [89, 19], [90, 2], [94, 70], [97, 29], [98, 6], [102, 54], [109, 27], [193, 2], [210, 12], [233, 41], [241, 51], [263, 21], [269, 11], [276, 10], [277, 11], [288, 16], [293, 17], [338, 59], [392, 6], [392, 26], [392, 42], [496, 30], [722, 30], [770, 14], [1058, 44], [1152, 27], [8191, 15], [19116, 24], [131071, 21]]
[23, [3, 12], [3, 181], [7, 3], [7, 9], [11, 127], [17, 79], [18, 6], [18, 17], [18, 64], [21, 61], [23, 1], [40, 36], [44, 68], [47, 3], [54, 80], [55, 15], [57, 1], [57, 17], [65, 3], [69, 9], [71, 65], [74, 64], [77, 23], [77, 37], [79, 49], [85, 1], [86, 54], [88, 26], [93, 3], [99, 1], [101, 65], [105, 47], [127, 3], [137, 43], [173, 35], [200, 18], [242, 28], [263, 13], [293, 7], [496, 22], [564, 50], [578, 1], [800, 2], [8128, 8], [14536, 32], [19116, 8], [510510, 8]]
[29, [5, 41], [14, 92], [18, 50], [18, 116], [22, 8], [26, 68], [29, 1], [46, 36], [47, 39], [48, 4], [61, 5], [63, 67], [72, 43], [83, 11], [88, 2], [88, 78], [91, 13], [97, 3], [162, 11], [229, 51], [283, 5], [306, 56], [338, 57], [450, 21], [82589933, 3]]
[31, [2, 5], [2, 101], [2, 146], [3, 169], [5, 3], [5, 161], [6, 17], [11, 38], [11, 93], [11, 107], [12, 14], [19, 35], [19, 37], [31, 1], [31, 2], [31, 11], [38, 19], [40, 30], [44, 30], [54, 67], [56, 52], [58, 1], [61, 55], [67, 2], [68, 1], [70, 54], [70, 58], [74, 21], [80, 30], [87, 13], [91, 15], [92, 2], [92, 14], [95, 27], [97, 49], [98, 3], [103, 9], [113, 3], [119, 53], [162, 27], [163, 8], [179, 21], [210, 14], [220, 4], [227, 19], [231, 2], [239, 33], [269, 37], [281, 61], [882, 1], [882, 6], [1152, 4], [1152, 28], [1210, 10], [8191, 7], [12496, 3]]
[37, [2, 68], [2, 125], [2, 243], [3, 90], [5, 4], [7, 6], [7, 79], [10, 3], [10, 5], [10, 74], [11, 40], [12, 98], [14, 2], [14, 35], [14, 138], [22, 7], [22, 21], [22, 23], [22, 74], [23, 10], [24, 6], [26, 31], [28, 3], [28, 11], [29, 50], [35, 2], [37, 1], [42, 16], [44, 3], [44, 19], [45, 11], [47, 16], [51, 2], [53, 87], [55, 43], [60, 94], [63, 3], [67, 74], [71, 4], [74, 5], [75, 8], [77, 34], [78, 4], [79, 6], [83, 2], [83, 10], [84, 1], [84, 32], [85, 81], [88, 3], [90, 9], [94, 16], [95, 37], [96, 1], [96, 48], [97, 4], [99, 5], [104, 4], [131, 6], [131, 45], [139, 2], [149, 43], [220, 27], [239, 18], [241, 28], [241, 47], [251, 26], [277, 10], [283, 33], [293, 10], [552, 18], [14316, 2], [15015, 27]]
[41, [2, 6], [2, 8], [2, 23], [2, 47], [2, 112], [2, 117], [2, 281], [2, 373], [2, 405], [2, 411], [6, 5], [6, 13], [7, 11], [11, 14], [11, 57], [12, 32], [12, 56], [12, 119], [15, 2], [15, 6], [17, 65], [18, 39], [20, 3], [22, 67], [24, 18], [33, 2], [35, 8], [35, 34], [37, 20], [37, 73], [38, 54], [40, 11], [40, 20], [40, 21], [40, 52], [41, 1], [42, 5], [43, 25], [43, 81], [44, 49], [45, 8], [45, 22], [45, 36], [47, 2], [48, 1], [48, 3], [50, 16], [51, 18], [52, 25], [55, 21], [56, 1], [57, 2], [59, 39], [61, 9], [62, 3], [62, 13], [62, 40], [63, 1], [65, 4], [65, 26], [66, 25], [66, 78], [69, 2], [70, 13], [70, 23], [70, 38], [71, 5], [71, 7], [73, 27], [75, 2], [76, 1], [78, 15], [78, 64], [79, 2], [79, 4], [79, 17], [80, 1], [82, 11], [84, 2], [85, 8], [88, 1], [88, 22], [92, 1], [94, 11], [94, 46], [96, 50], [97, 7], [97, 48], [98, 10], [98, 41], [103, 2], [103, 21], [104, 1], [105, 10], [105, 30], [107, 3], [107, 61], [109, 2], [113, 16], [119, 29], [127, 26], [127, 44], [127, 52], [163, 2], [167, 13], [167, 20], [173, 9], [181, 5], [193, 32], [197, 10], [197, 20], [210, 4], [220, 17], [223, 2], [227, 2], [229, 2], [231, 4], [257, 28], [263, 8], [277, 14], [283, 17], [284, 11], [288, 57], [293, 4], [385, 11], [385, 42], [439, 2], [578, 3], [720, 3], [770, 13], [966, 2], [966, 31], [968, 2], [1210, 24], [1352, 4], [2310, 8], [14288, 3], [14536, 5], [31704, 9], [9699690, 20], [223092870, 2], [8589869056, 3]]
[43, [2, 9], [2, 62], [2, 210], [2, 271], [2, 510], [3, 4], [3, 22], [3, 80], [3, 86], [6, 26], [6, 32], [6, 77], [7, 16], [7, 28], [7, 51], [7, 189], [10, 42], [11, 13], [11, 28], [11, 56], [13, 4], [13, 8], [13, 40], [13, 95], [13, 98], [14, 5], [14, 23], [14, 25], [15, 14], [17, 12], [17, 16], [17, 101], [17, 129], [18, 34], [19, 4], [19, 55], [20, 21], [20, 70], [21, 2], [21, 6], [21, 98], [22, 2], [22, 104], [23, 4], [24, 10], [24, 19], [24, 31], [24, 36], [26, 6], [26, 38], [26, 78], [26, 88], [28, 13], [28, 18], [29, 3], [29, 59], [31, 14], [31, 26], [33, 3], [33, 23], [33, 45], [34, 3], [34, 28], [34, 44], [35, 4], [37, 97], [38, 38], [39, 6], [40, 1], [40, 35], [42, 13], [43, 1], [43, 2], [43, 55], [44, 1], [45, 2], [46, 3], [46, 5], [47, 17], [48, 9], [50, 1], [51, 5], [51, 13], [51, 50], [52, 9], [53, 4], [54, 49], [57, 26], [58, 71], [59, 2], [59, 6], [59, 18], [60, 1], [60, 6], [62, 8], [62, 9], [62, 50], [63, 6], [65, 12], [65, 32], [66, 21], [66, 56], [67, 10], [67, 63], [68, 14], [68, 18], [69, 3], [69, 43], [70, 1], [70, 8], [70, 22], [70, 27], [71, 26], [73, 2], [73, 14], [74, 1], [75, 6], [75, 11], [75, 46], [75, 73], [78, 17], [79, 30], [79, 31], [79, 56], [80, 5], [80, 36], [80, 68], [82, 1], [82, 72], [83, 3], [86, 11], [87, 6], [87, 28], [88, 76], [90, 35], [91, 2], [91, 44], [92, 13], [92, 19], [93, 24], [93, 27], [94, 1], [95, 21], [96, 5], [97, 40], [98, 5], [98, 29], [99, 8], [102, 22], [102, 26], [104, 3], [104, 26], [104, 68], [104, 70], [105, 3], [105, 6], [107, 2], [107, 5], [109, 11], [119, 38], [127, 11], [131, 2], [137, 71], [139, 4], [157, 2], [157, 25], [167, 39], [179, 3], [179, 5], [181, 2], [191, 2], [191, 5], [191, 31], [199, 29], [200, 7], [223, 12], [227, 6], [227, 12], [227, 14], [227, 57], [231, 1], [231, 6], [233, 10], [241, 55], [257, 3], [263, 43], [269, 43], [271, 2], [271, 20], [276, 4], [277, 2], [277, 45], [306, 11], [385, 8], [396, 5], [439, 3], [496, 18], [496, 36], [552, 28], [648, 45], [660, 30], [722, 15], [770, 1], [828, 14], [968, 29], [1152, 9], [1152, 12], [1152, 29], [1155, 1], [1155, 2], [1210, 28], [1250, 47], [2310, 16], [15015, 12], [19116, 4], [2147483647, 5], [6469693230, 1], [200560490130, 10]]
[47, [2, 453], [3, 9], [28, 34], [30, 10], [40, 22], [47, 1], [65, 47], [77, 13], [78, 80], [82, 26], [93, 17], [98, 75], [120, 44], [200, 37], [578, 22], [696, 2], [968, 40]]
[53, [2, 20], [2, 78], [2, 214], [2, 347], [2, 450], [23, 101], [48, 50], [48, 70], [53, 1], [72, 18], [75, 31], [94, 2], [163, 61], [181, 53], [241, 3], [306, 8], [306, 50], [648, 30], [648, 44], [888, 14]]
[59, [3, 94], [6, 128], [7, 14], [7, 24], [7, 64], [10, 7], [10, 23], [11, 8], [11, 58], [11, 80], [13, 6], [13, 38], [14, 9], [14, 49], [15, 36], [17, 64], [19, 6], [19, 25], [20, 59], [20, 71], [24, 9], [24, 13], [26, 59], [26, 71], [28, 7], [28, 23], [29, 4], [29, 36], [31, 8], [31, 10], [33, 4], [33, 6], [35, 6], [38, 77], [39, 2], [39, 12], [42, 3], [44, 5], [45, 6], [45, 28], [45, 30], [51, 32], [51, 78], [52, 3], [52, 11], [55, 4], [56, 61], [57, 4], [58, 17], [59, 1], [60, 3], [60, 17], [61, 12], [65, 50], [66, 17], [69, 4], [69, 10], [69, 24], [70, 19], [70, 39], [71, 28], [73, 4], [73, 10], [74, 33], [75, 18], [75, 38], [77, 28], [78, 44], [84, 5], [86, 37], [86, 49], [87, 4], [87, 8], [89, 16], [90, 11], [95, 2], [97, 46], [99, 2], [103, 14], [103, 38], [104, 5], [105, 19], [119, 2], [127, 25], [131, 22], [137, 2], [149, 2], [151, 6], [151, 27], [162, 62], [167, 2], [173, 6], [179, 4], [179, 16], [191, 20], [193, 4], [193, 16], [197, 4], [199, 2], [199, 4], [200, 1], [211, 4], [220, 55], [233, 2], [251, 2], [263, 2], [269, 47], [271, 6], [281, 12], [385, 10], [439, 4], [564, 5], [720, 11], [14288, 7], [15472, 5], [131071, 4], [7420738134810, 1]]
[61, [30, 90], [39, 3], [43, 23], [45, 7], [52, 6], [52, 36], [60, 9], [61, 1], [67, 61], [75, 43], [76, 68], [104, 54], [137, 21], [284, 22], [496, 50], [1058, 12]]
[67, [2, 147], [14, 6], [19, 53], [45, 47], [57, 13], [67, 1], [99, 55], [968, 4], [968, 58]]
[71, [2, 43], [2, 177], [6, 14], [12, 58], [13, 53], [13, 113], [18, 77], [21, 11], [22, 36], [26, 66], [50, 2], [61, 11], [63, 33], [66, 70], [71, 1], [92, 60], [95, 25], [137, 33], [162, 1], [179, 23], [239, 45], [271, 7], [271, 53], [439, 31], [496, 8], [722, 12], [722, 27], [780, 30], [1210, 26], [510510, 4]]
[73, [2, 67], [3, 98], [5, 10], [6, 3], [7, 133], [10, 11], [10, 13], [12, 3], [17, 48], [20, 4], [22, 94], [23, 6], [28, 5], [31, 3], [34, 2], [34, 5], [43, 14], [46, 7], [57, 47], [57, 81], [60, 62], [63, 14], [65, 57], [73, 1], [73, 12], [74, 74], [76, 9], [78, 3], [86, 7], [97, 2], [98, 1], [105, 12], [127, 19], [137, 4], [173, 14], [200, 2], [229, 3], [263, 10], [496, 43], [968, 11], [1184, 3], [1210, 12], [2310, 25], [19116, 5], [30030, 11], [131071, 3], [33550336, 18]]
[79, [3, 113], [6, 4], [17, 39], [34, 56], [50, 6], [79, 1], [82, 5], [96, 26], [151, 67], [181, 45], [211, 53], [1250, 2]]
[83, [2, 376], [5, 5], [5, 36], [5, 57], [56, 44], [60, 88], [78, 12], [83, 1], [84, 46], [95, 57], [120, 28]]
[89, [2, 32], [2, 82], [3, 111], [7, 101], [37, 23], [47, 31], [57, 5], [68, 12], [89, 1], [113, 73], [450, 28], [660, 44], [510510, 2]]
[97, [2, 51], [2, 73], [7, 43], [19, 38], [38, 34], [43, 57], [68, 2], [97, 1], [98, 80], [103, 43], [107, 67], [131, 17], [293, 57], [392, 18], [1250, 9]]
[101, [2, 301], [2, 425], [29, 12], [31, 29], [45, 93], [55, 45], [73, 43], [73, 79], [99, 69], [101, 1], [181, 16], [1210, 2], [7420738134810, 8]]
[103, [2, 50], [6, 16], [24, 90], [44, 74], [50, 12], [72, 62], [103, 1], [242, 47], [396, 10]]
[107, [2, 255], [5, 223], [7, 165], [7, 171], [14, 94], [41, 29], [76, 78], [85, 31], [101, 31], [105, 61], [107, 1], [119, 3], [220, 2], [227, 41], [229, 17], [229, 39], [231, 57], [251, 3], [293, 9], [496, 60], [82589933, 13]]
[109, [3, 249], [10, 80], [18, 10], [28, 98], [30, 46], [55, 49], [79, 33], [83, 7], [85, 4], [109, 1], [131, 21], [276, 6], [338, 4], [578, 11], [660, 5], [1352, 16], [14288, 6]]
[113, [2, 11], [3, 38], [5, 31], [19, 50], [20, 5], [21, 70], [34, 15], [38, 3], [55, 3], [58, 50], [72, 21], [73, 22], [102, 12], [113, 1], [239, 31], [578, 28]]
[127, [2, 7], [5, 53], [53, 39], [97, 73], [101, 75], [127, 1], [127, 2], [139, 29], [211, 9], [1250, 6]]
[131, [3, 141], [19, 3], [30, 2], [33, 9], [66, 2], [66, 88], [119, 49], [131, 1], [162, 37]]
[137, [2, 396], [42, 42], [54, 28], [82, 16], [97, 57], [137, 1], [191, 47], [968, 54]]
[139, [61, 27], [77, 49], [139, 1], [284, 4]]
[149, [3, 55], [59, 45], [149, 1]]
[151, [18, 79], [96, 70], [103, 63], [151, 1], [162, 16], [210, 40], [15472, 38]]
[157, [20, 18], [20, 34], [60, 12], [65, 83], [157, 1], [241, 2], [242, 1]]
[163, [3, 47], [35, 9], [163, 1], [163, 51], [220, 26], [281, 2], [284, 32], [293, 2], [780, 4], [800, 8]]
[167, [45, 35], [109, 3], [167, 1]]
[173, [7, 31], [57, 59], [173, 1], [277, 3]]
[179, [14, 40], [40, 72], [60, 36], [61, 31], [87, 25], [109, 29], [179, 1], [200, 52], [227, 13], [241, 5], [14316, 8]]
[181, [12, 6], [149, 63], [181, 1]]
[191, [7, 63], [12, 5], [18, 112], [40, 84], [47, 48], [54, 22], [56, 2], [68, 25], [78, 14], [89, 15], [94, 3], [191, 1], [220, 3], [284, 5], [306, 34], [385, 1], [439, 13], [450, 3], [578, 5], [1152, 2], [1184, 19], [1210, 3]]
[193, [23, 39], [26, 2], [37, 10], [51, 67], [62, 55], [63, 5], [98, 4], [193, 1], [242, 10], [882, 31], [1155, 19], [15472, 40]]
[197, [15, 85], [197, 1]]
[199, [2, 110], [23, 71], [199, 1], [450, 36]]
[211, [2, 46], [3, 211], [33, 21], [43, 21], [48, 58], [65, 63], [76, 14], [211, 1], [338, 1]]
[223, [69, 19], [105, 23], [162, 68], [223, 1]]
[227, [58, 76], [227, 1]]
[229, [23, 33], [229, 1], [241, 49]]
[233, [14, 4], [120, 72], [229, 63], [233, 1]]
[239, [5, 93], [6, 204], [19, 7], [20, 14], [181, 3], [239, 1], [1152, 1]]
[241, [2, 279], [2, 346], [19, 11], [33, 89], [57, 7], [59, 25], [241, 1], [269, 35]]
[251, [191, 3], [251, 1], [263, 3]]
[257, [13, 10], [18, 3], [20, 112], [33, 39], [46, 2], [46, 56], [47, 19], [54, 4], [93, 2], [96, 9], [101, 15], [104, 8], [104, 40], [193, 13], [257, 1], [288, 44], [2147483647, 9]]
[263, [29, 7], [263, 1], [648, 8]]
[269, [53, 71], [101, 7], [127, 7], [269, 1], [1155, 41]]
[271, [18, 7], [271, 1]]
[277, [2, 103], [13, 83], [71, 6], [79, 61], [277, 1], [720, 1], [510510, 5]]
[281, [6, 40], [14, 46], [19, 27], [34, 4], [37, 74], [42, 48], [50, 38], [93, 21], [96, 28], [181, 7], [197, 5], [281, 1], [828, 4]]
[283, [2, 86], [48, 10], [283, 1], [392, 55]]
[293, [2, 53], [15, 47], [281, 67], [293, 1]][/CODE][SIZE=-1]At the beginning of each line, we can see the prime number which constitutes a branch of [URL="http://www.aliquotes.com/graphinfinisualidistresp.pdf"]the infinite graph of aliquot sequences[/URL].
For example, the first line tells us that in our project only 2^1 ends with the prime number 2.
The second line shows us all the sequences in our project that end with the prime number 3 : there are 2^2, 2^4, 2^55, 2^164, 2^305, 2^317, 3^1, 3^2...
And so on for all the primes after 2 and 3, up to 300.
Of course, the data for the prime numbers 2 and 5 are of no interest because each time, only one sequence ends with these two prime numbers.

First, I start by doing a hand analysis of each line.
For example, for the prime number 3, when I see [2, 2], [2, 4], [2, 55], [2, 164], [2, 305], [2, 317], I enter the integers 2,4,55,164,305,317 into the OEIS to see if it is a known sequence.
[/SIZE][SIZE=-1] [B]This would allow to predict the next one, because this is the reason of this whole project : to be able to predict with which prime number a sequence will end without calculating it ![/B][/SIZE]
[SIZE=-1]I proceed in the same way for [3, 1], [3, 2], [3, 5], [3, 247] by entering in the OEIS the list : 1,2,5,247 and so on, when there are more than three integers to enter in the OEIS.[/SIZE]
[SIZE=-1] There are many possible variations.[/SIZE]
[SIZE=-1]I thought that maybe we should redo this work by considering only the even exponents, only the odd exponents, only the prime exponents ?[/SIZE]
[SIZE=-1] Then, I printed all these lines by letting appear only the sequences whose base and exponent have the same parity, then the same with the opposite parity, then the same when the base and the exponent are both prime numbers...

Then, for each prime number, I place all the points in a reference frame where the x-axis is the base and the y-axis is the exponent.
You can find all these points placed in the attached file for each prime < 200.
But these clouds of points do not show any special curve or more than two points aligned on the same line.
This is the biggest part of the work.
The program that has been running for 2 weeks does this work.
Here is a small portion of the data for the prime number 3 :

[/SIZE][CODE]*********************************************************************************************************************************************************************************************************************************************
*********************************************************************************************************************************************************************************************************************************************
[3, [2, 2], [2, 4], [2, 55], [2, 164], [2, 305], [2, 317], [3, 1], [3, 2], [3, 5], [3, 247], [5, 38], [6, 152], [7, 4], [7, 77], [10, 124], [11, 2], [11, 15], [12, 1], [12, 2], [13, 15], [14, 76], [14, 80], [15, 1], [19, 15], [20, 2], [20, 8], [21, 21], [21, 55], [22, 80], [23, 3], [23, 109], [26, 1], [29, 2], [29, 69], [30, 1], [30, 82], [30, 92], [31, 79], [33, 1], [35, 49], [37, 11], [38, 11], [38, 30], [40, 14], [41, 2], [42, 1], [43, 15], [44, 58], [45, 1], [45, 34], [46, 1], [47, 13], [50, 73], [52, 1], [52, 34], [53, 2], [53, 27], [53, 30], [54, 1], [54, 10], [55, 53], [58, 18], [59, 49], [60, 86], [66, 1], [70, 70], [71, 2], [72, 1], [74, 6], [74, 20], [74, 78], [75, 45], [77, 5], [77, 19], [78, 1], [79, 97], [83, 43], [84, 30], [86, 1], [87, 1], [87, 17], [89, 2], [90, 1], [93, 49], [95, 5], [96, 42], [98, 45], [99, 3], [99, 71], [101, 2], [102, 1], [104, 58], [105, 1], [107, 11], [109, 13], [113, 2], [131, 57], [137, 3], [139, 33], [157, 5], [167, 63], [167, 79], [173, 2], [197, 2], [197, 23], [197, 27], [211, 2], [220, 16], [239, 3], [242, 41], [251, 33], [257, 2], [269, 2], [277, 9], [288, 1], [288, 3], [293, 11], [293, 23], [306, 17], [338, 2], [338, 13], [396, 11], [450, 1], [450, 19], [564, 2], [648, 1], [648, 56], [722, 37], [800, 21], [828, 24], [882, 5], [966, 6], [966, 34], [968, 8], [996, 12], [1058, 31], [1250, 10], [1352, 1], [2310, 36], [14288, 12], [223092870, 20]]
*********************************************************************************************************************************************************************************************************************************************
*********************************************************************************************************************************************************************************************************************************************

Number of items analyzed for this list : 141

========================================================================================
Search for one-variable polynomial functions of degree 3 ========================================================================================
dlim = 8
alim = 30
blim = 120
clim = 700
d = -8 / 8
d = -7 / 8
d = -6 / 8
d = -5 / 8
count = 3 for h = -4*x^3 + 23*x^2 + 61*x + -178 [[2, 4], [6, 152], [7, 4]]
d = -4 / 8
count = 3 for h = -3*x^3 + 16*x^2 + 25*x + 74 [[2, 164], [6, 152], [7, 4]]
count = 3 for h = -3*x^3 + 17*x^2 + 85*x + -322 [[3, 5], [6, 152], [7, 77]]
d = -3 / 8
count = 3 for h = -2*x^3 + 1*x^2 + 93*x + -10 [[2, 164], [6, 152], [7, 4]]
count = 3 for h = -2*x^3 + 20*x^2 + 76*x + -592 [[5, 38], [6, 152], [11, 2]]
count = 3 for h = -2*x^3 + 26*x^2 + -92*x + 98 [[2, 2], [3, 2], [5, 38]]
count = 3 for h = -2*x^3 + 27*x^2 + -94*x + 98 [[2, 2], [3, 5], [7, 77]]
count = 3 for h = -2*x^3 + 28*x^2 + -103*x + 112 [[2, 2], [3, 1], [7, 77]]
count = 3 for h = -2*x^3 + 30*x^2 + -95*x + 74 [[3, 5], [6, 152], [10, 124]]
count = 3 for h = -2*x^3 + 30*x^2 + -94*x + 68 [[3, 2], [6, 152], [11, 2]]
d = -2 / 8
count = 3 for h = -1*x^3 + 10*x^2 + -1*x + 134 [[2, 164], [10, 124], [11, 2]]
count = 3 for h = -1*x^3 + 10*x^2 + 23*x + -130 [[3, 2], [6, 152], [11, 2]]
count = 3 for h = -1*x^3 + 11*x^2 + 13*x + -106 [[3, 5], [6, 152], [10, 124]]
count = 3 for h = -1*x^3 + 15*x^2 + -53*x + 56 [[2, 2], [3, 5], [7, 77]]
count = 3 for h = -1*x^3 + 16*x^2 + -79*x + 266 [[2, 164], [6, 152], [11, 2]]
count = 3 for h = -1*x^3 + 16*x^2 + -62*x + 70 [[2, 2], [3, 1], [7, 77]]
count = 4 for h = -1*x^3 + 16*x^2 + -61*x + 68 [[2, 2], [3, 2], [5, 38], [11, 2]]
count = 3 for h = -1*x^3 + 17*x^2 + -66*x + 74 [[2, 2], [3, 2], [12, 2]]
count = 3 for h = -1*x^3 + 17*x^2 + -65*x + 74 [[2, 4], [3, 5], [10, 124]]
count = 3 for h = -1*x^3 + 18*x^2 + -80*x + 98 [[2, 2], [7, 77], [12, 2]]
count = 3 for h = -1*x^3 + 18*x^2 + -70*x + 80 [[2, 4], [3, 5], [13, 15]]
count = 3 for h = -1*x^3 + 19*x^2 + -115*x + 374 [[6, 152], [10, 124], [12, 2]]
count = 3 for h = -1*x^3 + 23*x^2 + -95*x + 110 [[2, 4], [3, 5], [6, 152]]
count = 3 for h = -1*x^3 + 24*x^2 + -103*x + 122 [[2, 4], [3, 2], [6, 152]]
count = 3 for h = -1*x^3 + 25*x^2 + -106*x + 122 [[2, 2], [3, 2], [20, 2]]
d = -1 / 8
count = 3 for h = 0*x^3 + -3*x^2 + 21*x + 134 [[2, 164], [6, 152], [11, 2]]
...
count = 3 for h = 0*x^3 + 0*x^2 + -1*x + 102 [[22, 80], [44, 58], [99, 3]]
count = 23 for h = 0*x^3 + 0*x^2 + 0*x + 1 [[3, 1], [12, 1], [15, 1], [26, 1], [30, 1], [33, 1], [42, 1], [45, 1], [46, 1], [52, 1], [54, 1], [66, 1], [72, 1], [78, 1], [86, 1], [87, 1], [90, 1], [102, 1], [105, 1], [288, 1], [450, 1], [648, 1], [1352, 1]]
count = 19 for h = 0*x^3 + 0*x^2 + 0*x + 2 [[2, 2], [3, 2], [11, 2], [12, 2], [20, 2], [29, 2], [41, 2], [53, 2], [71, 2], [89, 2], [101, 2], [113, 2], [173, 2], [197, 2], [211, 2], [257, 2], [269, 2], [338, 2], [564, 2]]
count = 5 for h = 0*x^3 + 0*x^2 + 0*x + 3 [[23, 3], [99, 3], [137, 3], [239, 3], [288, 3]]
...
count = 3 for h = 0*x^3 + 2*x^2 + -61*x + 454 [[21, 55], [22, 80], [23, 109]]
count = 4 for h = 0*x^3 + 2*x^2 + -60*x + 433 [[11, 15], [12, 1], [19, 15], [21, 55]]
...
count = 3 for h = 0*x^3 + 9*x^2 + -113*x + 354 [[2, 164], [7, 4], [10, 124]]
count = 3 for h = 0*x^3 + 12*x^2 + -59*x + 74 [[2, 4], [3, 5], [6, 152]]
count = 3 for h = 0*x^3 + 13*x^2 + -67*x + 86 [[2, 4], [3, 2], [6, 152]]
d = 0 / 8
count = 3 for h = 1*x^3 + -28*x^2 + -41*x + 350 [[2, 164], [3, 2], [29, 2]]
count = 3 for h = 1*x^3 + -25*x^2 + 106*x + -118 [[2, 2], [3, 2], [20, 2]]
count = 3 for h = 1*x^3 + -23*x^2 + 42*x + 55 [[2, 55], [3, 1], [21, 55]]
...
count = 3 for h = 1*x^3 + 1*x^2 + -23*x + 38 [[2, 4], [3, 5], [6, 152]]
count = 3 for h = 1*x^3 + 2*x^2 + -31*x + 50 [[2, 4], [3, 2], [6, 152]]
d = 1 / 8
count = 3 for h = 2*x^3 + -29*x^2 + 95*x + 74 [[2, 164], [7, 4], [10, 124]]
count = 3 for h = 2*x^3 + -28*x^2 + 103*x + -106 [[2, 4], [3, 5], [10, 124]]
count = 3 for h = 2*x^3 + -23*x^2 + 41*x + 158 [[2, 164], [5, 38], [7, 4]]
count = 3 for h = 2*x^3 + -21*x^2 + 70*x + -70 [[2, 2], [3, 5], [7, 77]]
count = 3 for h = 2*x^3 + -20*x^2 + 61*x + -56 [[2, 2], [3, 1], [7, 77]]
count = 3 for h = 2*x^3 + -14*x^2 + 32*x + -22 [[2, 2], [3, 2], [5, 38]]
count = 3 for h = 2*x^3 + -10*x^2 + 13*x + 2 [[2, 4], [3, 5], [6, 152]]
count = 3 for h = 2*x^3 + -9*x^2 + 5*x + 14 [[2, 4], [3, 2], [6, 152]]
count = 3 for h = 2*x^3 + 4*x^2 + -112*x + 248 [[3, 2], [5, 38], [6, 152]]
d = 2 / 8
count = 3 for h = 3*x^3 + -30*x^2 + -69*x + 398 [[2, 164], [3, 2], [11, 2]]
count = 3 for h = 3*x^3 + -24*x^2 + 63*x + -52 [[2, 2], [3, 2], [5, 38]]
count = 3 for h = 3*x^3 + -23*x^2 + -101*x + 434 [[2, 164], [3, 5], [10, 124]]
count = 3 for h = 3*x^3 + -21*x^2 + 49*x + -34 [[2, 4], [3, 5], [6, 152]]
count = 3 for h = 3*x^3 + -20*x^2 + 41*x + -22 [[2, 4], [3, 2], [6, 152]]
count = 3 for h = 3*x^3 + -10*x^2 + -49*x + 158 [[3, 2], [5, 38], [6, 152]]
d = 3 / 8
count = 3 for h = 4*x^3 + -24*x^2 + 14*x + 68 [[3, 2], [5, 38], [6, 152]]
count = 3 for h = 4*x^3 + -13*x^2 + -107*x + 398 [[2, 164], [5, 38], [6, 152]]
d = 4 / 8
count = 3 for h = 5*x^3 + -26*x^2 + -55*x + 338 [[2, 164], [5, 38], [6, 152]]
d = 5 / 8
d = 6 / 8
d = 7 / 8
d = 8 / 8

================================================================================================= Research functions exponential forms =================================================================================================
alim = 20
blim = 100
clim = 600
a = -20 / 20
a = -19 / 20
a = -18 / 20
a = -17 / 20
a = -16 / 20
a = -15 / 20
a = -14 / 20
a = -13 / 20
a = -12 / 20
a = -11 / 20
a = -10 / 20
a = -9 / 20
a = -8 / 20
a = -7 / 20
a = -6 / 20
count = 2 for h = 2 * -5^x + 255 [[2, 305], [3, 5]]
a = -5 / 20
a = -4 / 20
a = -3 / 20
count = 2 for h = -16 * -2^x + 119 [[2, 55], [3, 247]]
count = 2 for h = -1 * -2^x + 6 [[2, 2], [5, 38]]
count = 2 for h = 25 * -2^x + 205 [[2, 305], [3, 5]]
count = 2 for h = 26 * -2^x + 213 [[2, 317], [3, 5]]
a = -2 / 20
a = -1 / 20
a = 0 / 20
a = 1 / 20
count = 2 for h = 48 * 2^x + -137 [[2, 55], [3, 247]]
a = 2 / 20
count = 2 for h = -9 * 3^x + 245 [[2, 164], [3, 2]]
count = 2 for h = -3 * 3^x + 82 [[2, 55], [3, 1]]
a = 3 / 20
count = 2 for h = 4 * 4^x + -9 [[2, 55], [3, 247]]
a = 4 / 20
count = 2 for h = -3 * 5^x + 380 [[2, 305], [3, 5]]
a = 5 / 20
a = 6 / 20
a = 7 / 20
a = 8 / 20
a = 9 / 20
a = 10 / 20
a = 11 / 20
a = 12 / 20
a = 13 / 20
a = 14 / 20
a = 15 / 20
a = 16 / 20
a = 17 / 20
a = 18 / 20
a = 19 / 20
a = 20 / 20

========================================================================================
Search for polynomial functions with two variables of degree 2========================================================================================
flim = 5
elim = 5
dlim = 5
alim = 12
blim = 12
clim = 250
f = -5 / 5
count = 4 for h = -4*x^2 + -1*y^2 + 5*x*y + -2*x + -4*y + 15 [[2, 2], [2, 4], [3, 5], [13, 15]]
...
count = 7 for h = 4*x^2 + 0*y^2 + -4*x*y + -12*x + 12*y + 3 [[2, 2], [3, 1], [3, 2], [3, 5], [3, 247], [21, 21], [70, 70]]
count = 4 for h = 4*x^2 + 1*y^2 + -5*x*y + -11*x + 11*y + 3 [[2, 2], [3, 1], [21, 21], [70, 70]]
...
count = 4 for h = 4*x^2 + 1*y^2 + -5*x*y + 2*x + 4*y + -9 [[2, 2], [2, 4], [3, 5], [13, 15]]
f = 4 / 5
f = 5 / 5[/CODE][SIZE=-1]I am looking for curves whose equation is of degree 3 and which would have more than 3 points that belong to them exactly.
I print the curves that have 3 points so that I can check them.
I do the same for curves whose equation has this form : y = b * a^x + c.
[/SIZE][SIZE=-1] Finally, I also look for equations in two variables of degree 2 that have this form : f*x^2+e*y^2+d*x*y + a*x+b*y+c=p (p is the prime number, but since there is the constant c, I could have put 0 instead of p).[/SIZE]
[SIZE=-1]The coefficients a, b, c, ... are taken integer here, but future works could consider rational coefficients.
[/SIZE]
[SIZE=-1] To understand all this, let's show some examples for the prime number 3.
Not surprisingly, we find that for the prime number 3, we have the following data :
count = 19 for h = 0*x^3 + 0*x^2 + 0*x + 2 [[2, 2], [3, 2], [11, 2], [12, 2], [20, 2], [29, 2], [41, 2], [53, 2], [71, 2], [89, 2], [101, 2], [113, 2], [173, 2], [197, 2], [211, 2], [257, 2], [269, 2], [338, 2], [564, 2]]
count = 5 for h = 0*x^3 + 0*x^2 + 0*x + 3 [[23, 3], [99, 3], [137, 3], [239, 3], [288, 3]]
This means for example that 2^2, 3^2, 11^2, 12^2, ... end with the prime number 3.
This line gives us all the squares in our project that end in the prime number 3.
Below, we have the line that gives us all the cubes that end with the prime number 3.
I then do the same work with OEIS and sequences 2,3,11,12,20,29,41... and 23,99,137,239,288.

And for lines of this type :
count = 7 for h = 4*x^2 + 0*y^2 + -4*x*y + -12*x + 12*y + 3 [[2, 2], [3, 1], [3, 2], [3, 5], [3, 247], [21, 21], [70, 70]
At first I wanted to be happy and thought I had found something interesting, but I haven't.
This means that there are 7 [x,y] pairs displayed in the row that verify the equation 3 = 4*x^2 + 0*y^2 + -4*x*y + -12*x + 12*y + 3
If you look closely at the line, there is nothing extraordinary about it !

After talking with members of a team in the North-East of France, I still have other ideas to test, but that will come later.
I hope I will be able to spot something interesting and not miss it if there is one.
[/SIZE][SIZE=-1] For now : NOTHING ![/SIZE]

[SIZE=-1][QUOTE=EdH;612596]Thanks Jean-Luc! I'll do another update for the other thread a bit later. Are you interested in the frequency of primes <300 throughout the tables? Maybe I can resurrect some of my work from last year(s) and see if we match. It may be a while before I do, though.
[/QUOTE][/SIZE][SIZE=-1]Currently, I am only working on prime numbers <300 that end sequences.
[/SIZE][SIZE=-1]If you do some work on this frequency, I can then try to match what I presented above in the first table with your datas.
I am not working on the occurrences of primes in all terms of sequences.
[/SIZE][SIZE=-1][QUOTE=EdH;612596]
I've been thinking about the genealogy thread from back long ago and wondered what might be found trying to tie some of the terminated sequences together. I'm kind of wondering for how many iterations prior to termination most of the sequences are merged , but it's just a fleeting thought ATM. I have some ideas as to how to approach finding them, but haven't programmed anything yet. There are limited ways that a certain prime can be "Aliqueitly" arrived at via previous composite terms. It may be interesting to trace some backwards. Perhaps you've already worked there?[/QUOTE][/SIZE][SIZE=-1]I already tried to find the aliquot antecedents of the prime numbers on several iterations.
But the calculations quickly become unbearable.
Moreover, the graph is not connected because of the amiable numbers and maybe also because of the OE sequences which would go to infinity if the Catalan conjecture is false, which I think it is.
The study of this tree is the fundamental for the aliquot sequences !
But it took me days to make only the drawings presented on my website (see link above in the thread to see the graph).[/SIZE]
[SIZE=-1]I don't know how to draw automatically this graph with more numbers in a reasonable time.
I found this work so abominable that I preferred at the time to limit myself to study this tree by considering only the integer powers to simplify the problem.[/SIZE]
[SIZE=-1]Thus was born this project !
[/SIZE]

 LaurV 2022-09-04 15:39

[QUOTE=gd_barnes;612431]No. I need the last iteration of the elf file...not a web page of the last iteration of the sequence.[/QUOTE]
Well, then you get the index from there, and access by index. The only way to access a number in factorDB is by its index, and the index you get from the link I gave you. [CODE]http://factordb.com/index.php?showid=1100000003844791171[/CODE]
Rest is parsing.

 RichD 2022-09-05 22:21

Base 307 can be added at the next update. I know this data won't be consumed until next year but I had some time for another initialization. Same parity exponents terminated through 45 plus 53.

 gd_barnes 2022-09-05 23:01

1 Attachment(s)
I have initialized middle-sized to large opposite-parity exponents to a cofactor >= 110 digits (ECM to t35) for all bases > 1000. Some of the sequences hit down-drivers and became very interesting but there were no terminations. Many bases had already been done either by me or others so were not included. All bases in the 1058 thru 8128 range were either not applicable or had been done previously. Affected bases were:
8191, 12496, 14264, 14288, 14316, 14536, 15015, 15472, 19116, 30030, 31704, 510510, 9699690, 33550336, 223092870, 6469693230, 8589869056, 200560490130, and 7420738134810.

Attached is a document of the sequences that were tested.

Note that I am not doing work on anything that has already reached 100 digits current-size and is at index > ~6. With the typical initialization on the project of 100 digits, that's been the cutoff point.

My favorite one was 15472^23. It was previously tested to 100 digits but the DB workers had worked it down to 99 digits at I-1620. Since it didn't meet the 100-digit criteria any more, I went with it. It went on a wild ride down to 51 digits with subsequent multiple down-drivers though none that went that low. It finally hit a >=110-digit cofactor at I-3471 after adding > 1850 indexes.

Next I am working on opposite-parities for base 660. This base was previously only initialized to ~86-92 digits for many of the exponents so I'll be working on bringing them all to >= 110 digits. That is loaded up and running now. After that I'll be working on other bases in the 200 to 1000 range.

 SuikaPredator 2022-09-07 11:06

pushed 233^40 to i82, ecm'ed t25 on C114

now reserving 233^4

 garambois 2022-09-07 16:26

[QUOTE=SuikaPredator;612862]pushed 233^40 to i82, ecm'ed t25 on C114

now reserving 233^4[/QUOTE]
Hello,
Welcome to help us with our project.
Is the contributor acronym "SUI" suitable for you or would you like to suggest another one ?
Would you like to reserve the base 233 ?
You do not have to calculate all the sequences of this base, but only those that you like.

 garambois 2022-09-07 16:30

@RichD and Gary :
Thank you very much for your latest work.
They will be taken into account in the next update, certainly next weekend.

 SuikaPredator 2022-09-07 17:50

[QUOTE=garambois;612886]Hello,
Welcome to help us with our project.
Is the contributor acronym "SUI" suitable for you or would you like to suggest another one ?
Would you like to reserve the base 233 ?
You do not have to calculate all the sequences of this base, but only those that you like.[/QUOTE]

I prefer the contributor acronym "OSC".
It's ok to reserve the base 233 since I also calculate a few terms for other exponents occasionally.

 garambois 2022-09-07 18:36

OK, fine.
Thanks SuikaPredator.
This will be on the page next weekend.
I usually update once a week when there is activity.

 Happy5214 2022-09-09 09:53

I've handed off the odd-exponent base 210 sequences above exponent 40 to Gary. My desktop failed about a month ago, and I'm now down to one computer that's rotating between aliquot and Riesel projects, so I'm in a holding pattern for when I can return to aliquot work. I was able to turn the desktop into a FactorDB elf by running it off a live USB, in case you need ideas for old boxes with failed hard drives.

 gd_barnes 2022-09-10 01:04

Base 660 opposite-parity exponents 7 thru 59 have now been tested to cofactor >= 110 digits. This one was previously only tested to ~86-93 digits for many of the exponents.

 gd_barnes 2022-09-10 05:52

1 Attachment(s)
I have initialized middle-sized to large opposite-parity exponents to a cofactor >= 110 digits for all bases 195 thru 1000. I had done quite a bit of work on this in the base 200 to 400 range previously. The difference this time is I did all of the large exponents whereas before I stopped at 180 digits starting size. So no exponent went untouched. Affected bases were 197, 199, 210, 211, 220, 223, 227, 229, 233, 239, 307 (new base), 552, 564, 720, 770, and 966.

Attached is a document of the affected sequences.

Last time in the document I showed all sequences that were actually tested. This time it only shows the specific exponents that had a change. I did this because many of the exponents that were tested had no actual change due to prior work in the area.

There was a merge:
210^47 merges at index=1189 with 3366:i2

Note that Happy had released base 210 exponents > 40 to me so I feel a little weird about the merge happening there. (40 thru 59 were previously reserved.) Therefore it makes no difference to me who gets credit for the merge. It was the first merge/termination of this effort.

Regardless, I am done with base 210 so I release all exponents > 40.

I'm continuing with this effort for bases 100 to 195. No previous work has been done in this area and there are more exponents per base then for bases > 200 so things will take a little longer now.

 gd_barnes 2022-09-11 06:06

80^61 is a merge but the merge info is not shown on the page.

It merges at index=4473 with 660:i25.

 garambois 2022-09-11 08:41

Page updated.
Many thanks to all for your help.

[B]Added bases : 307 and 396[/B]
[B]Base 233 reserved for OSC[/B]
[B]Mergers added for bases 80 and 210
[/B][B]Updated bases : All the bases announced below[/B]
[CODE]23^119: Prime - GDB *
23^121: Prime - GDB *
67^89: Prime - GDB *
76^88: Prime - GDB *
77^85: Prime - GDB *
83^95: Prime - GDB *
84^96: Prime - GDB *
86^86: Prime - GDB *
94^86: Prime - GDB *
101^87: Prime - EDH *
173^77: Prime - GDB *
197^73: Prime - GDB *
197^75: Prime - GDB *
229^69: Prime - GDB *
241^69: Prime - VBC *
307^1: Prime - A *
307^3: Prime - A *
307^5: Prime - A *
307^7: Prime - A *
307^9: Prime - RFD *
307^11: Prime - RFD *
307^13: Prime - RFD *
307^15: Prime - RFD *
307^17: Prime - RFD *
307^19: Prime - RFD *
307^21: Prime - RFD *
307^23: Prime - RFD *
307^25: Prime - RFD *
307^27: Prime - RFD *
307^29: Prime - RFD *
307^31: Prime - RFD *
307^33: Prime - RFD *
*307^35: Prime - RFD *
307^37: Prime - RFD *
307^39: Prime - RFD *
307^41: Prime - RFD *
307^43: Prime - RFD *
307^45: Prime - RFD *
307^47: Prime - GDB *
307^49: Prime - GDB *
307^51: Prime - GDB *
307^53: Prime - A *
307^55: Prime - GDB *
307^57: Prime - GDB *
307^59: Prime - GDB *
307^61: Prime - GDB *
338^64: Prime - KRB *
392^63: Prime - GDB *
722^59: Prime - GDB *
1250^53: Prime - GDB *

base exponents
8191 30 to 40 *
12496 25 to 39 *
14264 25 to 39 *
14288 27 to 39 *
14316 27 to 39 *
14536 25 to 39 *
15015 30 to 40 *
15472 23 to 39 *
19116 27 to 39 *
30030 35,37,39 *
31704 27 to 39 *
510510 25,27,29 *
9699690 21,23,25 *
33550336 21,23,25 *
223092870 15,17,19 *
6469693230 13,15,17,19 *
8589869056 15,17,19 *
200560490130 11,13 *
7420738134810 9,11,13 *
197 46 to 72, 76 to 84, 90 *
199 46 to 52, 56 to 66, 72, 74, 86, 88, 90 *
210 41 to 51, 55, 57, 79 *
211 78, 80 *
220 77, 79 *
223 80 *
227 78 *
229 78 *
233 78, 80 *
239 80 *
307 42 to 64 (new base) *
552 55 *
564 37 to 45, 49 to 59 *
720 35 to 47, 51 to 59 *
770 59 *
966 49 to 57 *
660 *[/CODE]

 Happy5214 2022-09-11 13:29

[QUOTE=gd_barnes;613126]There was a merge:
210^47 merges at index=1189 with 3366:i2

Note that Happy had released base 210 exponents > 40 to me so I feel a little weird about the merge happening there. (40 thru 59 were previously reserved.) Therefore it makes no difference to me who gets credit for the merge. It was the first merge/termination of this effort.[/QUOTE]

Gary definitely gets the credit there. I did no work at all on that exponent, initializing or otherwise.

 EdH 2022-09-11 13:30

Thanks for all the work, Jean-Luc! I've updated the other thread.

I haven't had much time for factoring, but did look over the graphs a bit and tried to program a script for the prime terminations. I haven't noticed anything that stands out in the graphs yet. Disappointingly, my scripts aren't finding all the proper terminations as they should, so I don't have a verification set. I did do a recent update for my local set of sequences, but it didn't help. Most notable is right away my script won't show 223092870^20 as one of the sequences for 3. It clearly has the proper line in my .elf copy, but it just isn't being included. More later.

 Happy5214 2022-09-11 15:33

[QUOTE=EdH;613203]Most notable is right away my script won't show [B]223092870[/B]^20 as one of the sequences for 3. It clearly has the proper line in my .elf copy, but it just isn't being included. More later.[/QUOTE]

I obviously don't have a copy of your scripts, so I can't give advice based on that, but have you ruled out anything based on the length of the base? It appears to be the largest base we have with a sequence terminating at 3.

 EdH 2022-09-11 16:31

[QUOTE=Happy5214;613211]I obviously don't have a copy of your scripts, so I can't give advice based on that, but have you ruled out anything based on the length of the base? It appears to be the largest base we have with a sequence terminating at 3.[/QUOTE]Thanks! I haven't ruled out anything yet. I've been doing other things and had considered it may be the issue. I'm using bash and the script shouldn't be differentiating numbers vs. strings, but it's likely the cause. I'm looking at approaching the work with c++ from a distinctly different direction. Of course, I have several "projects" in work, so I have to clear some distractions first.

 garambois 2022-09-11 17:39

[QUOTE=EdH;613203]Thanks for all the work, Jean-Luc! I've updated the other thread.

I haven't had much time for factoring, but did look over the graphs a bit and tried to program a script for the prime terminations. I haven't noticed anything that stands out in the graphs yet. Disappointingly, my scripts aren't finding all the proper terminations as they should, so I don't have a verification set. I did do a recent update for my local set of sequences, but it didn't help. Most notable is right away my script won't show 223092870^20 as one of the sequences for 3. It clearly has the proper line in my .elf copy, but it just isn't being included. More later.[/QUOTE]

Karsten provided me with scripts that should corroborate my own results differently than I did with my own programs.
I just haven't been able to get them to work yet, because I'm not very good at them. But it should only be a matter of days now.

As for me, I have failed several times to write a program that gives the same result as what you present in [URL="https://www.mersenneforum.org/showpost.php?p=608623&postcount=1720"]post #1720[/URL].
But your results presented in this post look solid, I can't find any errors.
And I find nothing but randomness in the data.

 yoyo 2022-09-11 18:16

I'll take bases 70 71 72 and 73.

 EdH 2022-09-11 18:17

It may be a lofty goal, but I'm hoping to write a C++ program that will scour the entire set and create a listing of all terminating primes and all the sequences they terminate. A step to that end will of course be the list of those <300 that you already have.

 garambois 2022-09-11 18:32

[QUOTE=yoyo;613221]I'll take bases 70 71 72 and 73.[/QUOTE]
Many thanks !

Base 72 ?
Are you sure ?
Can you please check ?

 garambois 2022-09-11 18:39

[QUOTE=EdH;613222]It may be a lofty goal, but I'm hoping to write a C++ program that will scour the entire set and create a listing of all terminating primes and all the sequences they terminate. A step to that end will of course be the list of those <300 that you already have.[/QUOTE]
You mean to do the same work as in the first table in [URL="https://www.mersenneforum.org/showpost.php?p=612644&postcount=1845"]post #1845[/URL] but with all the primes ending the sequences in the project, right ?
For most of the primes, there will only be one sequence that ends with them, at least that's what I think.

 yoyo 2022-09-11 18:49

[QUOTE=garambois;613224]Many thanks !

Base 72 ?
Are you sure ?
Can you please check ?[/QUOTE]

Yes, for base 72 those 2 sequences:
72^89
72^91

 EdH 2022-09-11 20:46

[QUOTE=garambois;613226]You mean to do the same work as in the first table in [URL="https://www.mersenneforum.org/showpost.php?p=612644&postcount=1845"]post #1845[/URL] but with all the primes ending the sequences in the project, right ?
For most of the primes, there will only be one sequence that ends with them, at least that's what I think.[/QUOTE]This is no doubt true, but I hope to be able to list all the prime terminators for the entire set of sequences. I'm curious, what the largest is that occurs more than once. And, along the way, a subset will be those that meet the criteria for post #1845's first table (which will be used for partial verification). My program currently shows 8314 terminated sequences, based on an update a few days ago. It also matches your highest termination for prime 43:[code]Sequence 200560490130^10 is 43[/code]The format will need work, but that's minor.

 gd_barnes 2022-09-11 22:47

[QUOTE=SuikaPredator;612862]pushed 233^40 to i82, ecm'ed t25 on C114

now reserving 233^4[/QUOTE]

[QUOTE=garambois;612886]Hello,
Welcome to help us with our project.
Is the contributor acronym "SUI" suitable for you or would you like to suggest another one ?
Would you like to reserve the base 233 ?
You do not have to calculate all the sequences of this base, but only those that you like.[/QUOTE]

[QUOTE=SuikaPredator;612895]I prefer the contributor acronym "OSC".
It's ok to reserve the base 233 since I also calculate a few terms for other exponents occasionally.[/QUOTE]
Jean-Luc,

Suika only said that he occasionally works on exponents for base 233. The two that he has worked on have been for opposite-parity sequences. But you have reserved all exponents for both parities on the base for him.

Would it make sense to only reserve the opposite-parity sequences < ~120 (140) digits for him and release all others? That is, unless he says otherwise.

I ask this because reservations often become obsolete for areas of search that were never intended to be searched in the first place and it stops searches by others.

 SuikaPredator 2022-09-11 23:23

[QUOTE=gd_barnes;613235]Jean-Luc,

Suika only said that he occasionally works on exponents for base 233. The two that he has worked on have been for opposite-parity sequences. But you have reserved all exponents for both parities on the base for him.

Would it make sense to only reserve the opposite-parity sequences < ~120 (140) digits for him and release all others? That is, unless he says otherwise.

I ask this because reservations often become obsolete for areas of search that were never intended to be searched in the first place and it stops searches by others.[/QUOTE]
You are right, the remaining cofactors of >=60 exponents were indeed too large for me. Releasing them would probably be a better option.

 EdH 2022-09-12 00:20

The good news: My new program works great and only takes a couple minutes to scour the entire set of sequences.

The bad news: My new program has pointed out that the update script has not been doing its job well!

The extra news: After I fix the update script, it will still be at least 16 hours for it to make it through another update, due to the db limitations.

 richs 2022-09-12 01:04

I noticed that the website does not show me as having 385^4 reserved which I have been working on for months. Thanks!

 garambois 2022-09-12 18:59

[QUOTE=richs;613240]I noticed that the website does not show me as having 385^4 reserved which I have been working on for months. Thanks![/QUOTE]
The merging sequences are to be watched on the main project.
And on the main project, the sequence 903872 is reserved for you.
So everything is OK.

 garambois 2022-09-12 19:01

@yoyo and Gary and SuikaPredator :
I will try to update the reservations tomorrow night.

@Edwin :
I will follow your work closely with great interest.

Many thanks to all.

 gd_barnes 2022-09-12 21:51

[QUOTE=garambois;613286]The merging sequences are to be watched on the main project.
And on the main project, the sequence 903872 is reserved for you.
So everything is OK.[/QUOTE]
If we are not showing reservations on merged sequences, should 210^47 and 233^20 have their initials removed?

 EdH 2022-09-12 22:43

1 Attachment(s)
It was long awaited, but I finally have a C++ program that scours the whole set* in 15 seconds. There is a little bit of difference as explained further below. Here is the same set (with a highlighted difference for prime 3) as shown in post [URL="https://www.mersenneforum.org/showpost.php?p=612644&postcount=1845"]#1845[/URL]:[code][2, [2, 1]]
[3, [2, 2], [2, 4], [2, 55], [2, 164], [2, 305], [2, 317], [3, 1], [3, 2], [3, 5], [3, 247], [5, 38], [6, 152], [7, 4], [7, 77], [10, 124], [11, 2], [11, 15], [12, 1], [12, 2], [13, 15], [14, 76], [14, 80], [15, 1], [19, 15], [20, 2], [20, 8], [21, 21], [21, 55], [22, 80], [23, 3], [23, 109], [26, 1], [29, 2], [29, 69], [30, 1], [30, 82], [30, 92], [31, 79], [33, 1], [35, 49], [37, 11], [38, 11], [38, 30], [40, 14], [41, 2], [42, 1], [43, 15], [44, 58], [45, 1], [45, 34], [46, 1], [47, 13], [50, 73], [52, 1], [52, 34], [53, 2], [53, 27], [53, 30], [54, 1], [54, 10], [55, 53], [58, 18], [59, 49], [60, 86], [66, 1], [70, 70], [71, 2], [72, 1], [74, 6], [74, 20], [74, 78], [75, 45], [77, 5], [77, 19], [78, 1], [79, 97], [83, 43], [84, 30], [86, 1], [87, 1], [87, 17], [89, 2], [90, 1], [93, 49], [95, 5], [96, 42], [98, 45], [99, 3], [99, 71], [101, 2], [102, 1], [104, 58], [105, 1], [107, 11], [109, 13], [113, 2], [131, 57], [137, 3], [139, 33], [157, 5], [167, 63], [167, 79], [173, 2], [197, 2], [197, 23], [197, 27], [211, 2], [220, 16], [239, 3], [242, 41], [251, 33], [257, 2], [269, 2], [277, 9], [288, 1], [288, 3], [293, 11], [293, 23], [306, 17], [338, 2], [338, 13], [396, 11], [450, 1], [450, 19], [564, 2], [648, 1], [648, 56], [722, 37], [800, 21], [828, 24], [882, 5], [966, 6], [966, 34], [968, 8], [996, 12], [1058, 31], [1250, 10], [1352, 1], [2310, 36], [14288, 12], [[B]1264460, 18[/B]], [223092870, 20]]
[5, [5, 1]]
[7, [2, 3], [2, 10], [2, 12], [2, 141], [2, 278], [2, 387], [2, 421], [3, 6], [3, 8], [3, 118], [3, 198], [3, 305], [7, 1], [7, 2], [7, 8], [7, 127], [10, 1], [11, 5], [12, 21], [13, 2], [13, 87], [14, 1], [14, 19], [14, 21], [14, 130], [15, 10], [17, 24], [17, 91], [18, 13], [18, 52], [18, 70], [18, 134], [19, 2], [20, 1], [21, 8], [21, 17], [22, 1], [22, 19], [23, 11], [26, 3], [26, 19], [26, 50], [26, 80], [28, 9], [28, 47], [30, 52], [30, 70], [34, 1], [34, 7], [34, 9], [35, 11], [37, 2], [38, 1], [38, 13], [40, 2], [41, 49], [42, 2], [43, 20], [45, 4], [45, 55], [46, 33], [47, 8], [47, 42], [48, 61], [50, 17], [53, 8], [56, 38], [58, 5], [58, 27], [61, 2], [62, 1], [66, 5], [66, 31], [68, 10], [69, 70], [70, 48], [72, 25], [74, 11], [75, 1], [75, 63], [76, 39], [77, 2], [77, 16], [78, 23], [79, 7], [80, 28], [84, 31], [92, 32], [93, 29], [94, 22], [96, 3], [96, 7], [97, 5], [99, 19], [102, 2], [105, 2], [151, 2], [163, 4], [193, 3], [200, 24], [200, 56], [211, 65], [220, 15], [223, 4], [227, 10], [229, 4], [242, 39], [271, 3], [271, 34], [277, 25], [293, 55], [307, 2], [338, 39], [385, 57], [450, 12], [450, 17], [496, 31], [564, 21], [648, 40], [696, 7], [722, 51], [800, 51], [888, 5], [968, 60], [8128, 38], [14264, 7], [15015, 35], [15472, 3], [19116, 15], [131071, 8], [131071, 25]]
[11, [2, 60], [2, 316], [2, 480], [2, 499], [3, 15], [3, 189], [3, 303], [5, 15], [7, 143], [10, 20], [11, 1], [11, 137], [13, 31], [14, 14], [14, 28], [17, 2], [18, 1], [18, 55], [18, 76], [21, 1], [21, 47], [24, 2], [26, 36], [35, 83], [37, 50], [47, 47], [51, 1], [53, 15], [53, 67], [58, 2], [58, 24], [59, 81], [63, 85], [65, 2], [65, 33], [67, 3], [70, 2], [71, 61], [72, 4], [72, 58], [72, 63], [73, 3], [76, 28], [77, 15], [79, 3], [80, 3], [82, 2], [82, 54], [88, 54], [91, 1], [92, 30], [95, 63], [98, 2], [99, 13], [109, 15], [109, 75], [139, 5], [162, 70], [193, 57], [210, 58], [242, 25], [271, 23], [283, 27], [284, 19], [288, 4], [307, 49], [564, 30], [578, 50], [648, 41], [648, 42], [800, 54], [882, 50], [888, 26], [968, 32], [14288, 2], [14288, 4], [14288, 9], [31704, 16], [223092870, 4]]
[13, [2, 358], [3, 3], [3, 31], [3, 67], [5, 9], [11, 3], [11, 27], [13, 1], [20, 72], [23, 49], [23, 77], [24, 70], [35, 1], [38, 86], [39, 91], [43, 3], [43, 17], [50, 62], [50, 99], [56, 8], [62, 2], [69, 1], [70, 34], [73, 11], [75, 13], [79, 23], [93, 1], [94, 12], [96, 6], [103, 5], [104, 24], [104, 64], [131, 9], [167, 17], [173, 69], [179, 25], [181, 23], [197, 3], [229, 21], [263, 7], [263, 15], [271, 4], [392, 48], [392, 54], [648, 7], [770, 28], [968, 1], [1058, 7], [8191, 17], [15015, 9], [15015, 33], [6469693230, 2]]
[17, [3, 63], [6, 2], [7, 55], [13, 21], [15, 79], [17, 1], [19, 97], [23, 2], [24, 1], [24, 4], [38, 42], [39, 1], [45, 5], [46, 10], [51, 31], [55, 1], [58, 70], [60, 28], [78, 52], [84, 78], [85, 63], [92, 4], [96, 34], [99, 23], [119, 79], [131, 15], [157, 65], [162, 39], [271, 21], [396, 6], [1152, 31]]
[19, [2, 39], [2, 76], [2, 190], [2, 219], [2, 505], [3, 275], [3, 327], [5, 233], [10, 2], [10, 12], [10, 44], [12, 4], [12, 150], [13, 3], [13, 141], [15, 21], [19, 1], [22, 32], [34, 96], [40, 6], [41, 7], [41, 68], [42, 10], [42, 22], [45, 15], [55, 29], [59, 85], [60, 30], [65, 1], [70, 28], [71, 21], [72, 74], [76, 66], [77, 1], [79, 13], [88, 62], [89, 9], [89, 19], [90, 2], [94, 70], [97, 29], [98, 6], [102, 54], [109, 27], [193, 2], [210, 12], [233, 41], [241, 51], [263, 21], [269, 11], [276, 10], [277, 11], [288, 16], [293, 17], [338, 59], [392, 6], [392, 26], [392, 42], [496, 30], [722, 30], [770, 14], [1058, 44], [1152, 27], [8191, 15], [19116, 24], [131071, 21]]
[23, [3, 12], [3, 181], [7, 3], [7, 9], [11, 127], [17, 79], [18, 6], [18, 17], [18, 64], [21, 61], [23, 1], [40, 36], [44, 68], [47, 3], [54, 80], [55, 15], [57, 1], [57, 17], [65, 3], [69, 9], [71, 65], [74, 64], [77, 23], [77, 37], [79, 49], [85, 1], [86, 54], [88, 26], [93, 3], [99, 1], [101, 65], [105, 47], [127, 3], [137, 43], [173, 35], [200, 18], [242, 28], [263, 13], [293, 7], [496, 22], [564, 50], [578, 1], [800, 2], [8128, 8], [14536, 32], [19116, 8], [510510, 8]]
[29, [5, 41], [14, 92], [18, 50], [18, 116], [22, 8], [26, 68], [29, 1], [46, 36], [47, 39], [48, 4], [61, 5], [63, 67], [72, 43], [83, 11], [88, 2], [88, 78], [91, 13], [97, 3], [162, 11], [229, 51], [283, 5], [306, 56], [338, 57], [450, 21], [82589933, 3]]
[31, [2, 5], [2, 101], [2, 146], [3, 169], [5, 3], [5, 161], [6, 17], [11, 38], [11, 93], [11, 107], [12, 14], [19, 35], [19, 37], [31, 1], [31, 2], [31, 11], [38, 19], [40, 30], [44, 30], [54, 67], [56, 52], [58, 1], [61, 55], [67, 2], [68, 1], [70, 54], [70, 58], [74, 21], [80, 30], [87, 13], [91, 15], [92, 2], [92, 14], [95, 27], [97, 49], [98, 3], [103, 9], [113, 3], [119, 53], [162, 27], [163, 8], [179, 21], [210, 14], [220, 4], [227, 19], [231, 2], [239, 33], [269, 37], [281, 61], [882, 1], [882, 6], [1152, 4], [1152, 28], [1210, 10], [8191, 7], [12496, 3]]
[37, [2, 68], [2, 125], [2, 243], [3, 90], [5, 4], [7, 6], [7, 79], [10, 3], [10, 5], [10, 74], [11, 40], [12, 98], [14, 2], [14, 35], [14, 138], [22, 7], [22, 21], [22, 23], [22, 74], [23, 10], [24, 6], [26, 31], [28, 3], [28, 11], [29, 50], [35, 2], [37, 1], [42, 16], [44, 3], [44, 19], [45, 11], [47, 16], [51, 2], [53, 87], [55, 43], [60, 94], [63, 3], [67, 74], [71, 4], [74, 5], [75, 8], [77, 34], [78, 4], [79, 6], [83, 2], [83, 10], [84, 1], [84, 32], [85, 81], [88, 3], [90, 9], [91, 87], [94, 16], [95, 37], [96, 1], [96, 48], [97, 4], [99, 5], [104, 4], [131, 6], [131, 45], [139, 2], [149, 43], [220, 27], [239, 18], [241, 28], [241, 47], [251, 26], [277, 10], [283, 33], [293, 10], [307, 22], [552, 18], [14316, 2], [15015, 27]]
[41, [2, 6], [2, 8], [2, 23], [2, 47], [2, 112], [2, 117], [2, 281], [2, 373], [2, 405], [2, 411], [6, 5], [6, 13], [7, 11], [11, 14], [11, 57], [12, 32], [12, 56], [12, 119], [15, 2], [15, 6], [17, 65], [18, 39], [20, 3], [22, 67], [24, 18], [33, 2], [35, 8], [35, 34], [37, 20], [37, 73], [38, 54], [40, 11], [40, 20], [40, 21], [40, 52], [41, 1], [42, 5], [43, 25], [43, 81], [44, 49], [45, 8], [45, 22], [45, 36], [47, 2], [48, 1], [48, 3], [50, 16], [51, 18], [52, 25], [55, 21], [56, 1], [57, 2], [59, 39], [61, 9], [62, 3], [62, 13], [62, 40], [63, 1], [65, 4], [65, 26], [66, 25], [66, 78], [69, 2], [70, 13], [70, 23], [70, 38], [71, 5], [71, 7], [73, 27], [75, 2], [76, 1], [78, 15], [78, 64], [79, 2], [79, 4], [79, 17], [80, 1], [82, 11], [84, 2], [85, 8], [88, 1], [88, 22], [92, 1], [94, 11], [94, 46], [96, 50], [97, 7], [97, 48], [98, 10], [98, 41], [103, 2], [103, 21], [104, 1], [105, 10], [105, 30], [107, 3], [107, 61], [109, 2], [113, 16], [119, 29], [127, 26], [127, 44], [127, 52], [163, 2], [167, 13], [167, 20], [173, 9], [181, 5], [193, 32], [197, 10], [197, 20], [197, 75], [210, 4], [220, 17], [223, 2], [227, 2], [229, 2], [231, 4], [257, 28], [263, 8], [277, 14], [283, 17], [284, 11], [288, 57], [293, 4], [385, 11], [385, 42], [439, 2], [578, 3], [720, 3], [770, 13], [966, 2], [966, 31], [968, 2], [1210, 24], [1352, 4], [2310, 8], [14288, 3], [14536, 5], [31704, 9], [9699690, 20], [223092870, 2], [8589869056, 3]]
[43, [2, 9], [2, 62], [2, 210], [2, 271], [2, 510], [3, 4], [3, 22], [3, 80], [3, 86], [6, 26], [6, 32], [6, 77], [7, 16], [7, 28], [7, 51], [7, 189], [10, 42], [11, 13], [11, 28], [11, 56], [13, 4], [13, 8], [13, 40], [13, 95], [13, 98], [14, 5], [14, 23], [14, 25], [15, 14], [17, 12], [17, 16], [17, 101], [17, 129], [18, 34], [19, 4], [19, 55], [20, 21], [20, 70], [21, 2], [21, 6], [21, 98], [22, 2], [22, 104], [23, 4], [24, 10], [24, 19], [24, 31], [24, 36], [26, 6], [26, 38], [26, 78], [26, 88], [28, 13], [28, 18], [29, 3], [29, 59], [31, 14], [31, 26], [33, 3], [33, 23], [33, 45], [34, 3], [34, 28], [34, 44], [35, 4], [37, 97], [38, 38], [39, 6], [40, 1], [40, 35], [42, 13], [43, 1], [43, 2], [43, 55], [44, 1], [45, 2], [46, 3], [46, 5], [47, 17], [48, 9], [50, 1], [51, 5], [51, 13], [51, 50], [52, 9], [53, 4], [54, 49], [57, 26], [58, 71], [59, 2], [59, 6], [59, 18], [60, 1], [60, 6], [62, 8], [62, 9], [62, 50], [63, 6], [65, 12], [65, 32], [66, 21], [66, 56], [67, 10], [67, 63], [68, 14], [68, 18], [69, 3], [69, 43], [70, 1], [70, 8], [70, 22], [70, 27], [71, 26], [73, 2], [73, 14], [74, 1], [75, 6], [75, 11], [75, 46], [75, 73], [78, 17], [79, 30], [79, 31], [79, 56], [80, 5], [80, 36], [80, 68], [82, 1], [82, 72], [83, 3], [86, 11], [87, 6], [88, 76], [90, 35], [91, 2], [91, 44], [92, 13], [92, 19], [93, 24], [93, 27], [94, 1], [95, 21], [96, 5], [97, 40], [98, 5], [98, 29], [99, 8], [102, 22], [102, 26], [104, 3], [104, 26], [104, 68], [104, 70], [105, 3], [105, 6], [107, 2], [107, 5], [109, 11], [119, 38], [127, 11], [131, 2], [137, 71], [139, 4], [157, 2], [157, 25], [167, 39], [179, 3], [179, 5], [181, 2], [191, 2], [191, 5], [191, 31], [199, 29], [200, 7], [223, 12], [227, 6], [227, 12], [227, 14], [227, 57], [231, 1], [231, 6], [233, 10], [241, 55], [257, 3], [263, 43], [269, 43], [271, 2], [271, 20], [276, 4], [277, 2], [277, 45], [306, 11], [307, 3], [385, 8], [396, 5], [439, 3], [496, 18], [496, 36], [552, 28], [648, 45], [660, 30], [696, 15], [722, 15], [770, 1], [828, 14], [968, 29], [1152, 9], [1152, 12], [1152, 29], [1155, 1], [1155, 2], [1210, 28], [1250, 47], [2310, 16], [15015, 12], [19116, 4], [2147483647, 5], [6469693230, 1], [200560490130, 10]]
[47, [2, 453], [3, 9], [28, 34], [30, 10], [40, 22], [47, 1], [65, 47], [77, 13], [78, 80], [82, 26], [93, 17], [98, 75], [120, 44], [200, 37], [578, 22], [696, 2], [968, 40]]
[53, [2, 20], [2, 78], [2, 214], [2, 347], [2, 450], [23, 101], [48, 50], [48, 70], [53, 1], [72, 18], [75, 31], [94, 2], [163, 61], [181, 53], [241, 3], [306, 8], [306, 50], [648, 30], [648, 44], [648, 58], [888, 14]]
[59, [3, 94], [6, 128], [7, 14], [7, 24], [7, 64], [10, 7], [10, 23], [11, 8], [11, 58], [11, 80], [13, 6], [13, 38], [14, 9], [14, 49], [15, 36], [17, 64], [19, 6], [19, 25], [20, 59], [20, 71], [24, 9], [24, 13], [26, 59], [26, 71], [28, 7], [28, 23], [29, 4], [29, 36], [31, 8], [31, 10], [33, 4], [33, 6], [35, 6], [38, 77], [39, 2], [39, 12], [42, 3], [44, 5], [45, 6], [45, 28], [45, 30], [51, 32], [51, 78], [52, 3], [52, 11], [55, 4], [56, 61], [57, 4], [58, 17], [59, 1], [60, 3], [60, 17], [61, 12], [65, 50], [66, 17], [69, 4], [69, 10], [69, 24], [70, 19], [70, 39], [71, 28], [73, 4], [73, 10], [74, 33], [75, 18], [75, 38], [77, 28], [78, 44], [84, 5], [86, 37], [86, 49], [87, 4], [87, 8], [89, 16], [90, 11], [95, 2], [97, 46], [99, 2], [103, 14], [103, 38], [104, 5], [105, 19], [119, 2], [127, 25], [131, 22], [137, 2], [149, 2], [151, 6], [151, 27], [162, 62], [167, 2], [173, 6], [179, 4], [179, 16], [191, 20], [193, 4], [193, 16], [197, 4], [199, 2], [199, 4], [200, 1], [211, 4], [220, 55], [233, 2], [251, 2], [263, 2], [269, 47], [271, 6], [281, 12], [385, 10], [439, 4], [564, 5], [720, 11], [14288, 7], [15472, 5], [131071, 4], [7420738134810, 1]]
[61, [30, 90], [39, 3], [43, 23], [45, 7], [52, 6], [52, 36], [60, 9], [61, 1], [67, 61], [75, 43], [76, 68], [104, 54], [137, 21], [284, 22], [496, 50], [1058, 12]]
[67, [2, 147], [14, 6], [19, 53], [45, 47], [57, 13], [67, 1], [99, 55], [968, 4], [968, 58], [1264460, 4]]
[71, [2, 43], [2, 177], [6, 14], [12, 58], [13, 53], [13, 113], [18, 77], [21, 11], [22, 36], [26, 66], [50, 2], [61, 11], [63, 33], [66, 70], [71, 1], [92, 60], [95, 25], [137, 33], [162, 1], [179, 23], [239, 45], [271, 7], [271, 53], [439, 31], [496, 8], [722, 12], [722, 27], [780, 30], [1210, 26], [510510, 4]]
[73, [2, 67], [3, 98], [5, 10], [6, 3], [7, 133], [10, 11], [10, 13], [12, 3], [17, 48], [20, 4], [22, 94], [23, 6], [28, 5], [31, 3], [34, 2], [34, 5], [43, 14], [46, 7], [57, 47], [57, 81], [60, 62], [63, 14], [65, 57], [73, 1], [73, 12], [74, 74], [76, 9], [78, 3], [86, 7], [97, 2], [98, 1], [105, 12], [127, 19], [137, 4], [173, 14], [200, 2], [229, 3], [263, 10], [307, 25], [496, 43], [968, 11], [1184, 3], [1210, 12], [2310, 25], [19116, 5], [30030, 11], [131071, 3], [524287, 8], [33550336, 18]]
[79, [3, 113], [6, 4], [17, 39], [34, 56], [50, 6], [79, 1], [82, 5], [96, 26], [151, 67], [181, 45], [211, 53], [1250, 2]]
[83, [2, 376], [5, 5], [5, 36], [5, 57], [56, 44], [60, 88], [78, 12], [83, 1], [84, 46], [95, 57], [120, 28]]
[89, [2, 32], [2, 82], [3, 111], [7, 101], [37, 23], [47, 31], [57, 5], [68, 12], [89, 1], [113, 73], [450, 28], [660, 44], [510510, 2]]
[97, [2, 51], [2, 73], [7, 43], [19, 38], [26, 110], [38, 34], [43, 57], [68, 2], [97, 1], [98, 80], [103, 43], [107, 67], [131, 17], [293, 57], [392, 18], [1250, 9]]
[101, [2, 301], [2, 425], [29, 12], [31, 29], [45, 93], [55, 45], [73, 43], [73, 79], [99, 69], [101, 1], [181, 16], [1210, 2], [7420738134810, 8]]
[103, [2, 50], [6, 16], [24, 90], [44, 74], [50, 12], [72, 62], [103, 1], [242, 47], [396, 10]]
[107, [2, 255], [5, 223], [7, 165], [7, 171], [14, 94], [41, 29], [76, 78], [85, 31], [101, 31], [105, 61], [107, 1], [119, 3], [220, 2], [227, 41], [229, 17], [229, 39], [231, 57], [251, 3], [293, 9], [496, 60], [82589933, 13]]
[109, [3, 249], [10, 80], [18, 10], [28, 98], [30, 46], [55, 49], [79, 33], [83, 7], [85, 4], [109, 1], [131, 21], [276, 6], [338, 4], [578, 11], [660, 5], [1352, 16], [14288, 6]]
[113, [2, 11], [3, 38], [5, 31], [19, 50], [20, 5], [21, 70], [34, 15], [38, 3], [55, 3], [58, 50], [72, 21], [73, 22], [102, 12], [113, 1], [239, 31], [578, 28]]
[127, [2, 7], [5, 53], [53, 39], [97, 73], [101, 75], [127, 1], [127, 2], [139, 29], [211, 9], [1250, 6]]
[131, [3, 141], [19, 3], [30, 2], [33, 9], [66, 2], [66, 88], [119, 49], [131, 1], [162, 37]]
[137, [2, 396], [42, 42], [54, 28], [82, 16], [97, 57], [137, 1], [191, 47], [968, 54]]
[139, [61, 27], [77, 49], [139, 1], [284, 4]]
[149, [3, 55], [59, 45], [149, 1]]
[151, [18, 79], [96, 70], [103, 63], [151, 1], [162, 16], [210, 40], [15472, 38]]
[157, [20, 18], [20, 34], [60, 12], [65, 83], [157, 1], [241, 2], [242, 1]]
[163, [3, 47], [35, 9], [163, 1], [163, 51], [220, 26], [281, 2], [284, 32], [293, 2], [780, 4], [800, 8]]
[167, [45, 35], [109, 3], [167, 1]]
[173, [7, 31], [57, 59], [173, 1], [277, 3]]
[179, [14, 40], [40, 72], [60, 36], [61, 31], [87, 25], [109, 29], [179, 1], [200, 52], [227, 13], [241, 5], [14316, 8]]
[181, [12, 6], [149, 63], [181, 1]]
[191, [7, 63], [12, 5], [18, 112], [40, 84], [47, 48], [54, 22], [56, 2], [68, 25], [78, 14], [89, 15], [94, 3], [191, 1], [220, 3], [284, 5], [306, 34], [385, 1], [439, 13], [450, 3], [578, 5], [1152, 2], [1184, 19], [1210, 3]]
[193, [23, 39], [26, 2], [37, 10], [51, 67], [62, 55], [63, 5], [98, 4], [193, 1], [242, 10], [882, 31], [1155, 19], [15472, 40]]
[197, [15, 85], [197, 1]]
[199, [2, 110], [23, 71], [199, 1], [450, 36]]
[211, [2, 46], [3, 211], [33, 21], [43, 21], [48, 58], [65, 63], [76, 14], [211, 1], [338, 1]]
[223, [69, 19], [105, 23], [162, 68], [223, 1]]
[227, [58, 76], [227, 1]]
[229, [23, 33], [229, 1], [241, 49]]
[233, [14, 4], [120, 72], [229, 63], [233, 1]]
[239, [5, 93], [6, 204], [19, 7], [20, 14], [181, 3], [239, 1], [1152, 1]]
[241, [2, 279], [2, 346], [19, 11], [33, 89], [57, 7], [59, 25], [241, 1], [269, 35]]
[251, [191, 3], [251, 1], [263, 3]]
[257, [13, 10], [18, 3], [20, 112], [33, 39], [46, 2], [46, 56], [47, 19], [54, 4], [93, 2], [96, 9], [101, 15], [104, 8], [104, 40], [193, 13], [257, 1], [288, 44], [780, 32], [2147483647, 9]]
[263, [29, 7], [263, 1], [648, 8]]
[269, [53, 71], [101, 7], [127, 7], [269, 1], [1155, 41]]
[271, [18, 7], [271, 1]]
[277, [2, 103], [13, 83], [71, 6], [79, 61], [277, 1], [720, 1], [510510, 5]]
[281, [6, 40], [14, 46], [19, 27], [34, 4], [37, 74], [42, 48], [50, 38], [93, 21], [96, 28], [181, 7], [197, 5], [281, 1], [828, 4]]
[283, [2, 86], [48, 10], [283, 1], [392, 55]]
[293, [2, 53], [15, 47], [281, 67], [293, 1]][/code]I found that you had included most of the reserved bases that have not been added to the tables yet. I included all of them. That's why 1264460^18 shows up for prime 3. I've only done a little bit of spot checking, so the file would need serious validation before it is considered correct.

My program shows 7460 unique terminating primes, with a total of 9549 terminated sequences.

* whole set, in this case, means all the bases that have tables, plus all the reserved bases that are mentioned near the top of the main page. However, the sequences that the db won't provide valid .elf files for are not currently included. i will address these eventually, but not for now, since none of them are currently terminated.

 richs 2022-09-12 23:07

[QUOTE=garambois;613286]The merging sequences are to be watched on the main project.
And on the main project, the sequence 903872 is reserved for you.
So everything is OK.[/QUOTE]

Merci beaucoup!

 gd_barnes 2022-09-13 11:43

I saw a couple of merged sequences that were at < 120 digits so I decided to rectify that:

91^8 is now at 130/121
239^6 is now at 120/116

I'm done with them. Update reported to the main project thread.

 garambois 2022-09-13 16:46

[QUOTE=gd_barnes;613298]If we are not showing reservations on merged sequences, should 210^47 and 233^20 have their initials removed?[/QUOTE]
Yes, you are right !
Thanks !

 garambois 2022-09-13 17:33

Page updated.
Many thanks to all for your help.

[B]Added base : 696[/B]
[B]Updated bases : 93, 131, 223, 307, 9699690 and 70, 71, 72, 73, 210, 233[/B]
[B]Base reservations made and corrected for bases : 70, 71, 72, 73, 210, 233[/B]

 gd_barnes 2022-09-14 08:15

[QUOTE=EdH;613301]I found that you had included most of the reserved bases that have not been added to the tables yet. I included all of them. That's why 1264460^18 shows up for prime 3. I've only done a little bit of spot checking, so the file would need serious validation before it is considered correct.

My program shows 7460 unique terminating primes, with a total of 9549 terminated sequences.

* whole set, in this case, means all the bases that have tables, plus all the reserved bases that are mentioned near the top of the main page. However, the sequences that the db won't provide valid .elf files for are not currently included. i will address these eventually, but not for now, since none of them are currently terminated.[/QUOTE]
Is there an explanation for why the prime 43 terminates so many more sequences than any others?

 garambois 2022-09-14 13:54

In the main project, the same is true.
It is by far the prime number 43 that is the end of the largest number of sequences.
This is not only true for our project n^i.
I don't know if anyone has an explanation ?

 garambois 2022-09-14 14:08

1 Attachment(s)
[QUOTE=EdH;613301]It was long awaited, but I finally have a C++ program that scours the whole set* in 15 seconds. There is a little bit of difference as explained further below. Here is the same set (with a highlighted difference for prime 3) as shown in post [URL="https://www.mersenneforum.org/showpost.php?p=612644&postcount=1845"]#1845[/URL]:
...
...
...

My program shows 7460 unique terminating primes, with a total of 9549 terminated sequences.
...
...[/QUOTE]

Thank you very much Edwin.
I will study this closely soon enough.
I attach the result given by Karsten's scripts.
So we get the result in three different ways.
Karsten's script gives this in a few seconds.
A lot of thanks to Karsten !
We still have to check that our three lists match: the one in post [URL="https://www.mersenneforum.org/showpost.php?p=612644&postcount=1845"]#1845[/URL], the one in post [URL="https://www.mersenneforum.org/showpost.php?p=613301&postcount=1877"]#1877[/URL] and this post.
I don't have time to do that in theI don't have time to do that in the next 2 or 3 days.

 kar_bon 2022-09-14 14:39

You missed prime 257 as ending in the new "graph.txt".

There're some bases which are not listed taken in the first attempt and some newly terminated seqs, too.
Bases like 780, 828, 888 or terminations like 26^110.

In your first file there're some extra spaces. I will send you a small update of my script to change the output format to the others, so you can catch differences easier.

 EdH 2022-09-14 15:18

Agree that matching the formatting will be necessary to employ software verification. My program outputs a different format, as well, but I can make two search/replace edits to match Jean-Luc's format. (I also removed the extra spaces from Jean-Luc's list for the comparisons I did.)

Matching for updates will be challenging. I'm always amazed at how much has changed within a few days. Now that the newer db limits are in place, what used to take less than an hour is taking 18 hours. I could probably shorten that by watching more closely, but for now, it works comfortably without reaching the limits.

I am contemplating a program that would work directly with the db just checking last lines. It should be able to do the entire set without hitting the limits, but it would be much slower than the current 15 seconds using the local set. The advantage would be up to date results, but that may not really be a major issue ATM.

 garambois 2022-09-14 15:40

Thank you very much Karsten.
I hadn't seen about 257 !
Yes, I am missing a few bases, but I am almost done with 780.
It's true that for bases 396, 696, 780, 828, 888 and 996, there will be many more than in post #1845.
At first glance, our three programs are a good match.
Edwin, I also don't think it's a major problem if we don't have the data exactly up to date to the day.
The prime numbers 601 and 761 should be included in my study, it seems to me.
I also note that the Mersenne primes have at least three sequences, contrary to others "of comparable size" but this is quite normal if one thinks a little.

 warachwe 2022-09-14 16:59

[QUOTE=gd_barnes;613398]Is there an explanation for why the prime 43 terminates so many more sequences than any others?[/QUOTE]

[QUOTE=garambois;613415]In the main project, the same is true.
It is by far the prime number 43 that is the end of the largest number of sequences.
This is not only true for our project n^i.
I don't know if anyone has an explanation ?[/QUOTE]

I think, with no evidence to back it up, it might be because 43 have many values of "reverse aliquot" (don't know what it's actually called) in the first few terms. So it's more like grouping sequence that "end" in those numbers together.

Maybe we can try to compare the number of , say, 6 digits "reverse aliquot" of each prime with the number of sequences that end with that prime?

 gd_barnes 2022-09-14 20:40

I like the idea that 43 could come from quite a few numbers in the reverse aliquot situation. That is the iteration before the number 43 could theoretically be many different values. It would be interesting to see an analysis of that.

 gd_barnes 2022-09-14 20:49

Jean-Luc,

I've noticed in the past that Yoyo usually only works on sequences up to 140 digits. Has this changed? I ask because reservations are shown for exponents of all sizes on bases 70, 71, and 73. I see that they've already advanced many of the exponents on those bases at <= 140 digits but none > 140 digits.

If this is true, then exponents > 75 could be released for all 3 bases.

Edit: Yoyo terminated 69^70 !

Gary

 VBCurtis 2022-09-14 20:54

[QUOTE=warachwe;613430]I think, with no evidence to back it up, it might be because 43 have many values of "reverse aliquot" (don't know what it's actually called) in the first few terms. So it's more like grouping sequence that "end" in those numbers together.

Maybe we can try to compare the number of , say, 6 digits "reverse aliquot" of each prime with the number of sequences that end with that prime?[/QUOTE]

This was exactly my conclusion too. :tu:

 EdH 2022-09-14 21:38

Releasing base 98.

 EdH 2022-09-15 13:15

For those interested, here are a couple generations of numbers that can result in 43:[code]Prime 43 first generation:
50 -> 43
185 -> 43
341 -> 43
377 -> 43
437 -> 43
Prime 43 second generation:
40 -> 50 -> 43
94 -> 50 -> 43
387 -> 185 -> 43
543 -> 185 -> 43
895 -> 185 -> 43
1011 -> 341 -> 43
1119 -> 377 -> 43
1299 -> 437 -> 43
1903 -> 185 -> 43
2155 -> 437 -> 43
2839 -> 185 -> 43
6103 -> 377 -> 43
6439 -> 185 -> 43
6943 -> 185 -> 43
7123 -> 437 -> 43
7291 -> 341 -> 43
8023 -> 185 -> 43
8119 -> 377 -> 43
8383 -> 185 -> 43
9019 -> 341 -> 43
10063 -> 377 -> 43
13771 -> 341 -> 43
16579 -> 341 -> 43
18283 -> 437 -> 43
18703 -> 377 -> 43
19099 -> 341 -> 43
20299 -> 437 -> 43
21331 -> 341 -> 43
22339 -> 341 -> 43
24139 -> 341 -> 43
24319 -> 377 -> 43
24931 -> 341 -> 43
25651 -> 341 -> 43
28459 -> 341 -> 43
28783 -> 377 -> 43
28891 -> 341 -> 43
29299 -> 437 -> 43
29719 -> 377 -> 43
30883 -> 437 -> 43
32743 -> 377 -> 43
33823 -> 377 -> 43
35263 -> 377 -> 43
44923 -> 437 -> 43
45499 -> 437 -> 43
46003 -> 437 -> 43
47083 -> 437 -> 43[/code]As compared with 47:[code]Prime 47 first generation:
129 -> 47
205 -> 47
493 -> 47
Prime 47 second generation:
261 -> 129 -> 47
725 -> 205 -> 47
995 -> 205 -> 47
1379 -> 205 -> 47
2071 -> 129 -> 47
2123 -> 205 -> 47
2435 -> 493 -> 47
2483 -> 205 -> 47
3007 -> 129 -> 47
4087 -> 129 -> 47
4163 -> 205 -> 47
5363 -> 205 -> 47
6179 -> 205 -> 47
6227 -> 493 -> 47
6683 -> 205 -> 47
7379 -> 205 -> 47
8003 -> 205 -> 47
9179 -> 205 -> 47
9563 -> 205 -> 47
10379 -> 205 -> 47
10403 -> 205 -> 47
13427 -> 493 -> 47
14291 -> 493 -> 47
19307 -> 493 -> 47
23267 -> 493 -> 47
25547 -> 493 -> 47
26291 -> 493 -> 47
29891 -> 493 -> 47
30587 -> 493 -> 47
33947 -> 493 -> 47
40067 -> 493 -> 47
41747 -> 493 -> 47
42827 -> 493 -> 47
49067 -> 493 -> 47[/code]

 garambois 2022-09-15 17:01

[QUOTE=gd_barnes;613444]Jean-Luc,

I've noticed in the past that Yoyo usually only works on sequences up to 140 digits. Has this changed? I ask because reservations are shown for exponents of all sizes on bases 70, 71, and 73. I see that they've already advanced many of the exponents on those bases at <= 140 digits but none > 140 digits.

If this is true, then exponents > 75 could be released for all 3 bases.

Edit: Yoyo terminated 69^70 !

Gary[/QUOTE]
I remind you that on [URL="https://yafu.myfirewall.org/yafu/download/ali/ali.txt.all"]this page[/URL] you can see on which sequences yoyo (i.e. yafu) actively works.
All the sequences that are not in this list are available for you to work on yourself.
But the sequences in this list are not available.
You have to give yafu time to "clean up" !
And after this cleaning, I will update the reservations, around the beginning of November, this delay seems to me reasonable.

Congratulations to yoyo for the completed calculation of the 69^70 non-matching parity sequence !

 garambois 2022-09-15 17:14

For the prime number 43, I can add some statistics that I had done a few years ago, thanks to [URL="http://www.aliquotes.com/aliquote_base.htm#alibasefonda"]my fundamental database on aliquot sequences[/URL].
But at that time, I only had the sequences up to 10,000,000 (today, 30,000,000, maybe I should make new statistics ?).
Beware, for these statistics, all sequences <10,000,000 that have a term that exceeds 10^50 are considered Open-End and so, here, we must underestimate the number of sequences that end with 43.
Here is what the statistics say.
Of the first 10,000,000 sequences that start with the integers from 1 to 10,000,000, there are :
- 666638 that end with the prime number 43.
- 456843 that end with the prime number 59.
- 437318 that end with the prime number 41.

 gd_barnes 2022-09-16 03:52

[QUOTE=garambois;613508]I remind you that on [URL="https://yafu.myfirewall.org/yafu/download/ali/ali.txt.all"]this page[/URL] you can see on which sequences yoyo (i.e. yafu) actively works.
All the sequences that are not in this list are available for you to work on yourself.
But the sequences in this list are not available.
You have to give yafu time to "clean up" !
And after this cleaning, I will update the reservations, around the beginning of November, this delay seems to me reasonable.

Congratulations to yoyo for the completed calculation of the 69^70 non-matching parity sequence ![/QUOTE]
Thank you for the info. I was unaware of it.

I do not know what you mean by "you have to give yafu time to clean up". Does that mean that the list on that page is out of date? In other words, why do you have to wait until November to make your page reservations match theirs? It's a little confusing for people who are unaware of the page.

 garambois 2022-09-16 17:58

I don't have to wait until November, I choose to do that, because I think it's a good deadline.
I don't know how long it really takes yafu to "decide" to drop a sequence and automatically remove it from this list ?
Because I understood that yafu works like that.
But at the moment, it seems to me that there are still way too many sequences in the list that yafu is likely to work on.

 gd_barnes 2022-09-16 22:09

[QUOTE=garambois;613560]I don't have to wait until November, I choose to do that, because I think it's a good deadline.
I don't know how long it really takes yafu to "decide" to drop a sequence and automatically remove it from this list ?
Because I understood that yafu works like that.
But at the moment, it seems to me that there are still way too many sequences in the list that yafu is likely to work on.[/QUOTE]
Once again, thank you for the info. Now that makes sense. They are slow to remove them from the list. I will go off of their list for reservations. If I'm interested in one of their reserved sequences and it looks like they've stopped working on it, I'll ask them directly.

It's been deserted around here since the FactorDB went down. I was lucky that I had downloaded a lot of elfs for my various efforts before that happened so my machines have kept mostly busy with it all. But I'm almost done with them. I'm getting a little worried about the site. It's been ~2 days now.

I have a lot of information to enter into the DB regarding my larger exponent opposite-parity effort here. I'm done searching bases 100-195. I only have elfs saved off down to base 97 so am working on those now.

 EdH 2022-09-16 23:54

I've got a full set of .elfs from a recent update for all the tables. If you have some specific ones you're interested in, I can dig through and upload them.

BTW, here's the full index 2 for 7420738134810^14:[code]2 . c182 = 16016867029051535909281714695624144790320582160894836559533941276246821065324848812304319999471215177629407690206509347992575037845626243418170713804242383756754000753999672887885675 = 3^5 * 5^2 * 7^2 * 11 * 13^2 * 19 * 31 * 4397223379 * 63695801008003101125656552019171763059887853 * 175449118859425685093746579891161527440802504681023093824441968053920577368008221980886615248441968625302598292789153[/code]

 gd_barnes 2022-09-17 05:50

[QUOTE=EdH;613569]I've got a full set of .elfs from a recent update for all the tables. If you have some specific ones you're interested in, I can dig through and upload them.

BTW, here's the full index 2 for 7420738134810^14:[code]2 . c182 = 16016867029051535909281714695624144790320582160894836559533941276246821065324848812304319999471215177629407690206509347992575037845626243418170713804242383756754000753999672887885675 = 3^5 * 5^2 * 7^2 * 11 * 13^2 * 19 * 31 * 4397223379 * 63695801008003101125656552019171763059887853 * 175449118859425685093746579891161527440802504681023093824441968053920577368008221980886615248441968625302598292789153[/code][/QUOTE]
I was lucky. I had downloaded all of the applicable elfs for my same-parity ECM effort for sequences with starting size > 185 digits. I did that only a few hours before it went down. I started that late Thursday and it should keep me busy through early Sunday or so. I should have at least 3 terminations! :-) If the DB is not up by then, I'll ask for some from you. Between that and the opposite-parity effort here, I will be spending many hours entering stuff into the DB when it comes back up.

A lot of things here and elsewhere depend on the FactorDB. I hope that everything will be OK with it and that little to no data was lost.

 garambois 2022-09-17 06:55

I also have now already 2 programs down !
I hope FactorDB will come back today...

 EdH 2022-09-17 14:09

Good to see it's back up. I think it seems slow, as often occurs after coming back from the depths. I think it's still rebuilding some things. The sequences are taking a while to display.

Interestingly, 7420738134810^14 is still showing abundance at term 4. Most matched parity sequences turn deficient at term 1, don't they?

Are there any stats I can dig for from my end to supplement your work, Jean-Luc?

 RichD 2022-09-18 01:20

Reserving all prime bases below 350 for initialization. (311, 313, 317, 331, 337, 347, 349)

Base 317 can be added at the next update. I occasionally look ahead and perform some work on sequences but this one seemed to have more work than I would do part-time.

 garambois 2022-09-18 08:25

I have good news :
All of Karsten's, Edwin's and my results match.
Our programs are good !
The only differences between our results come from the fact that we did not do our scans at the same time and that in the meantime sequences were added for some primes.

:smile:

 garambois 2022-09-18 08:27

[QUOTE=RichD;613601]Reserving all prime bases below 350 for initialization. (311, 313, 317, 331, 337, 347, 349)

Base 317 can be added at the next update. I occasionally look ahead and perform some work on sequences but this one seemed to have more work than I would do part-time.[/QUOTE]
Many thanks RichD.
Base 317 will be added to the page next week.

 garambois 2022-09-18 08:54

[QUOTE=EdH;613588]
Interestingly, 7420738134810^14 is still showing abundance at term 4. Most matched parity sequences turn deficient at term 1, don't they?[/QUOTE]Sometimes I do work on the first terms of sequences and on the abundance of these first terms, as I exposed for example in post [URL="https://www.mersenneforum.org/showpost.php?p=572872&postcount=921"]#921[/URL].
But these works are often limited by the non matching parity sequences for which we are only at index 1 !
Because interesting things happen between the index term 1 and 2.
For bases 3 and 5, we do not have this problem, but for base 6, the problem starts to appear with the sequences 6^189, 6^207 and 6^209.
For the sequences with non corresponding parity, it is therefore interesting to try to remove all these 1's and to have instead 2's or 3's, which allows to do interesting things.

[QUOTE=EdH;613588]Are there any stats I can dig for from my end to supplement your work, Jean-Luc?[/QUOTE]
Thank you very much Edwin, but there are no new tracks emerging at this time.
I know there are a lot of people who occasionally follow this thread.
If any reader has an idea or question, please feel free to ask.
Any idea is interesting and can start us on a new track.
Don't be afraid to ask questions, even if you think it seems too trivial.
We can often come up with very interesting things with trivial questions.
And if the question is more complicated, don't hesitate either.
If I don't understand it, there will always be someone who does and it will give them ideas.

 EdH 2022-09-18 16:21

[QUOTE=garambois;613612]I have good news :
All of Karsten's, Edwin's and my results match.
Our programs are good !
The only differences between our results come from the fact that we did not do our scans at the same time and that in the meantime sequences were added for some primes.

:smile:[/QUOTE]Good news, indeed - thanks!

 EdH 2022-09-18 16:35

[QUOTE=garambois;613509]For the prime number 43, I can add some statistics that I had done a few years ago, thanks to [URL="http://www.aliquotes.com/aliquote_base.htm#alibasefonda"]my fundamental database on aliquot sequences[/URL].
But at that time, I only had the sequences up to 10,000,000 (today, 30,000,000, maybe I should make new statistics ?).
Beware, for these statistics, all sequences <10,000,000 that have a term that exceeds 10^50 are considered Open-End and so, here, we must underestimate the number of sequences that end with 43.
Here is what the statistics say.
Of the first 10,000,000 sequences that start with the integers from 1 to 10,000,000, there are :
- 666638 that end with the prime number 43.
- 456843 that end with the prime number 59.
- 437318 that end with the prime number 41.[/QUOTE]I resurrected my seqinfo program and modified it to work with the current regina_file of 2-30M. (I'm not sure the status of Aillias' version.) Anyway, here is what it shows for that full set:[code]1242103 sequences found for 41
1893305 sequences found for 43
1298078 sequences found for 59[/code]

 gd_barnes 2022-09-19 02:25

1 Attachment(s)
I have initialized middle-sized to large opposite-parity exponents to a cofactor >= 110 digits for all bases 100 thru 195.

All bases in that range were affected with the exception of double-square base 162.

Also done were newly added bases 396 and 696.

Attached is a document of the specific affected sequences.

I'm continuing with this effort for bases < 100.

 RichD 2022-09-19 12:50

Bases 311 and 313 can be added at the next update.

 richs 2022-09-19 14:29

I'll reserve 34^105

 yoyo 2022-09-19 17:03

I'll take bases 76, 78 and 79.
77 is reserved by Jean-Luc Garambois.

yoyo

 EdH 2022-09-19 18:02

The new thread has been created and I realized a way to use a different post as the first, so I won't need to edit someone else's. The new thread is at [URL="https://www.mersenneforum.org/showthread.php?t=28082"]Index 1 Sequence Work for the "n^i" Aliquot Project[/URL]. I'll update the list from time to time with added bases and removed sequences.

 garambois 2022-09-19 19:34

@Gary, RichD, richs, yoyo :
Thank you very much for your work, your reservations, your initializations.
All of this will be on the page when we next update it in less than a week.

@Edwin :
Thank you very much for starting the new sub-project thread to move the sequences from index 1 to a higher index !

 gd_barnes 2022-09-21 05:12

313^46 terminated by me in a cycle!

This is my first opposite-parity termination in ages! It's also the first of the opposite-parity initialization effort. :smile:

This one was remarkable. It went almost straight down from its starting size of 115 digits! It started with a downdriver and did not lose it until 55 digits. After a brief foray up to 57 digits, it regained the downdriver almost exclusively until the end.

 garambois 2022-09-21 08:01

Wow, one more 2-cycle...
Congrats !

 gd_barnes 2022-09-21 08:25

[QUOTE=EdH;613709]The new thread has been created and I realized a way to use a different post as the first, so I won't need to edit someone else's.[/QUOTE]

If you can tell me a way to do that, that would be great. I have on occasion had a need to do such a thing on the two projects that I mod. I have also had to edit someone else's post if they are the one to start the conversation.

 EdH 2022-09-21 12:23

[QUOTE=gd_barnes;613817]If you can tell me a way to do that, that would be great. I have on occasion had a need to do such a thing on the two projects that I mod. I have also had to edit someone else's post if they are the one to start the conversation.[/QUOTE]1. I started the new thread with a "placeholder" post.
2. I looked for the most recent post I made previous to the first one I was going to move and copied it to the new thread rather than moving it.
3. I deleted the "placeholder" post, leaving just the copied one.
4. I moved all the relevant posts from this thread to the other.
5. I completely removed the previous text from the copied first post and entered the new description.

BTW, Congrats on the cycle find!

 gd_barnes 2022-09-21 12:26

Nice! I think I thought of something like this before but wasn't able to make it work. Perhaps I tried to move one of my posts that was slightly prior to the relevant first post instead of copying it. Thanks for the explanation.

 gd_barnes 2022-09-22 09:36

105^40 is a merge but the merge info. is not shown on the page.

It merges at index=2662 with 14160:i4.

 gd_barnes 2022-09-22 09:56

1 Attachment(s)
I have initialized middle-sized to large opposite-parity exponents to a cofactor >= 110 digits for all bases 90 thru 99.

All bases in the range were affected.

Also done were new bases 311, 313, and 317 for exponents > 40 although they are not yet shown on the page.

Attached is a document of the specific affected sequences for the 90s bases.

Note that Ed is doing some work on the index=1 effort in this area for cofactors > ~135 digits. So there could be additional exponents that are updated after this posting.

I'm continuing with this effort for bases < 90. 80 thru 89 are running now.

The 80s and 90s are the largest amount of work for this effort. Yoyo hasn't reached here yet and the size of the sequences go up very high. So there are a lot of untouched or little touched sequences.

 RichD 2022-09-22 12:12

Bases 331 and 337 can be added at the next update.

 gd_barnes 2022-09-23 15:05

2 Attachment(s)
I have initialized middle-sized to large opposite-parity exponents to a cofactor >= 110 digits for all bases 80 thru 89.

Also done were newly added bases 331 and 337 for exponents > 40 although they are not yet shown on the page.

Attached is a document of the specific affected sequences for the 80s bases.

Note that the index=1 effort is overlapping with this. I've also included any changes as a result of that. Additionally, several sequences in the 90s were changed since the last time I posted about this so I'm attaching an updated document for bases 90 to 99.

I'll take a break for a while and then continue with bases < 80.

On another note, it looks like this was missed with the last update:
[QUOTE=gd_barnes;613332]I saw a couple of merged sequences that were at < 120 digits so I decided to rectify that:

91^8 is now at 130/121
239^6 is now at 120/116

I'm done with them. Update reported to the main project thread.[/QUOTE]

 RichD 2022-09-24 22:01

Bases 347 and 349 can be added at the next update. I have a couple low exponents that still need a little more work to bring them to 100+ digits but all same parity exponents (that I would be working on) are complete. The subproject can get a jump before these sequences appear in the table.

 EdH 2022-09-24 22:50

Thanks Rich! I'm working on it. . .

 garambois 2022-09-25 08:23

[QUOTE=yoyo;613706]I'll take bases 76, 78 and 79.
77 is reserved by Jean-Luc Garambois.

yoyo[/QUOTE]
Base 79 is also already reserved !
What should I do : delete the old reservations for Unconnected and Sergiosi and reserve for yoyo instead ?

 gd_barnes 2022-09-25 08:38

[QUOTE=garambois;614088]Base 79 is also already reserved !
What should I do : delete the old reservations for Unconnected and Sergiosi and reserve for yoyo instead ?[/QUOTE]
Contact them and see if they are still working on it. I don't know the case here, but it's been my experience that reservations with no work in ~2-3 months are often something that people forgot about releasing and had no intent of continuing.

 garambois 2022-09-25 08:40

I don't know what's happening on FactorDB ?
The situation is catastrophic : I can only update one base and I have to wait an hour to update a second one.
It is therefore impossible for me to update this week !
I managed to add the bases 311, 313, 317, 331, 337, 780.
I added the merge that Gary mentioned in post #1920.
I'm still thinking of adding the yoyo and richs reservations, once I get a response to my previous post for base 79.

If the restrictions on FactorDB have increased again, I don't know how I'll be able to make my updates ?
To load a single base, it's very time consuming.
Maybe FactorDB has to rebuild them after the long maintenance works the other day ?
I hope the problem is only from there and not from new restrictions.

 garambois 2022-09-25 08:51

[QUOTE=gd_barnes;614089]Contact them and see if they are still working on it.[/QUOTE]
Done.
Many thanks.

 gd_barnes 2022-09-25 09:22

[QUOTE=garambois;614090]
If the restrictions on FactorDB have increased again, I don't know how I'll be able to make my updates ?
To load a single base, it's very time consuming.
Maybe FactorDB has to rebuild them after the long maintenance works the other day ?
I hope the problem is only from there and not from new restrictions.[/QUOTE]
I have not noticed a restriction change.

I have noticed that any sequence that has not been accessed since the outage has to be rebuilt again. That almost definitely is your problem.

You may have to just keep updating one base an hour. Maybe try for 2 an hour. Consider working from largest down to smallest base. There's fewer exponents on the bigger bases.

Unfortunately nearly every base was touched this time with a combination of the index 1 effort, my ECM effort on the same-parity sequences > 185 digits, my initialization of higher exponents on opposite parities, all of the Yoyo work, and new bases by you and Rich. I know it will be a huge update.

 garambois 2022-09-25 09:31

I'll try to make as much progress as possible !
But at this rate, it will certainly take me several days, even weeks.

 EdH 2022-09-25 13:28

[QUOTE=garambois;614090]. . .
I managed to add the bases 311, 313, 317, 331, 337, 780.
. . .[/QUOTE]I'm not finding these pages. Is an update of the server pending?

 garambois 2022-09-25 13:47

[QUOTE=EdH;614113]I'm not finding these pages. Is an update of the server pending?[/QUOTE]
I'm waiting for some answers about the 79 base, see post #1928.
I will post what I have done later tonight.
Sometimes it takes me 2 or 3 hours to update a single base.
So I will not insist.

 EdH 2022-09-25 14:04

Thanks! I misread your update as having been the pages. I'm in no hurry. All my scripts are based on the current state and I probably won't update the other threads again until you're done for the day.:smile:

 garambois 2022-09-25 18:24

Page updated.
Many thanks to all for your help.

[B]Added bases : 311, 313, 317, 331, 337, 347, 349, 780.[/B]
[B]Updated bases : some bases for which Edwin's thread reported terminated matched parity sequences.[/B]
[B]Base reservations : bases 76 and 78 for yoyo, sequence 34^105 for richs.[/B]
[B]Add a fusion : base 105^40
[/B]
Unfortunately, I couldn't do anything else because of the slowness of FactorDB[B] ![/B]
I will continue during the week.

 gd_barnes 2022-09-26 01:37

I just thought of something: I will manually access some full bases. I'll start with the largest bases and see how long it takes me. I'll then let you know what I've done and you can see if it helps you out.

I'll do this a little later tonight (early morning GMT).

 richs 2022-09-26 03:47

Releasing 34^105 at index 7. The C139 is ecm'd to t35.

 gd_barnes 2022-09-26 09:23

A little info. for you Jean-Luc:

I pulled up each sequence on your page starting at the largest base 7420738134810. Of course, the sequences with more iterations take longer because they have to be rebuilt each time. They can take a lot of time but I don't wait for them to come up on my screen. I just keep clicking on the links on your pages. The same-parity ones all come up fast so I quickly hit the back button and go on to the next one.

Going backwards by base, I hit my limit on the 5th base 6469693230 within ~10-15 minutes but it does not give an error/warning message. After hitting my limit, each time I click a link it simply pulls up the page with the count of page requests, IDs created, database queries, CPU (wall clock time) and the Counting since time. It does not display a red warning message like it does when too many IDs are created.

When I started this, all of the above counts were zero. At this moment, it shows 142 page requests, 0 IDs created, 1640372 database queries, and 345.7 CPU (wall clock time). I don't know if I went over the limit on queries or CPU time. I pulled up the counts page a few times throughout the process to get an idea of what might be the limits on some of the categories. My best guess is that I'm limited to 1500000 (1.5M) database queries within an hour. The "Counting since" categories shows the count started at 10:50am site time. At the time of this post, it is ~11:20am site time. So assuming that the limit that I hit is an hourly limit, I'll be able to do this again in ~30 minutes.

It is my thinking that if people keep doing this, you will much more quickly be able to update your pages in a reasonable amount of time.

Another thought: Is there a way for you to set up an automated process to just simply click on the links until it hits a limit, then wait an hour, do it again, etc.? If that could be automated somehow, that would help a lot. I don't think there needs to be any update going on, just access each sequence in order.

 gd_barnes 2022-09-26 10:13

I think there is a better way. I'm issuing a WGET command to download the ELF files for all sequences in each base. This does not seem to affect the limits but it seems to force the rebuild of each sequence.

I'll let you know how this goes. I've done it with 2 bases so far.

 EdH 2022-09-26 11:45

[QUOTE=gd_barnes;614174]. . .
Another thought: Is there a way for you to set up an automated process to just simply click on the links until it hits a limit, then wait an hour, do it again, etc.? If that could be automated somehow, that would help a lot. I don't think there needs to be any update going on, just access each sequence in order.[/QUOTE]That's how I update my local set. I have a script that runs several bases and then sleeps for an hour. I turn it loose and check on it now and then. I'll start it today and see if it helps. Last time it took about 15 hours. I need to add the new bases to my set, anyway. Let's see how long it takes this time and whether I hit a limit. I'm not sure it will help overall, since it only touches the db for local sequences that are still open, but it might help a bit.

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