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Old 2016-04-20, 08:55   #6
axn
 
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Jun 2003

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Quote:
Originally Posted by rogue View Post
Carol Primes (b^n-1)^2-2:
Code:
   base      
     2    (n < 100000) 2, 3, 4, 6, 7, 10, 12, 15, 18, 19, 21, 25, 27, 55, 129, 132, 159, 171, 175, 315, 324, 358, 393, 435, 786, 1459, 1707, 2923, 6462, 14289, 39012, 51637
     2    (n > 100000) 100224, 108127, 110953, 175749, 185580, 226749, 248949, 253987, 520363
     6    6, 7, 20, 47, 255, 274, 279, 308, 1162, 2128, 3791, 9028, 9629, 10029, 13202, 38660, 46631, 48257
    10    8, 21, 123, 4299, 6128, 11760, 18884, 40293
    14    1, 6, 13, 45, 74, 240, 553, 12348, 13659
    22    8, 35, 88, 503, 8642, 8743, 14475
    26    159, 879, 4744, 5602
    38    1, 2, 13, 560
   204    5, 7, 40, 11867, 14458, 1752, 18929
Kynea Primes (b^n+1)^2-2:
Code:
   base      
     2    (n < 100000) 1, 2, 3, 5, 8, 9, 12, 15, 17,18, 21, 23, 27, 32, 51, 65, 87, 180, 242, 467, 491, 501, 507, 555, 591, 680, 800, 1070, 1650, 2813, 3281, 4217, 5153, 6287, 6365, 10088, 10367, 37035, 45873, 69312
     2    (n > 100000) 102435, 106380, 108888, 110615, 281621, 369581, 376050, 442052
     6    9, ,12, 30, 49, 56, 115, 118, 376, 432, 1045, 1310, 6529, 7768, 8430, 21942, 26930, 33568
    10    22, 123, 351, 1061
    14    1, 5, 60, 72, 118, 181, 245, 310, 498, 820, 962, 2212, 3928, 584, 5937
    22    3, 166, 814, 1851, 2197, 3172, 3865, 19791
    26    1, 2, 8, 78, 79, 111, 5276, 8226
    38    6, 279, 3490
   204    40, 3645, 23750
Mark, some of the smaller primes seem to be missing from this list (possibly because cksieve sieves them out). I have generated all primes for 6 <= b <= 100, n <= 64 using PARI/GP.

Carol
Code:
6:1,2,6,7,20,47
10:1,8,21
12:3,29,51
14:1,6,13,45
18:2,8,30
20:1,2,53
22:1,8,35
24:2,27
26:
28:1,22
30:1,6,19,30
34:1,4
38:1,2,13
40:4,15,39
42:3,6,14,15,29
44:1,7,30
46:12
48:1,2,4,6,12,13
50:1,3,4,9,31
52:2,14,24
54:9,17
56:1,2,3,11
58:
60:2,5
62:1
66:12
68:4,59
70:1,5,9,18,24
72:1,9
74:
76:1,2,32,37,51
78:1,2
80:
82:24
84:4
86:3,39
88:2,5,9
90:1,5,43
92:3,4,6,60
94:1,2
96:5
98:2,21
Kynea
Code:
6:1,2,3,4,9,12,30,49,56
10:22
12:1,2,8,60
14:1,5,60
18:1,10,21,25,31
20:1,15,44
22:3
24:24
26:1,2,8
28:1,2,11,15
30:2,3,57
34:1,2,14,29,61
38:6
40:2,49
42:1,3,4
44:3
46:1,54
48:1
50:4,38
52:3,5
54:1
56:8,14
58:2,21,35
60:1,9,21,49
62:1,2
66:
68:1,3,6,32
70:1,7,11
72:
74:1,3
76:1,2,3,22,29
78:3,5,13
80:29,34,45
82:3,9
84:
86:8,18,36
88:1,40
90:11
92:1,2
94:5
96:2,13,15,54
98:4,12,35
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