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2021-01-03, 10:41   #67
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

D8516 Posts

Quote:
Family x{d}y (where d is base-b digit, x.y are base-b strings (may be empty)) in base b means family xddd...dddy in base b, i.e. means this set {xy, xdy, xddy, xdddy, xddddy, xdddddy, xddddddy, ...} in base b

2021-01-03, 11:07   #68
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

3,461 Posts

Quote:
 Originally Posted by sweety439 search the simple families x{0}y with gcd(x,y) = 1, gcd(y,b) = 1, gcd(x+y,b-1) = 1 Such primes are ALWAYS minimal prime (start with 2 digits) in base b, except when the base (b) is prime, and x = 1 (while 10 is prime and a subsequence of the prime, but with LaurV's suggestion, the prime 10 (i.e. the prime = base) is also not counted just as the primes < base, all such primes (i.e. all smallest primes of the form x{0}y) is ALWAYS minimal prime (start with b+1) in base b)
the formula of family x{0}y in base b is very easy, it is just x*b^n+y

since any number ending with the digit 0 is divisible by the base (b) and thus cannot be prime >b (our set is the primes >b in base b), and any number cannot begin with the digit 0, therefore, all digits 0 in the numbers in the minimal set of our set (in any base b>=2) are middle digits (i.e. neither the left-most digit nor the right-most digit).

2021-01-03, 11:10   #69
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

3,461 Posts

Quote:
 Originally Posted by sweety439 Minimal set of prime-strings (> base, as LaurV's suggestion) in bases 2 to 12 (only bases 2 to 8 are proved to be complete)
start searching bases 13 to 16

Code:
13: {14, 16, 1A, 23, 25, 2B, 32, 34, 38, 41, 47, 49, 52, 56, 58, 61, 65, 6B, 76, 7A, 7C, 83, 85, 89, 9A, A1, A7, A9, B6, B8, C1, C7, CB, 10C, 119, 11B, 122, 133, 155, 157, 173, 179, 17B, 188, 197, 1B1, 1B5, 1CC, 209, 212, 218, 229, 272, 274, 281, 287, 292, 296, 298, 29C, 2C9, 311, 313, 331, 33B, 355, 371, 373, 379, 397, 3A6, 3AA, 3B3, 3B9, 3BB, 3CA, 43C, 445, 44B, 45A, 463, 4A3, 4A5, 4B2, 4B4, 4BA, 50C, 511, 515, 533, 54A, 551, 559, 571, 575, 57B, 595, 599, 5B3, 5B9, 5CC, 607, 629, 63A, 643, 674, 704, 715, 724, 728, 731, 737, 739, 742, 751, 75B, 773, 775, 779, 782, 784, 791, 793, 797, 7B1, 812, 818, 874, 878, 8AB, 8B4, 902, 919, 922, 926, 92C, 937, 93B, 946, 95B, 962, 968, 971, 977, 979, 982, 98C, 9B3, 9B5, A03, A3C, A45, A4B, A54, AA3, AAB, B02, B0C, B11, B15, B17, B24, B33, B39, B42, B57, B59, B71, B93, B9B, BA4, BAA, BB1, BB9, BC2, BCC, C29, C43, C98, CA3, 1013, 1031, 1037, 105B, 1075, 10B7, 10BB, 1105, 1112, 1121, 1127, 113C, 1172, 1187, 1208, 1211, 1277, 12C8, 1307, 1309, 131C, 139C, 151C, 1721, 1727, 1787, 1901, 1909, 1912, 1918, 193C, 1981, 198B, 199C, 19B2, 19C3, 1B29, 1BB2, 1BBC, 1C28, 1C39, 2021, 2078, 2117, 2201, 2221, 2267, 2278, 2627, 2678, 2711, 2771, 2788, 3037, 3053, 306A, 3077, 3091, 309B, 30AC, 3305, 353C, 35AB, 35BA, 35BC, 3677, 3905, 390B, 39C5, 3A0C, 3AB5, 3B5C, 3C35, 3C59, 3C95, 403A, 40AB, 4333, 435B, 4403, 44C3, 4535, 4544, 454C, 45B5, 45BB, 480B, 4B35, 4B5B, 4C36, 5057, 5077, 509B, 50A4, 5107, 5305, 530B, 539C, 53AB, 53C9, 5444, 5455, 54C4, 5503, 5545, 55AB, 5774, 5794, 590B, 594B, 5974, 59B4, 5A4C, 5A53, 5AA4, 5AB5, 5ABB, 5ACA, 5B4B, 5B5A, 5BA5, 5CA4, 6227, 6278, 6667, 6698, 6733, 6872, 6928, 6944, 694C, 6973, 6986, 6997, 69C8, 6AC3, 6C92, 6C94, 7019, 7057, 70B5, 7103, 710B, 7118, 7127, 7129, 7172, 7178, 7192, 7211, 7217, 7219, 7271, 7303, 7408, 7433, 7444, 7505, 7507, 7574, 770B, 7774, 7778, 7787, 7871, 7877, 7888, 794B, 7994, 79B4, 7B43, 7B74, 7B94, 7BB2, 8027, 8072, 8081, 80BA, 8171, 8207, 821C, 848B, 8687, 8711, 8722, 87BB, 8867, 88B2, 88BA, 8B22, 8B2A, 8BAC, 9004, 9017, 9031, 9053, 9055, 9073, 9091, 90BB, 90C8, 9107, 9118, 913C, 9181, 91C3, 9284, 935C, 93C5, 9424, 9428, 9448, 9509, 959C, 96C4, 9703, 9743, 9745, 974B, 97B2, 9811, 981B, 987B, 98B1, 991C, 9967, 9998, 9B12, 9B74, 9B92, 9BBC, 9C55, 9C86, 9CC4, A0BA, A306, A436, A535, A5B5, A636, A6C3, A80B, AB04, AB22, AB35, AB3B, AB4C, AB55, ABAC, ABB5, AC36, ACA5, B044, B04A, B0B7, B129, B1B2, B219, B222, B291, B299, B2CA, B35A, B3A5, B404, B44C, B45B, B4B3, B501, B51C, B55A, B5A5, B5AB, B5C3, B707, B792, B794, B905, B912, B9C5, BA5B, BAB3, BB03, BB45, BB72, BBA5, BBB2, BC44, BC53, BC95, BC99, C30A, C36A, C395, C454, C535, C553, C593, C944, C953, C964, CC94, 10015, 10051, 10099, 10118, 10291, 10712, 10772, 10811, 10877, 10921, 10B92, 11111, 11135, 11171, 111C8, 11531, 11C03, 13001, 13177, 13777, 13915, 13951, 13991, 159BB, 17018, 17102, 17111, 17117, 17171, 17177, 17708, 17711, 17801, 18071, 18101, 18271, 18B27, 19003, 19153, 19315, 19351, 19591, 19913, 19951, 1C099, 20171, 20177, 20207, 20227, 20777, 21011, 21077, 2111C, 21707, 22207, 30017, 300B5, 301C9, 3033A, 303A3, 303C5, 3050B, 305C9, 3095C, 30B05, 31007, 3159B, 31999, 31C09, 3330A, 33353, 33593, 33757, 33C5C, 33CC5, 35003, 3591B, 39353, 39539, 39935, 39995, 3ACCC, 3C5C3, 3CC53, 40043, 40306, 405C4, 408BC, 40BBB, 40C54, 43066, 4366A, 4443A, 45055, 45505, 45554, 4555C, 455BC, 455C3, 45C04, 488BC, 4B03B, 4B0B5, 4B55C, 4BB0B, 4C003, 4C054, 4C5C4, 50053, 500B1, 5035A, 504B5, 5053A, 50554, 505B4, 50A35, 50B07, 50BBA, 5139B, 519BB, 51BB7, 535AC, 53A5C, 53AC5, 53BAC, 54004, 54035, 5403B, 545C3, 54B05, 54B5C, 54BBC, 54C53, 55357, 5535B, 553AC, 554BC, 55537, 55544, 5554C, 55577, 555A4, 555BB, 55A5C, 55B04, 55B55, 55B77, 55BB5, 55BC4, 55C54, 55C5A, 57403, 591BB, 59443, 59BB7, 5A044, 5AC04, 5AC35, 5B001, 5B007, 5B0AB, 5B0B4, 5B4C5, 5B544, 5B555, 5B5BB, 5B744, 5B777, 5BA0B, 5BB44, 5BB55, 5BBC4, 5BC54, 5C039, 5C35A, 5C53A, 60098, 60964, 60988, 60A63, 66094, 66377, 66692, 66694, 669C2, 669C4, 66A36, 67022, 67099, 67222, 67277, 67772, 68627, 69088, 690C4, 69808, 69994, 6A663, 7007B, 70181, 70222, 70277, 70772, 70808, 70B0B, 70B29, 71113, 71711, 71908, 71999, 7199B, 71BB7, 71BBB, 74035, 74305, 7430B, 74503, 75443, 75454, 75535, 77072, 77108, 77177, 77717, 77BBB, 78011, 79BBB, 7B007, 7B7B7, 7B7BB, 7BBB3, 7BBB7, 80117, 80221, 80771, 80777, 80807, 8084B, 80B7B, 80BBB, 81107, 8400B, 86267, 87107, 87277, 87727, 87B27, 88111, 88201, 88702, 88771, 8888B, 88B77, 88BBB, 8B1BC, 8B727, 90035, 90059, 90088, 90095, 9009B, 90101, 90103, 90305, 90488, 904CC, 90574, 90644, 9064C, 90806, 908B7, 9090B, 90994, 90B09, 90C35, 90C59, 90C64, 91111, 91135, 91315, 9180B, 92008, 92408, 92488, 93359, 93395, 944C2, 944CC, 94505, 9455C, 94804, 94888, 94C0C, 94C33, 94C4C, 95045, 95504, 95573, 955C4, 95C54, 96044, 97BBB, 98066, 98408, 98444, 98804, 98848, 99001, 99005, 9900B, 99074, 990BC, 99113, 99175, 99278, 99335, 99454, 994C3, 99517, 99593, 9984B, 99881, 99904, 99917, 99935, 99955, 99973, 999BB, 999C2, 999C4, 99B99, 9B00B, 9B04B, 9B0B4, 9B1BB, 9BB04, 9C059, 9C244, 9C404, 9C44C, 9C488, 9C503, 9C5C9, 9C644, 9C664, 9CC88, 9CCC2, A00B4, A05BB, A08B2, A08BC, A0BC4, A3336, A3633, A443A, A4443, A50BB, A55C5, A5AAC, A5BBA, A5C53, A5C55, AACC5, AB05B, AB0BB, AB40A, ABBBC, ABC4A, ACC5A, ACCC3, B0053, B0075, B010B, B0455, B0743, B0774, B0909, B0BB4, B2277, B2A2C, B3005, B351B, B37B5, B3A0B, B3ABC, B3B0A, B400A, B4035, B403B, B4053, B4305, B4BC5, B4C0A, B504B, B50BA, B530A, B5454, B54BC, B54C5, B5544, B55B5, B5B44, B5B4C, B5BB5, B7403, B7535, B77BB, B7955, B7B7B, B9207, B9504, B9999, BA055, BA305, BABC5, BAC35, BB054, BB05A, BB207, BB3B5, BB4C3, BB504, BB544, BB54C, BB5B5, BB753, BB7B7, BBABC, BBB04, BBB4C, BBB55, BBBAC, BC035, BC455, C0353, C0359, C03AC, C0904, C0959, C0A5A, C0CC5, C3059, C335C, C5A0A, C5A44, C5AAC, C6692, C69C2, C904C, C9305, C9905, C995C, C99C5, C9C04, C9C59, C9CC2, CA50A, CA5AC, CAA05, CAA5A, CC335, CC544, CC5AA, CC935, CC955, 100039, 100178, 100718, 100903, 101177, 101708, 101711, 101777, 102017, 102071, 103999, 107081, 107777, 108217, 109111, 109151, 110078, 110108, 110717, 111017, 111103, 1111C3, 111301, 111707, 113501, 115103, 117017, 117107, 117181, 117701, 120701, 13C999, 159103, 170717, 177002, 177707, 180002, 187001, 18C002, 19111C, 199903, 1B0007, 1BB077, 1BBB07, 1C0903, 1C8002, 1C9993, 200027, 207107, 217777, 219991, 220027, 222227, 270008, 271007, 277777, 290444, 300059, 300509, 303359, 303995, 309959, 30B50A, 3336AC, 333707, 33395C, 335707, 3360A3, 350009, 36660A, 3666AC, 370007, 377B07, 39001C, 399503, 3BC005, 400366, 400555, 400B3B, 400B53, 400BB5, 400CC3, 4030B5, 40B053, 40B30B, 40B505, 43600A, 450004, 4A088B, 4B0503, 4B5C05, 4BBBB5, 4BC505, 500039, 50045B, 50405B, 504B0B, 50555B, 5055B5, 505B0A, 509003, 50A50B, 50B045, 50B054, 539B01, 550054, 5500BA, 55040B, 553BC5, 5553C5, 55550B, 5555C3, 555C04, 55B00A, 55BB0B, 570007, 5A500B, 5A555B, 5AC505, 5B055B, 5B0B5B, 5B5B5C, 5B5BC5, 5BB05B, 5BBB0B, 5BBB54, 5BBBB4, 5BBC0A, 5BC405, 5C5A5A, 5CA5A5, 600694, 6060A3, 609992, 637777, 6606A3, 6660A3, 667727, 667808, 668777, 669664, 670088, 679988, 696064, 69C064, 6A6333, 700727, 700811, 700909, 70098B, 700B92, 701117, 701171, 701717, 707027, 707111, 707171, 707201, 707801, 70788B, 7080BB, 708101, 70881B, 70887B, 70B227, 710012, 710177, 711002, 711017, 711071, 717707, 718001, 718111, 720077, 722002, 727777, 74BB3B, 74BB53, 770102, 770171, 770801, 777112, 777202, 777727, 777772, 778801, 77B772, 780008, 78087B, 781001, 788B07, 79088B, 794555, 7B000B, 7B0535, 7B077B, 7B2777, 7B4BBB, 7BB4BB, 800021, 800717, 801077, 80BB07, 811117, 870077, 8777B7, 877B77, 880177, 88071B, 88077B, 8808BC, 887017, 88707B, 888227, 88877B, 8887B7, 888821, 888827, 888BB7, 8B001B, 8B00BB, 8BBB77, 8BBBB7, 900097, 900BC9, 901115, 903935, 904033, 90440C, 908008, 908866, 909359, 909C05, 90B944, 90C95C, 90CC95, 91008B, 91115C, 911503, 920888, 930335, 933503, 935903, 940033, 94040C, 940808, 94CCCC, 950005, 950744, 95555C, 9555C5, 95C003, 95C005, 96400C, 96440C, 96664C, 966664, 966994, 969094, 969964, 97008B, 97080B, 975554, 97800B, 97880B, 980006, 980864, 980B07, 984884, 986006, 986606, 986644, 988006, 988088, 988664, 988817, 988886, 988B0B, 98B007, 990115, 990151, 990694, 990B44, 990C5C, 991501, 993059, 99408B, 994555, 995404, 995435, 996694, 9978BB, 998087, 999097, 999103, 99944C, 999503, 9995C3, 999754, 999901, 99990B, 999B09, 99B4C4, 99C0C5, 99C539, 99CC05, 9B9444, 9B9909, 9C0484, 9C0808, 9C2888, 9C400C, 9C4CCC, 9C6994, 9C90C5, 9C9C5C, 9CC008, 9CC5C3, 9CC905, 9CCC08, A0055B, A005AC, A0088B, A00B2C, A00BBB, A0555C, A05CAA, A0A5AC, A0A5CA, A0AC05, A0AC5A, A0B50B, A0BB0B, A0BBB4, A0C5AC, A3660A, A5050B, A555AC, A5B00B, AA0C05, AAA05C, AAA0C5, AAC05C, AB4444, ABB00B, AC050A, AC333A, B0001B, B00099, B0030B, B004B5, B00A35, B00B54, B030BA, B05043, B0555B, B05B0A, B05B5B, B07B53, B09074, B09755, B09975, B09995, B0AB0B, B0B04B, B0B535, B0BB53, B4C055, B50003, B5003A, B500A3, B50504, B50B04, B53BC5, B54BBB, B550BB, B555BC, B55C55, B5B004, B5B0BB, B5B50B, B5B554, B5B55C, B5B5B4, B5BBB4, B5BBBC, B5BC0A, B5C045, B5C054, B70995, B70B3B, B74555, B74B55, B99921, B99945, BAC505, BB0555, BB077B, BB0B5B, BB0BB5, BB500A, BB53BC, BB53C5, BB5505, BB55BC, BB5BBA, BB5C0A, BB7BB4, BBB00A, BBB74B, BBBB54, BBBBAB, BC5054, BC5504, C00094, C00694, C009C4, C00C05, C03035, C050AA, C05309, C05404, C0544C, C05AC4, C05C39, C06092, C06694, C09035, C094CC, C09992, C09994, C09C4C, C09C95, C0CC3A, C0CC92, C33539, C35009, C4C555, C50309, C50AAA, C53009, C550A5, C555CA, C55A5A, C55CA5, C5AC55, C60094, C60694, C93335, C95405, C99094, CA05CA, CA0AC5, CA555C, CAC5CA, CC05A4, CC0AA5, CC0C05, CC3509, CC4555, CC5039, CC5554, CC555A, CC6092, CCC0C5, CCC353, CCC959, CCC9C2, 1000271, 1000802, 1000871, 1001771, 1001801, 1007078, 1008002, 1008107, 1008701, 1010117, 1027001, 1070771, 1077107, 1077701, 1080107, 1101077, 1110008, 1111078, 1115003, 1117777, 1170008, 1170101, 1700078, 1700777, 1800017, 1877017, 18B7772, 18BBB0B, 1999391, 1999931, 1BBBB3B, 2011001, 2107001, 2110001, 2700017, 2700707, 300000A, 3000019, 3000A33, 3003335, 3003395, 3009335, 300A05B, 3010009, 30A3333, 3335C09, 3339359, 3353777, 336A333, 3393959, 33AC333, 3537007, 3577777, 3636337, 3757777, 395C903, 3AC3333, 40003B5, 400B0B3, 400BBC3, 403B005, 405050B, 40B5555, 40BB555, 40CC555, 4436606, 4444306, 45C5555, 4BC5555, 4C55555, 4CC5004, 4CCC0C3, 500001B, 50003A5, 50005BA, 500B55B, 501000B, 505004B, 505B05B, 50B50B5, 50B550B, 50BB004, 5300009, 5400B0B, 54B000B, 5500BBB, 550B05B, 553000A, 5537777, 555054B, 55505BA, 5550B74, 5555054, 5555BAC, 5555C05, 555B005, 555C00A, 555CA55, 55AC005, 55AC555, 55B005B, 55CA0A5, 5A00004, 5AA5C05, 5B05B05, 5B50B05, 5B5C004, 5BBBBB5, 5BBBBCA, 5C00093, 5C003A5, 5C00A0A, 5C0A055, 5C505AA, 5C5555A, 6000692, 600A333, 606A333, 6363337, 6720002, 6906664, 7000112, 7000712, 7001201, 7001777, 7005553, 70088B7, 7009555, 7010771, 7070881, 7088107, 709800B, 70B9992, 7100021, 7100081, 7100087, 7101107, 7110101, 7120001, 7170077, 7200202, 7270007, 74BBB05, 7700027, 7700201, 7700221, 7700881, 7701017, 7701101, 7707101, 7707701, 7711001, 7770101, 7771201, 7777001, 7777021, 7777102, 77777B7, 777B207, 777B777, 7780001, 77881BB, 788001B, 798000B, 7B00955, 7B00995, 7B55553, 7B55555, 7B77722, 7BB777B, 7BBB40B, 800000B, 8000BB7, 8001B0B, 8010011, 8010101, 8020111, 80B100B, 81B000B, 8677777, 8770001, 8777071, 8801B07, 88040BC, 8822177, 8880007, 8882777, 8887772, 8888087, 8888801, 888B07B, 888B10B, 8B0B00B, 8B777B2, 8BB000B, 9000008, 9000013, 9001151, 9086666, 9088864, 9094003, 9097808, 9099905, 90B99C9, 9151003, 9170008, 91BBBB7, 9244444, 9290111, 940C444, 9430003, 944404C, 94444C4, 944C044, 944C444, 9555005, 9555557, 9644404, 964444C, 96640CC, 9800008, 98800B7, 98884BB, 9888844, 9888884, 98BBB0B, 990888B, 9909C95, 990C94C, 9939953, 9944443, 9955555, 9988807, 998BB07, 99905C9, 9990C95, 9991115, 9994033, 9996644, 9997B44, 999B201, 999CC95, 99CCC5C, 9B20001, 9BBBB44, 9C03335, 9C04444, 9C08888, 9C640CC, 9C80008, 9C99994, 9CC9959, A00AA5C, A00AAC5, A00C50A, A00C555, A00C5AA, A05C00A, A0C005A, A0C0555, A0C555A, A30000A, A33500A, A55553A, A55555C, A5C00AA, A5CAAAA, A8BBB0A, AA00AC5, AA00C5A, AA05C0A, AA5CAAA, AAAC5AA, AAC0555, AC005AA, AC0555A, AC5000A, AC5505A, AC5550A, AC66663, ACC0555, B00007B, B0003AB, B000435, B0004BB, B000A3B, B000B5A, B000BA3, B003777, B005054, B005504, B0055BB, B00777B, B007B3B, B00A0BB, B00AB05, B00B0BA, B00B555, B00B55B, B00BB5B, B00BBB3, B040B0B, B04B00B, B050054, B0500B4, B0554BB, B05B055, B070005, B073B05, B0B00AB, B0B0A0B, B0B50BB, B0B550B, B0B554B, B0BABBB, B0BB305, B1BBB3B, B30000B, B377B77, B400B0B, B4C5005, B5000B4, B5003B5, B505505, B550004, B550055, B555555, B555C05, B5B005B, B5C5505, B70000B, B7B300B, B7BB777, B7BBBBB, B920001, B99545C, B99954C, B999744, BA000BB, BABBB0B, BB000AB, BB0055B, BB05B0B, BB074BB, BB0BABB, BB4000B, BB4430A, BB500BB, BB540BB, BB5555B, BB5BBBB, BB74B0B, BB77B44, BB7B40B, BBB005B, BBB0077, BBB00B5, BBB3007, BBB4444, BBB4B0B, BBB500B, BBB7B3B, BBB7BB5, BBBAB0B, BBBB375, BBBB3B7, BBBBB7B, 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Last fiddled with by sweety439 on 2021-01-04 at 14:10

 2021-01-03, 11:13 #70 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 346110 Posts Largest minimal primes in simple families for bases 13 to 16 (written in decimal): x{y} and {x}y: Code: 13, {1}, 1: 30941 13, 1, {1}: 30941 13, {1}, 2: 2381 13, 1, {2}: 197 13, {1}, 3: 883708283 13, 1, {3}: 211 13, {1}, 4: 17 13, 1, {4}: 17 13, 1, {5}: 239 13, {1}, 6: 19 13, 1, {6}: 19 13, 1, {7}: 253217502498750291800692183145337720992638880271493569431738157631027569095215561 13, 1, {8}: 281 13, {1}, 9: 191 13, 1, {9}: 27130132404659193376721686434661 13, {1}, 10: 23 13, 1, {10}: 23 13, {1}, 11: 193 13, 1, {11}: 820195757799727198696695842441476208994963187388611974376331352215246160014077762227387500472080168786083449145277773838858800795991958180632280974279961571375401216690067428169654353503039823288371270608465421195831630752643523277310127185899536482776399744897654945387104284638368882957170938237278749541598968947323011480936838588602269948473325034154837529102013688233548651627077006312693219100274314806851388327828512220445130387062692274032398838117351850000439212156970074507805886649022038706852334408911410638474707605620484783396663735375992701354072765197190488304749330337810593696686818871540035682031309739770552183078238960961 13, {1}, 12: 36898271981403391525359432679065451 13, 1, {12}: 337 13, {2}, 1: 4759 13, 2, {1}: 106637277112689077 13, {2}, 3: 29 13, 2, {3}: 29 13, {2}, 5: 31 13, 2, {5}: 31 13, {2}, 7: 804473 13, 2, {7}: 959173 13, {2}, 9: 373 13, {2}, 11: 37 13, 2, {11}: 37 13, {3}, 1: 547 13, 3, {1}: 521 13, {3}, 2: 41 13, 3, {2}: 41 13, {3}, 4: 43 13, 3, {4}: 43 13, {3}, 5: 6220138738168647434831423806501836269264860388724755065149565951442236175936796719067011700334477855412396475124991691344796424350196661821800919998163958711515136934394634097179800502201458093822871 13, 3, {5}: 577 13, 3, {7}: 2923035083 13, {3}, 8: 47 13, 3, {8}: 47 13, 3, {10}: 647 13, {3}, 11: 557 13, 3, {11}: 661 13, {4}, 1: 53 13, 4, {1}: 53 13, {4}, 3: 3534833123 13, 4, {3}: 9337 13, {4}, 5: 733 13, 4, {5}: 13799574804865291194219202692403868309075434457702185936718792737 13, {4}, 7: 59 13, 4, {7}: 59 13, {4}, 9: 61 13, 4, {9}: 61 13, {4}, 11: 739 13, {5}, 1: 911 13, 5, {1}: 859 13, {5}, 2: 67 13, 5, {2}: 67 13, {5}, 3: 4418541403 13, 5, {3}: 887 13, {5}, 4: 277256920492991599 13, 5, {4}: 11717 13, {5}, 6: 71 13, 5, {6}: 71 13, 5, {7}: 89921716241132417850870043495861784708189815671814466610282151602592361843582839405888101361717803180497433838124247307746249298923864405720133765156792108299126338169033221693415179426566058950783399084612596039386427021973466021161486411164221010228501523 13, {5}, 8: 73 13, 5, {8}: 73 13, {5}, 9: 919 13, 5, {9}: 971 13, {5}, 11: 3604339966408890811 13, 5, {11}: 815662743439 13, 5, {12}: 1013 13, {6}, 1: 79 13, 6, {1}: 79 13, {6}, 5: 83 13, 6, {5}: 83 13, {6}, 7: 14281 13, 6, {7}: 9624308578305020228623 13, {6}, 11: 89 13, 6, {11}: 89 13, {7}, 1: 178099219309623994113347865115830245881192672331136086644940932390281437773862542264058288467257753659801600961075130547842788841314191170557163588785806820352498775469685611756153126667905685532469070927112200362751893732722602014850726541568809237898479136618304580608401918281234930143064257920309170965969499129532757126377921069913907908471671716574775646406870993578835592914767961359736945068963155952491960373644449418976551172435322847621930721542144058540845006834135041368564051814099612330378729974668784588333951075548113502723356005589020090498660438660159816508080021058414799091444088419142837713138761057222122289170719363548408846549381700350017033339161308029642370902736513421829569951497819557491865511689513661142885392815700489495652470272195143512237819660601060635160718950091398065703223634277265560584842616957317643843802700518533058037207116004784352250055837483109124201522964355475650386943932211405298597905457035869654221665584889762003382262425915627119116388998518127939798007098237014217655662706251901683109346257926396141021838296111310372968225022079707942822795129744698997404408233889930805048836987175297692891091686536077480054995854699722419639970465336199946812908942288140516904083829095941075082576747429233198452931491612278651981884049653724609828879600848950258125404977404144280808141884961849927596265042459349498828074205132275149771178481317527349922743964367067517723323072236797216719438348669059261865669008875549670954883841127641347209610157306553559175511522826280497259599838188113180381333755455900349307408532955497746124837076056334168406604339828775363723268449080391071951364995984584279858031164184210011834081 13, {7}, 2: 2815633 13, 7, {2}: 425554642597531069476088349319265344520247822549860785329030452393239592223053102610453 13, {7}, 3: 1277 13, {7}, 4: 16657 13, 7, {4}: 16111 13, {7}, 5: 1279 13, {7}, 6: 97 13, 7, {6}: 97 13, {7}, 8: 16661 13, 7, {8}: 16843 13, {7}, 9: 1283 13, {7}, 10: 101 13, 7, {10}: 101 13, {7}, 11: 176677145512151 13, {7}, 12: 103 13, 7, {12}: 103 13, {8}, 1: 201916737728161 13, {8}, 3: 107 13, 8, {3}: 107 13, {8}, 5: 109 13, 8, {5}: 109 13, {8}, 7: 948090435833789898349839159224250448489822963231314463923791 13, 8, {7}: 91021952951 13, {8}, 9: 113 13, 8, {9}: 113 13, {8}, 11: 247531 13, 8, {11}: 107838136118779143544110144382426092596204365203552428434248370827269303781694390904131147239057991725836898042412261207750257957583868509005708271654322505648777710176276577432900281939636108415883809919452408705622432187985384594384558596142925993309255985009535307478523156581759235779167162869019703196846751228017411378948853640401871368029723240618590933942573810568367308325289 13, {9}, 1: 121215212228974701436931483878589891140303089832220953724825443452928225193998713337930372911067805791799869147809411855365238746332705480023760792811129961633638311977064834817213347105220337863208732908350674718836123175940417328579685338580206495293657407565505774954042639105332034212418635645417015477944123471063765451261909023510740139021 13, 9, {1}: 259429 13, 9, {2}: 1549 13, {9}, 4: 68799997644951462493799712001 13, 9, {4}: 36748846266526697 13, {9}, 5: 1513040167438129868806971467209988783047172742217267483154894329901717663980542315652349848778853894915555170807951322572378209558278635157172717513628242832984817118678991631720815452108000099210400379825153731084262244319493812890311789045794884092831356123242061758082732806604188005520228674939217665328388067373699901394102699076617987792004875548394303529748128202045356868637958421168851264492251414451671881645020719873271254395994874212298538928180953385418967331680881078358158544926445810098124494008083153487609262254200180462767265649895085196812223539172699394835278304012594889076972978898251549233575133572026086685197059747614441040152909798221820479642718133459387770777298554261474133030690753241864544153004060794064644652707512761735881885543957256884192628158805686561809594061924393932922840678322622784462425947093214038759553887929649916953155720669786551358215226363554462047120571340688059948977555505902980499655568680185582793237970604923030974220265795047325241015419809657491893019473031136829858500145730181190585716816328018616913990223894736777230358689553647254936178082288866348094694739653443883605310239766413123460690534793812785934073248428969751425870653389046775244015718236495145673518071665801891709920766181983586792103960637565600979310820525883807031028492116501924047338205921075081927116926896242518609770952106202341273961329572020549726342482699063714395183214771739428693004365223506346305628182421466017950778081664584660392184816346242270287808532367340974202505243 13, 9, {5}: 0 13, 9, {7}: 1619 13, {9}, 8: 21419 13, 9, {8}: 1332632087873 13, {9}, 10: 127 13, 9, {10}: 127 13, {9}, 11: 193272315039175487326233511816066059384236614936125602856112933108936878519237472904660314716980770567675038998906449425413153983914911198004481338508457524880312210951611198276223531290887108690292738026664067061295245572474703602610246125803179560118335836826468952746508374948156130103443176084512499609881640980577720176544209084145250756004293999763606271755552801884151163797064193306051490695131926580100826963694188422295198532753628423986864538180785129561486984798531474623258138617820724652921878726441978127950818375993469697424536456843865475449486163418975049457428208240361723655765920087962062440804142883445511641266703241468837936119086839611677856638014115541263266704520590558533279312304037176827720788243643056423797345536794811687465498057714283585292329995513313040502867333497441355894682583294242422882099383092926007095933296099723170595507590307152252179729407846066017402908790460912572771982724554085389116205103789017519828339606017138742770709364271683876516827264126734705389614550068455954555083870819276074206224473000405522699421186643568300931 13, 9, {11}: 188465890767567927768109 13, {10}, 1: 131 13, 10, {1}: 131 13, {10}, 3: 1823 13, {10}, 7: 137 13, 10, {7}: 137 13, {10}, 9: 139 13, 10, {9}: 139 13, {10}, 11: 1831 13, 10, {11}: 19564417634903 13, {11}, 1: 2003 13, 11, {1}: 1873 13, {11}, 2: 26171 13, 11, {2}: 24533 13, {11}, 3: 9720791083 13, 11, {3}: 1901 13, 11, {4}: 9244948171 13, {11}, 5: 16947116540528994433003374971133476766755585467759746042637787 13, 11, {5}: 55106069 13, {11}, 6: 149 13, 11, {6}: 149 13, 11, {7}: 275614952732329653238232466846964959764342234851112847239174811330605042147473869409955112827912038180459570611709057122713557738754852977301670028971129467515066229407333223877783672306282366369543871115968877415280318537960852589377566524955025517265527862915865085457853330890387002896522575722038083366786743993408179910457825505003824935898016650965949690327645173471015392053739386753124739151576511051033085127452855493526018723218218416151702223054562562122092583257452732969841804887384398911206575041813220337355043752278695720428137 13, {11}, 8: 151 13, 11, {8}: 151 13, {11}, 9: 2011 13, 11, {9}: 335591 13, {11}, 10: 52950113757237678592993805854491324369268684216704693554936717423836128996957000831399984295437037597224946915093310665683439 13, 11, {10}: 1999 13, {11}, 12: 16836900297891418080414469547118518955584357920776290786511507224819852347973193037600665289070901330976115445902783343792856149076064327963454445124840887022352433623214149015015943271257627167012185236811023315748308075343126054090560004563875124190448995227748073744916159908957819701603274854998000296763254125672206384758348891742961717040363229489213108521955314350073857925001010097317113705164622416602981584525394558649693204742511309000575073486313783914987497483013408328355077527202814535784777000148396721007194688339582681878366906510944731328876064735814127172451578146421749559114747412555063799277435883965467381 13, 11, {12}: 2027 13, {12}, 1: 157 13, 12, {1}: 157 13, {12}, 5: 1792160394029 13, {12}, 7: 163 13, 12, {7}: 163 13, {12}, 11: 167 13, 12, {11}: 167 14, {1}, 1: 211 14, 1, {1}: 211 14, {1}, 3: 17 14, 1, {3}: 17 14, {1}, 5: 19 14, 1, {5}: 19 14, {1}, 9: 23 14, 1, {9}: 23 14, {1}, 11: 41381 14, 1, {11}: 70921 14, {1}, 13: 223 14, 1, {13}: 76831 14, {2}, 1: 29 14, 2, {1}: 29 14, {2}, 3: 31 14, 2, {3}: 31 14, 2, {5}: 467 14, {2}, 9: 37 14, 2, {9}: 37 14, {2}, 11: 431 14, 2, {11}: 557 14, {2}, 13: 41 14, 2, {13}: 41 14, {3}, 1: 43 14, 3, {1}: 43 14, {3}, 5: 47 14, 3, {5}: 47 14, {3}, 11: 53 14, 3, {11}: 53 14, {3}, 13: 643 14, {4}, 1: 32434921 14, 4, {1}: 156619 14, {4}, 3: 59 14, 4, {3}: 59 14, {4}, 5: 61 14, 4, {5}: 61 14, 4, {9}: 919 14, {4}, 11: 67 14, 4, {11}: 67 14, {4}, 13: 853 14, 4, {13}: 0 14, {5}, 1: 71 14, 5, {1}: 71 14, {5}, 3: 73 14, 5, {3}: 73 14, {5}, 9: 79 14, 5, {9}: 79 14, {5}, 11: 1061 14, {5}, 13: 83 14, 5, {13}: 83 14, {6}, 1: 48652381 14, {6}, 5: 89 14, 6, {5}: 89 14, {6}, 11: 248231 14, {6}, 13: 97 14, 6, {13}: 97 14, {7}, 1: 1471 14, 7, {1}: 271867 14, {7}, 3: 101 14, 7, {3}: 101 14, {7}, 5: 103 14, 7, {5}: 103 14, {7}, 9: 107 14, 7, {9}: 107 14, {7}, 11: 109 14, 7, {11}: 109 14, {7}, 13: 1483 14, 7, {13}: 1567 14, {8}, 1: 113 14, 8, {1}: 113 14, 8, {3}: 1613 14, 8, {5}: 1527891201751406184274498849901197440218663 14, {8}, 9: 14893189141836674105809869073123801 14, 8, {9}: 333923 14, {8}, 11: 3178964943473909010162782853260586588933938914164889347525573201287387822569505763054988368562457051 14, 8, {11}: 1733 14, {8}, 13: 1693 14, 8, {13}: 0 14, {9}, 1: 127 14, 9, {1}: 127 14, {9}, 5: 131 14, 9, {5}: 131 14, {9}, 11: 137 14, 9, {11}: 137 14, {9}, 13: 139 14, 9, {13}: 139 14, {10}, 1: 81087301 14, {10}, 3: 450545636966997425132717095409966070465562893779498582938637002140743 14, 10, {3}: 5502353 14, {10}, 9: 149 14, 10, {9}: 149 14, {10}, 11: 151 14, 10, {11}: 151 14, {10}, 13: 2113 14, {11}, 1: 2311 14, 11, {1}: 0 14, {11}, 3: 157 14, 11, {3}: 157 14, 11, {5}: 437351 14, {11}, 9: 163 14, 11, {9}: 163 14, {11}, 13: 167 14, 11, {13}: 167 14, {12}, 1: 2521 14, 12, {1}: 1273070779 14, {12}, 5: 173 14, 12, {5}: 173 14, {12}, 11: 179 14, 12, {11}: 179 14, {12}, 13: 181 14, 12, {13}: 181 14, {13}, 1: 2731 14, 13, {1}: 19298779963 14, 13, {3}: 2593 14, {13}, 5: 0 14, 13, {5}: 276540164647 14, {13}, 9: 191 14, 13, {9}: 191 14, {13}, 11: 193 14, 13, {11}: 193 15, {1}, 1: 241 15, 1, {1}: 241 15, {1}, 2: 17 15, 1, {2}: 17 15, {1}, 4: 19 15, 1, {4}: 19 15, {1}, 7: 303629285816214089001622765197550636782710041318620954247 15, 1, {7}: 337 15, {1}, 8: 23 15, 1, {8}: 23 15, {1}, 11: 251 15, 1, {11}: 401 15, {1}, 13: 12204253 15, 1, {13}: 433 15, {1}, 14: 29 15, 1, {14}: 29 15, {2}, 1: 31 15, 2, {1}: 31 15, {2}, 7: 37 15, 2, {7}: 37 15, {2}, 11: 41 15, 2, {11}: 41 15, {2}, 13: 43 15, 2, {13}: 43 15, {3}, 1: 417041800362721 15, 3, {1}: 691 15, {3}, 2: 47 15, 3, {2}: 47 15, {3}, 4: 2440849 15, 3, {4}: 739 15, {3}, 7: 727 15, 3, {7}: 787 15, {3}, 8: 53 15, 3, {8}: 53 15, {3}, 11: 162731 15, 3, {11}: 491182564871651 15, {3}, 13: 733 15, 3, {13}: 883 15, {3}, 14: 59 15, 3, {14}: 59 15, {4}, 1: 61 15, 4, {1}: 61 15, {4}, 7: 67 15, 4, {7}: 67 15, {4}, 11: 71 15, 4, {11}: 71 15, {4}, 13: 73 15, 4, {13}: 73 15, {5}, 1: 1201 15, 5, {1}: 2924441266741 15, {5}, 2: 18077 15, 5, {2}: 3905357 15, {5}, 4: 79 15, 5, {4}: 79 15, {5}, 7: 13729771207 15, 5, {7}: 1237 15, {5}, 8: 83 15, 5, {8}: 83 15, {5}, 11: 271211 15, 5, {11}: 1301 15, {5}, 13: 1213 15, 5, {13}: 15194280133 15, {5}, 14: 89 15, 5, {14}: 89 15, {6}, 1: 4881691 15, 6, {1}: 1037360491 15, {6}, 7: 97 15, 6, {7}: 97 15, {6}, 11: 101 15, 6, {11}: 101 15, {6}, 13: 103 15, 6, {13}: 103 15, {7}, 1: 379681 15, 7, {1}: 80547991 15, {7}, 2: 107 15, 7, {2}: 107 15, {7}, 4: 109 15, 7, {4}: 109 15, {7}, 8: 113 15, 7, {8}: 113 15, {7}, 11: 218946945190429691 15, 7, {11}: 2588949882704871041434151 15, {7}, 13: 1693 15, 7, {13}: 1783 15, {8}, 1: 28921 15, 8, {1}: 27241 15, {8}, 7: 127 15, 8, {7}: 127 15, {8}, 11: 131 15, 8, {11}: 131 15, {8}, 13: 1933 15, 8, {13}: 30133 15, {9}, 1: 2161 15, 9, {1}: 103329241 15, {9}, 2: 137 15, 9, {2}: 137 15, {9}, 4: 139 15, 9, {4}: 139 15, {9}, 7: 24713588167 15, 9, {7}: 2137 15, {9}, 8: 1647572543 15, 9, {8}: 2153 15, {9}, 11: 488171 15, 9, {11}: 495401 15, {9}, 13: 5560557338173 15, 9, {13}: 502633 15, {9}, 14: 149 15, 9, {14}: 149 15, {10}, 1: 151 15, 10, {1}: 151 15, {10}, 7: 157 15, 10, {7}: 157 15, {10}, 11: 2411 15, 10, {11}: 8190401 15, {10}, 13: 163 15, 10, {13}: 163 15, {11}, 1: 881786829315764563424246641 15, 11, {1}: 560491 15, {11}, 2: 167 15, 11, {2}: 167 15, {11}, 4: 39769 15, 11, {4}: 2539 15, {11}, 7: 2647 15, 11, {7}: 130992187 15, {11}, 8: 173 15, 11, {8}: 173 15, {11}, 13: 596653 15, 11, {13}: 2683 15, {11}, 14: 179 15, 11, {14}: 179 15, {12}, 1: 181 15, 12, {1}: 181 15, {12}, 7: 2887 15, 12, {7}: 42187 15, {12}, 11: 191 15, 12, {11}: 191 15, {12}, 13: 193 15, 12, {13}: 193 15, {13}, 1: 3121 15, 13, {1}: 661741 15, {13}, 2: 197 15, 13, {2}: 197 15, {13}, 4: 199 15, 13, {4}: 199 15, {13}, 7: 705127 15, 13, {7}: 3037 15, {13}, 8: 10577003 15, 13, {8}: 2318805803 15, {13}, 11: 91488544954572405131 15, 13, {11}: 157027901 15, {13}, 14: 535461077009 15, 13, {14}: 408700964355468749 15, {14}, 1: 211 15, 14, {1}: 211 15, {14}, 11: 3371 15, 14, {11}: 42527645637007506364690405981881277901 15, {14}, 13: 223 15, 14, {13}: 223 16, {1}, 1: 17 16, 1, {1}: 17 16, {1}, 3: 19 16, 1, {3}: 19 16, {1}, 5: 277 16, 1, {5}: 0 16, {1}, 7: 23 16, 1, {7}: 23 16, {1}, 9: 281 16, 1, {9}: 409 16, {1}, 11: 283 16, 1, {11}: 443 16, {1}, 13: 29 16, 1, {13}: 29 16, {1}, 15: 31 16, 1, {15}: 31 16, {2}, 1: 8737 16, 2, {1}: 581714951868689 16, {2}, 3: 547 16, 2, {3}: 563 16, {2}, 5: 37 16, 2, {5}: 37 16, {2}, 7: 725935716098002055388532495854438851111 16, 2, {7}: 631 16, {2}, 9: 41 16, 2, {9}: 41 16, {2}, 11: 43 16, 2, {11}: 43 16, {2}, 13: 557 16, 2, {13}: 733 16, {2}, 15: 47 16, 2, {15}: 47 16, {3}, 1: 253530120045645880299340641073 16, 3, {1}: 13171233041 16, {3}, 5: 53 16, 3, {5}: 53 16, {3}, 7: 823 16, 3, {7}: 887 16, {3}, 11: 59 16, 3, {11}: 59 16, {3}, 13: 61 16, 3, {13}: 61 16, {4}, 1: 0 16, 4, {1}: 16657 16, {4}, 3: 67 16, 4, {3}: 67 16, {4}, 5: 1093 16, 4, {5}: 1109 16, {4}, 7: 71 16, 4, {7}: 71 16, {4}, 9: 73 16, 4, {9}: 73 16, {4}, 11: 17483 16, 4, {11}: 19387 16, 4, {13}: 444540081354816304286954136617869418478679481821 16, {4}, 15: 79 16, 4, {15}: 79 16, {5}, 1: 1361 16, 5, {1}: 1297 16, {5}, 3: 83 16, 5, {3}: 83 16, {5}, 7: 1367 16, 5, {7}: 1399 16, {5}, 9: 89 16, 5, {9}: 89 16, {5}, 11: 21851 16, 5, {11}: 1613789866474427 16, {5}, 13: 1373 16, 5, {13}: 24029 16, {6}, 1: 97 16, 6, {1}: 97 16, {6}, 5: 101 16, 6, {5}: 101 16, {6}, 7: 103 16, 6, {7}: 103 16, {6}, 11: 107 16, 6, {11}: 107 16, {6}, 13: 109 16, 6, {13}: 109 16, {7}, 1: 113 16, 7, {1}: 113 16, {7}, 3: 1907 16, 7, {3}: 0 16, {7}, 5: 125269877 16, 7, {5}: 1877 16, {7}, 9: 1913 16, 7, {9}: 498073 16, {7}, 11: 32069089147 16, 7, {11}: 1979 16, {7}, 13: 2004318077 16, 7, {13}: 9972184721795404625107398548957 16, {7}, 15: 127 16, 7, {15}: 127 16, {8}, 1: 143165569 16, 8, {1}: 0 16, {8}, 3: 131 16, 8, {3}: 131 16, {8}, 5: 34949 16, 8, {5}: 0 16, {8}, 7: 56166555556563832905556281431290897236744050880292859335632521351 16, 8, {7}: 34679 16, {8}, 9: 137 16, 8, {9}: 137 16, {8}, 11: 139 16, 8, {11}: 139 16, {8}, 13: 8947853 16, 8, {13}: 2269 16, 8, {15}: 0 16, {9}, 1: 39313 16, 9, {1}: 594193 16, {9}, 5: 149 16, 9, {5}: 149 16, {9}, 7: 151 16, 9, {7}: 151 16, {9}, 11: 2459 16, 9, {11}: 637883 16, {9}, 13: 157 16, 9, {13}: 157 16, {10}, 1: 733007751841 16, 10, {1}: 41233 16, {10}, 3: 163 16, 10, {3}: 163 16, {10}, 7: 167 16, 10, {7}: 167 16, {10}, 9: 2729 16, 10, {9}: 2713 16, {10}, 11: 2731 16, 10, {11}: 43963 16, {10}, 13: 173 16, 10, {13}: 173 16, {11}, 1: 48049 16, 11, {1}: 2833 16, {11}, 3: 179 16, 11, {3}: 179 16, {11}, 5: 181 16, 11, {5}: 181 16, {11}, 7: 2999 16, 11, {7}: 49248958327 16, {11}, 9: 3001 16, 11, {9}: 2969 16, {11}, 13: 12303293 16, 11, {13}: 3037 16, {11}, 15: 191 16, 11, {15}: 191 16, {12}, 1: 193 16, 12, {1}: 193 16, {12}, 5: 197 16, 12, {5}: 197 16, {12}, 7: 199 16, 12, {7}: 199 16, {12}, 11: 0 16, 12, {11}: 3259 16, {12}, 13: 0 16, 12, {13}: 843229 16, {13}, 1: 3722304977 16, 13, {1}: 0 16, {13}, 3: 211 16, 13, {3}: 211 16, {13}, 5: 3541 16, 13, {5}: 3413 16, {13}, 7: 908759 16, 13, {7}: 882551 16, {13}, 9: 999198637325934041 16, 13, {9}: 73749768669482915691491069321318626688914012237296060805206525525363591813836272035774910527919776180923677912554968891935394987986240496179621997893655532569315694783635803112700208508303413378891202384198997794213422176304573334413545606463639516918296257466344350258969657713796137622531892391975484473872559979575727003547753581022912486703477573912049826765132053211177341761946288632815391744689614375401028459100583268869723038988660204614984245471691470023113466364417874725337512714447532250846778586077760659205293618044147237229216306717637040861705334444181470200752974579322509544738704990857820454867202261704090678797538558326245584064671252468247095559023662993480878895077936090038599163027885118597295012047000583187251486272120581780591332114804425847265975339536610666721934463637123044596968540088909735294287236975077640291184075261370631154339959438296960077041200837369288569872632621900878776171600339056308989379011831334774153700978537796879728062464221403872190754080933322090903482454554035388405527848042146114638163297543714301665763439499883062039897590145382317298449300948509392928786633391596392577283746404680586571591203059252060135897745743650628381225179713605144028836751431506430002554673660083008864161778283325595456594614681 16, {13}, 11: 3547 16, 13, {11}: 0 16, {13}, 15: 223 16, 13, {15}: 223 16, {14}, 1: 61153 16, {14}, 3: 227 16, 14, {3}: 227 16, {14}, 5: 229 16, 14, {5}: 229 16, {14}, 9: 233 16, 14, {9}: 233 16, {14}, 11: 1300876803247619683256250232571154421182187 16, 14, {11}: 58304019973926508829195794288364830930948296694792337729075131089632305865113112154282586276837027138881157744159537913596428450753911485229682880296019616116874769754520009659 16, {14}, 13: 3821 16, 14, {13}: 15588829 16, {14}, 15: 239 16, 14, {15}: 239 16, {15}, 1: 241 16, 15, {1}: 241 16, {15}, 7: 0 16, 15, {7}: 66428827511 16, {15}, 11: 251 16, 15, {11}: 251 16, {15}, 13: 4093 16, 15, {13}: 1039837 x{0}y: Code: 13, 1, 4: 17 13, 1, 6: 19 13, 1, 10: 23 13, 1, 12: 181 13, 2, 3: 29 13, 2, 5: 31 13, 2, 9: 347 13, 2, 11: 37 13, 3, 2: 41 13, 3, 4: 43 13, 3, 8: 47 13, 3, 10: 14480437 13, 4, 1: 53 13, 4, 3: 54020737582614507942458917440610823901767221634062888289700852810815079724323258965596943883469013562594127941397398999016481603427622205011908900266071076096475248216593088654359952926621741299090558666311191216978954704152791 13, 4, 7: 59 13, 4, 9: 61 13, 5, 2: 67 13, 5, 6: 71 13, 5, 8: 73 13, 5, 12: 857 13, 6, 1: 79 13, 6, 5: 83 13, 6, 7: 1021 13, 6, 11: 89 13, 7, 4: 1187 13, 7, 6: 97 13, 7, 10: 101 13, 7, 12: 103 13, 8, 3: 107 13, 8, 5: 109 13, 8, 9: 113 13, 8, 11: 38614483 13, 9, 2: 1523 13, 9, 4: 19777 13, 9, 8: 43441289 13, 9, 10: 127 13, 10, 1: 131 13, 10, 3: 1693 13, 10, 7: 137 13, 10, 9: 139 13, 11, 2: 1861 13, 11, 6: 149 13, 11, 8: 151 13, 11, 12: 1871 13, 12, 1: 157 13, 12, 5: 2729251996728070131798006327033140931418231688924554627711654775633915597843291014832282995312758790354592964227251689466987151209150175544113 13, 12, 7: 163 13, 12, 11: 167 14, 1, 1: 197 14, 1, 3: 17 14, 1, 5: 19 14, 1, 9: 23 14, 1, 11: 0 14, 1, 13: 2177953337809371149 14, 2, 1: 29 14, 2, 3: 31 14, 2, 5: 397 14, 2, 9: 37 14, 2, 13: 41 14, 3, 1: 43 14, 3, 5: 47 14, 3, 11: 53 14, 3, 13: 601 14, 4, 1: 0 14, 4, 3: 59 14, 4, 5: 61 14, 4, 11: 67 14, 4, 13: 797 14, 5, 1: 71 14, 5, 3: 73 14, 5, 9: 79 14, 5, 11: 991 14, 5, 13: 83 14, 6, 1: 45177217 14, 6, 5: 89 14, 6, 11: 1187 14, 6, 13: 97 14, 7, 1: 1373 14, 7, 3: 101 14, 7, 5: 103 14, 7, 9: 107 14, 7, 11: 109 14, 7, 13: 0 14, 8, 1: 113 14, 8, 3: 1571 14, 8, 9: 21961 14, 8, 11: 1579 14, 8, 13: 0 14, 9, 1: 127 14, 9, 5: 131 14, 9, 11: 137 14, 9, 13: 139 14, 10, 1: 75295361 14, 10, 9: 149 14, 10, 11: 151 14, 10, 13: 1973 14, 11, 1: 0 14, 11, 3: 157 14, 11, 5: 2161 14, 11, 9: 163 14, 11, 13: 167 14, 12, 5: 173 14, 12, 11: 179 14, 12, 13: 181 14, 13, 1: 2549 14, 13, 3: 2551 14, 13, 5: 35677 14, 13, 9: 191 14, 13, 11: 193 15, 1, 2: 17 15, 1, 4: 19 15, 1, 8: 23 15, 1, 14: 29 15, 2, 1: 31 15, 2, 7: 37 15, 2, 11: 41 15, 2, 13: 43 15, 3, 2: 47 15, 3, 8: 53 15, 3, 14: 59 15, 4, 1: 61 15, 4, 7: 67 15, 4, 11: 71 15, 4, 13: 73 15, 5, 4: 79 15, 5, 8: 83 15, 5, 14: 89 15, 6, 7: 97 15, 6, 11: 101 15, 6, 13: 103 15, 7, 2: 107 15, 7, 4: 109 15, 7, 8: 113 15, 8, 1: 1801 15, 8, 7: 127 15, 8, 11: 131 15, 9, 2: 137 15, 9, 4: 139 15, 9, 8: 1537734383 15, 9, 14: 149 15, 10, 1: 151 15, 10, 7: 157 15, 10, 13: 163 15, 11, 2: 167 15, 11, 4: 8353129 15, 11, 8: 173 15, 11, 14: 179 15, 12, 1: 181 15, 12, 7: 2707 15, 12, 11: 191 15, 12, 13: 193 15, 13, 2: 197 15, 13, 4: 199 15, 13, 14: 2939 15, 14, 1: 211 15, 14, 11: 10631261 15, 14, 13: 223 16, 1, 1: 17 16, 1, 3: 19 16, 1, 7: 23 16, 1, 13: 29 16, 1, 15: 31 16, 2, 5: 37 16, 2, 9: 41 16, 2, 11: 43 16, 2, 15: 47 16, 3, 1: 769 16, 3, 5: 53 16, 3, 11: 59 16, 3, 13: 61 16, 4, 3: 67 16, 4, 7: 71 16, 4, 9: 73 16, 4, 13: 274877906957 16, 4, 15: 79 16, 5, 3: 83 16, 5, 9: 89 16, 5, 11: 1291 16, 6, 1: 97 16, 6, 5: 101 16, 6, 7: 103 16, 6, 11: 107 16, 6, 13: 109 16, 7, 1: 113 16, 7, 9: 1801 16, 7, 15: 127 16, 8, 3: 131 16, 8, 5: 2053 16, 8, 9: 137 16, 8, 11: 139 16, 8, 15: 2063 16, 9, 5: 149 16, 9, 7: 151 16, 9, 13: 157 16, 10, 1: 40961 16, 10, 3: 163 16, 10, 7: 167 16, 10, 9: 11529215046068469769 16, 10, 13: 173 16, 11, 3: 179 16, 11, 5: 181 16, 11, 15: 191 16, 12, 1: 193 16, 12, 5: 197 16, 12, 7: 199 16, 12, 11: 3083 16, 13, 1: 3329 16, 13, 3: 211 16, 13, 9: 55834574857 16, 13, 15: 223 16, 14, 3: 227 16, 14, 5: 229 16, 14, 9: 233 16, 14, 15: 239 16, 15, 1: 241 16, 15, 7: 3847 16, 15, 11: 251 16, 15, 13: 3853 Last fiddled with by sweety439 on 2021-01-03 at 15:43
2021-01-03, 15:49   #71
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

346110 Posts

Quote:
 Originally Posted by sweety439 Largest minimal primes in simple families for bases 13 to 16 (written in decimal): x{y} and {x}y: Code: 13, {1}, 1: 30941 13, 1, {1}: 30941 13, {1}, 2: 2381 13, 1, {2}: 197 13, {1}, 3: 883708283 13, 1, {3}: 211 13, {1}, 4: 17 13, 1, {4}: 17 13, 1, {5}: 239 13, {1}, 6: 19 13, 1, {6}: 19 13, 1, {7}: 253217502498750291800692183145337720992638880271493569431738157631027569095215561 13, 1, {8}: 281 13, {1}, 9: 191 13, 1, {9}: 27130132404659193376721686434661 13, {1}, 10: 23 13, 1, {10}: 23 13, {1}, 11: 193 13, 1, {11}: 820195757799727198696695842441476208994963187388611974376331352215246160014077762227387500472080168786083449145277773838858800795991958180632280974279961571375401216690067428169654353503039823288371270608465421195831630752643523277310127185899536482776399744897654945387104284638368882957170938237278749541598968947323011480936838588602269948473325034154837529102013688233548651627077006312693219100274314806851388327828512220445130387062692274032398838117351850000439212156970074507805886649022038706852334408911410638474707605620484783396663735375992701354072765197190488304749330337810593696686818871540035682031309739770552183078238960961 13, {1}, 12: 36898271981403391525359432679065451 13, 1, {12}: 337 13, {2}, 1: 4759 13, 2, {1}: 106637277112689077 13, {2}, 3: 29 13, 2, {3}: 29 13, {2}, 5: 31 13, 2, {5}: 31 13, {2}, 7: 804473 13, 2, {7}: 959173 13, {2}, 9: 373 13, {2}, 11: 37 13, 2, {11}: 37 13, {3}, 1: 547 13, 3, {1}: 521 13, {3}, 2: 41 13, 3, {2}: 41 13, {3}, 4: 43 13, 3, {4}: 43 13, {3}, 5: 6220138738168647434831423806501836269264860388724755065149565951442236175936796719067011700334477855412396475124991691344796424350196661821800919998163958711515136934394634097179800502201458093822871 13, 3, {5}: 577 13, 3, {7}: 2923035083 13, {3}, 8: 47 13, 3, {8}: 47 13, 3, {10}: 647 13, {3}, 11: 557 13, 3, {11}: 661 13, {4}, 1: 53 13, 4, {1}: 53 13, {4}, 3: 3534833123 13, 4, {3}: 9337 13, {4}, 5: 733 13, 4, {5}: 13799574804865291194219202692403868309075434457702185936718792737 13, {4}, 7: 59 13, 4, {7}: 59 13, {4}, 9: 61 13, 4, {9}: 61 13, {4}, 11: 739 13, {5}, 1: 911 13, 5, {1}: 859 13, {5}, 2: 67 13, 5, {2}: 67 13, {5}, 3: 4418541403 13, 5, {3}: 887 13, {5}, 4: 277256920492991599 13, 5, {4}: 11717 13, {5}, 6: 71 13, 5, {6}: 71 13, 5, {7}: 89921716241132417850870043495861784708189815671814466610282151602592361843582839405888101361717803180497433838124247307746249298923864405720133765156792108299126338169033221693415179426566058950783399084612596039386427021973466021161486411164221010228501523 13, {5}, 8: 73 13, 5, {8}: 73 13, {5}, 9: 919 13, 5, {9}: 971 13, {5}, 11: 3604339966408890811 13, 5, {11}: 815662743439 13, 5, {12}: 1013 13, {6}, 1: 79 13, 6, {1}: 79 13, {6}, 5: 83 13, 6, {5}: 83 13, {6}, 7: 14281 13, 6, {7}: 9624308578305020228623 13, {6}, 11: 89 13, 6, {11}: 89 13, {7}, 1: 178099219309623994113347865115830245881192672331136086644940932390281437773862542264058288467257753659801600961075130547842788841314191170557163588785806820352498775469685611756153126667905685532469070927112200362751893732722602014850726541568809237898479136618304580608401918281234930143064257920309170965969499129532757126377921069913907908471671716574775646406870993578835592914767961359736945068963155952491960373644449418976551172435322847621930721542144058540845006834135041368564051814099612330378729974668784588333951075548113502723356005589020090498660438660159816508080021058414799091444088419142837713138761057222122289170719363548408846549381700350017033339161308029642370902736513421829569951497819557491865511689513661142885392815700489495652470272195143512237819660601060635160718950091398065703223634277265560584842616957317643843802700518533058037207116004784352250055837483109124201522964355475650386943932211405298597905457035869654221665584889762003382262425915627119116388998518127939798007098237014217655662706251901683109346257926396141021838296111310372968225022079707942822795129744698997404408233889930805048836987175297692891091686536077480054995854699722419639970465336199946812908942288140516904083829095941075082576747429233198452931491612278651981884049653724609828879600848950258125404977404144280808141884961849927596265042459349498828074205132275149771178481317527349922743964367067517723323072236797216719438348669059261865669008875549670954883841127641347209610157306553559175511522826280497259599838188113180381333755455900349307408532955497746124837076056334168406604339828775363723268449080391071951364995984584279858031164184210011834081 13, {7}, 2: 2815633 13, 7, {2}: 425554642597531069476088349319265344520247822549860785329030452393239592223053102610453 13, {7}, 3: 1277 13, {7}, 4: 16657 13, 7, {4}: 16111 13, {7}, 5: 1279 13, {7}, 6: 97 13, 7, {6}: 97 13, {7}, 8: 16661 13, 7, {8}: 16843 13, {7}, 9: 1283 13, {7}, 10: 101 13, 7, {10}: 101 13, {7}, 11: 176677145512151 13, {7}, 12: 103 13, 7, {12}: 103 13, {8}, 1: 201916737728161 13, {8}, 3: 107 13, 8, {3}: 107 13, {8}, 5: 109 13, 8, {5}: 109 13, {8}, 7: 948090435833789898349839159224250448489822963231314463923791 13, 8, {7}: 91021952951 13, {8}, 9: 113 13, 8, {9}: 113 13, {8}, 11: 247531 13, 8, {11}: 107838136118779143544110144382426092596204365203552428434248370827269303781694390904131147239057991725836898042412261207750257957583868509005708271654322505648777710176276577432900281939636108415883809919452408705622432187985384594384558596142925993309255985009535307478523156581759235779167162869019703196846751228017411378948853640401871368029723240618590933942573810568367308325289 13, {9}, 1: 121215212228974701436931483878589891140303089832220953724825443452928225193998713337930372911067805791799869147809411855365238746332705480023760792811129961633638311977064834817213347105220337863208732908350674718836123175940417328579685338580206495293657407565505774954042639105332034212418635645417015477944123471063765451261909023510740139021 13, 9, {1}: 259429 13, 9, {2}: 1549 13, {9}, 4: 68799997644951462493799712001 13, 9, {4}: 36748846266526697 13, {9}, 5: 1513040167438129868806971467209988783047172742217267483154894329901717663980542315652349848778853894915555170807951322572378209558278635157172717513628242832984817118678991631720815452108000099210400379825153731084262244319493812890311789045794884092831356123242061758082732806604188005520228674939217665328388067373699901394102699076617987792004875548394303529748128202045356868637958421168851264492251414451671881645020719873271254395994874212298538928180953385418967331680881078358158544926445810098124494008083153487609262254200180462767265649895085196812223539172699394835278304012594889076972978898251549233575133572026086685197059747614441040152909798221820479642718133459387770777298554261474133030690753241864544153004060794064644652707512761735881885543957256884192628158805686561809594061924393932922840678322622784462425947093214038759553887929649916953155720669786551358215226363554462047120571340688059948977555505902980499655568680185582793237970604923030974220265795047325241015419809657491893019473031136829858500145730181190585716816328018616913990223894736777230358689553647254936178082288866348094694739653443883605310239766413123460690534793812785934073248428969751425870653389046775244015718236495145673518071665801891709920766181983586792103960637565600979310820525883807031028492116501924047338205921075081927116926896242518609770952106202341273961329572020549726342482699063714395183214771739428693004365223506346305628182421466017950778081664584660392184816346242270287808532367340974202505243 13, 9, {5}: 0 13, 9, {7}: 1619 13, {9}, 8: 21419 13, 9, {8}: 1332632087873 13, {9}, 10: 127 13, 9, {10}: 127 13, {9}, 11: 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54020737582614507942458917440610823901767221634062888289700852810815079724323258965596943883469013562594127941397398999016481603427622205011908900266071076096475248216593088654359952926621741299090558666311191216978954704152791 13, 4, 7: 59 13, 4, 9: 61 13, 5, 2: 67 13, 5, 6: 71 13, 5, 8: 73 13, 5, 12: 857 13, 6, 1: 79 13, 6, 5: 83 13, 6, 7: 1021 13, 6, 11: 89 13, 7, 4: 1187 13, 7, 6: 97 13, 7, 10: 101 13, 7, 12: 103 13, 8, 3: 107 13, 8, 5: 109 13, 8, 9: 113 13, 8, 11: 38614483 13, 9, 2: 1523 13, 9, 4: 19777 13, 9, 8: 43441289 13, 9, 10: 127 13, 10, 1: 131 13, 10, 3: 1693 13, 10, 7: 137 13, 10, 9: 139 13, 11, 2: 1861 13, 11, 6: 149 13, 11, 8: 151 13, 11, 12: 1871 13, 12, 1: 157 13, 12, 5: 2729251996728070131798006327033140931418231688924554627711654775633915597843291014832282995312758790354592964227251689466987151209150175544113 13, 12, 7: 163 13, 12, 11: 167 14, 1, 1: 197 14, 1, 3: 17 14, 1, 5: 19 14, 1, 9: 23 14, 1, 11: 0 14, 1, 13: 2177953337809371149 14, 2, 1: 29 14, 2, 3: 31 14, 2, 5: 397 14, 2, 9: 37 14, 2, 13: 41 14, 3, 1: 43 14, 3, 5: 47 14, 3, 11: 53 14, 3, 13: 601 14, 4, 1: 0 14, 4, 3: 59 14, 4, 5: 61 14, 4, 11: 67 14, 4, 13: 797 14, 5, 1: 71 14, 5, 3: 73 14, 5, 9: 79 14, 5, 11: 991 14, 5, 13: 83 14, 6, 1: 45177217 14, 6, 5: 89 14, 6, 11: 1187 14, 6, 13: 97 14, 7, 1: 1373 14, 7, 3: 101 14, 7, 5: 103 14, 7, 9: 107 14, 7, 11: 109 14, 7, 13: 0 14, 8, 1: 113 14, 8, 3: 1571 14, 8, 9: 21961 14, 8, 11: 1579 14, 8, 13: 0 14, 9, 1: 127 14, 9, 5: 131 14, 9, 11: 137 14, 9, 13: 139 14, 10, 1: 75295361 14, 10, 9: 149 14, 10, 11: 151 14, 10, 13: 1973 14, 11, 1: 0 14, 11, 3: 157 14, 11, 5: 2161 14, 11, 9: 163 14, 11, 13: 167 14, 12, 5: 173 14, 12, 11: 179 14, 12, 13: 181 14, 13, 1: 2549 14, 13, 3: 2551 14, 13, 5: 35677 14, 13, 9: 191 14, 13, 11: 193 15, 1, 2: 17 15, 1, 4: 19 15, 1, 8: 23 15, 1, 14: 29 15, 2, 1: 31 15, 2, 7: 37 15, 2, 11: 41 15, 2, 13: 43 15, 3, 2: 47 15, 3, 8: 53 15, 3, 14: 59 15, 4, 1: 61 15, 4, 7: 67 15, 4, 11: 71 15, 4, 13: 73 15, 5, 4: 79 15, 5, 8: 83 15, 5, 14: 89 15, 6, 7: 97 15, 6, 11: 101 15, 6, 13: 103 15, 7, 2: 107 15, 7, 4: 109 15, 7, 8: 113 15, 8, 1: 1801 15, 8, 7: 127 15, 8, 11: 131 15, 9, 2: 137 15, 9, 4: 139 15, 9, 8: 1537734383 15, 9, 14: 149 15, 10, 1: 151 15, 10, 7: 157 15, 10, 13: 163 15, 11, 2: 167 15, 11, 4: 8353129 15, 11, 8: 173 15, 11, 14: 179 15, 12, 1: 181 15, 12, 7: 2707 15, 12, 11: 191 15, 12, 13: 193 15, 13, 2: 197 15, 13, 4: 199 15, 13, 14: 2939 15, 14, 1: 211 15, 14, 11: 10631261 15, 14, 13: 223 16, 1, 1: 17 16, 1, 3: 19 16, 1, 7: 23 16, 1, 13: 29 16, 1, 15: 31 16, 2, 5: 37 16, 2, 9: 41 16, 2, 11: 43 16, 2, 15: 47 16, 3, 1: 769 16, 3, 5: 53 16, 3, 11: 59 16, 3, 13: 61 16, 4, 3: 67 16, 4, 7: 71 16, 4, 9: 73 16, 4, 13: 274877906957 16, 4, 15: 79 16, 5, 3: 83 16, 5, 9: 89 16, 5, 11: 1291 16, 6, 1: 97 16, 6, 5: 101 16, 6, 7: 103 16, 6, 11: 107 16, 6, 13: 109 16, 7, 1: 113 16, 7, 9: 1801 16, 7, 15: 127 16, 8, 3: 131 16, 8, 5: 2053 16, 8, 9: 137 16, 8, 11: 139 16, 8, 15: 2063 16, 9, 5: 149 16, 9, 7: 151 16, 9, 13: 157 16, 10, 1: 40961 16, 10, 3: 163 16, 10, 7: 167 16, 10, 9: 11529215046068469769 16, 10, 13: 173 16, 11, 3: 179 16, 11, 5: 181 16, 11, 15: 191 16, 12, 1: 193 16, 12, 5: 197 16, 12, 7: 199 16, 12, 11: 3083 16, 13, 1: 3329 16, 13, 3: 211 16, 13, 9: 55834574857 16, 13, 15: 223 16, 14, 3: 227 16, 14, 5: 229 16, 14, 9: 233 16, 14, 15: 239 16, 15, 1: 241 16, 15, 7: 3847 16, 15, 11: 251 16, 15, 13: 3853
Forms are not listed here means they have a NUMERICAL covering set (including trivial 1-cover) (only for families x{y} and {x}y, for families x{0}y, only families with trivial 1-cover (the trivial factor must divides either b or b-1) are not listed)

Forms with 0 means either they make a full covering set with (all or partial) ALGEBRAIC factors or they are not ruled out as only contain composites but have no primes or PRPs with length <= 5000

Last fiddled with by sweety439 on 2021-01-06 at 12:52

 2021-01-03, 15:51 #72 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 3,461 Posts All of the primes are minimal primes (start with b+1) except the case which the repeating digit (i.e. x in {x}y, or y in x{y}) is 1 (the x{0}y case is always minimal primes (start with b+1), but if x = 1 and the base is prime, then the corresponding primes are not minimal primes (start with b)) Last fiddled with by sweety439 on 2021-01-03 at 15:52
2021-01-04, 04:16   #73
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

D8516 Posts

Quote:
 Originally Posted by sweety439 start searching bases 13 to 16 the minimal primes (start with b+1) are

Code:
13: {14, 16, 1A, 23, 25, 2B, 32, 34, 38, 41, 47, 49, 52, 56, 58, 61, 65, 6B, 76, 7A, 7C, 83, 85, 89, 9A, A1, A7, A9, B6, B8, C1, C7, CB, 10C, 119, 11B, 122, 133, 155, 157, 173, 179, 17B, 188, 197, 1B1, 1B5, 1CC, 209, 212, 218, 229, 272, 274, 281, 287, 292, 296, 298, 29C, 2C9, 311, 313, 331, 33B, 355, 371, 373, 379, 397, 3A6, 3AA, 3B3, 3B9, 3BB, 3CA, 43C, 445, 44B, 45A, 463, 4A3, 4A5, 4B2, 4B4, 4BA, 50C, 511, 515, 533, 54A, 551, 559, 571, 575, 57B, 595, 599, 5B3, 5B9, 5CC, 607, 629, 63A, 643, 674, 704, 715, 724, 728, 731, 737, 739, 742, 751, 75B, 773, 775, 779, 782, 784, 791, 793, 797, 7B1, 812, 818, 874, 878, 8AB, 8B4, 902, 919, 922, 926, 92C, 937, 93B, 946, 95B, 962, 968, 971, 977, 979, 982, 98C, 9B3, 9B5, A03, A3C, A45, A4B, A54, AA3, AAB, B02, B0C, B11, B15, B17, B24, B33, B39, B42, B57, B59, B71, B93, B9B, BA4, BAA, BB1, BB9, BC2, BCC, C29, C43, C98, CA3, 1013, 1031, 1037, 105B, 1075, 10B7, 10BB, 1105, 1112, 1121, 1127, 113C, 1172, 1187, 1208, 1211, 1277, 12C8, 1307, 1309, 131C, 139C, 151C, 1721, 1727, 1787, 1901, 1909, 1912, 1918, 193C, 1981, 198B, 199C, 19B2, 19C3, 1B29, 1BB2, 1BBC, 1C28, 1C39, 2021, 2078, 2117, 2201, 2221, 2267, 2278, 2627, 2678, 2711, 2771, 2788, 3037, 3053, 306A, 3077, 3091, 309B, 30AC, 3305, 353C, 35AB, 35BA, 35BC, 3677, 3905, 390B, 39C5, 3A0C, 3AB5, 3B5C, 3C35, 3C59, 3C95, 403A, 40AB, 4333, 435B, 4403, 44C3, 4535, 4544, 454C, 45B5, 45BB, 480B, 4B35, 4B5B, 4C36, 5057, 5077, 509B, 50A4, 5107, 5305, 530B, 539C, 53AB, 53C9, 5444, 5455, 54C4, 5503, 5545, 55AB, 5774, 5794, 590B, 594B, 5974, 59B4, 5A4C, 5A53, 5AA4, 5AB5, 5ABB, 5ACA, 5B4B, 5B5A, 5BA5, 5CA4, 6227, 6278, 6667, 6698, 6733, 6872, 6928, 6944, 694C, 6973, 6986, 6997, 69C8, 6AC3, 6C92, 6C94, 7019, 7057, 70B5, 7103, 710B, 7118, 7127, 7129, 7172, 7178, 7192, 7211, 7217, 7219, 7271, 7303, 7408, 7433, 7444, 7505, 7507, 7574, 770B, 7774, 7778, 7787, 7871, 7877, 7888, 794B, 7994, 79B4, 7B43, 7B74, 7B94, 7BB2, 8027, 8072, 8081, 80BA, 8171, 8207, 821C, 848B, 8687, 8711, 8722, 87BB, 8867, 88B2, 88BA, 8B22, 8B2A, 8BAC, 9004, 9017, 9031, 9053, 9055, 9073, 9091, 90BB, 90C8, 9107, 9118, 913C, 9181, 91C3, 9284, 935C, 93C5, 9424, 9428, 9448, 9509, 959C, 96C4, 9703, 9743, 9745, 974B, 97B2, 9811, 981B, 987B, 98B1, 991C, 9967, 9998, 9B12, 9B74, 9B92, 9BBC, 9C55, 9C86, 9CC4, A0BA, A306, A436, A535, A5B5, A636, A6C3, A80B, AB04, AB22, AB35, AB3B, AB4C, AB55, ABAC, ABB5, AC36, ACA5, B044, B04A, B0B7, B129, B1B2, B219, B222, B291, B299, B2CA, B35A, B3A5, B404, B44C, B45B, B4B3, B501, B51C, B55A, B5A5, B5AB, B5C3, B707, B792, B794, B905, B912, B9C5, BA5B, BAB3, BB03, BB45, BB72, BBA5, BBB2, BC44, BC53, BC95, BC99, C30A, C36A, C395, C454, C535, C553, C593, C944, C953, C964, CC94, 10015, 10051, 10099, 10118, 10291, 10712, 10772, 10811, 10877, 10921, 10B92, 11111, 11135, 11171, 111C8, 11531, 11C03, 13001, 13177, 13777, 13915, 13951, 13991, 159BB, 17018, 17102, 17111, 17117, 17171, 17177, 17708, 17711, 17801, 18071, 18101, 18271, 18B27, 19003, 19153, 19315, 19351, 19591, 19913, 19951, 1C099, 20171, 20177, 20207, 20227, 20777, 21011, 21077, 2111C, 21707, 22207, 30017, 300B5, 301C9, 3033A, 303A3, 303C5, 3050B, 305C9, 3095C, 30B05, 31007, 3159B, 31999, 31C09, 3330A, 33353, 33593, 33757, 33C5C, 33CC5, 35003, 3591B, 39353, 39539, 39935, 39995, 3ACCC, 3C5C3, 3CC53, 40043, 40306, 405C4, 408BC, 40BBB, 40C54, 43066, 4366A, 4443A, 45055, 45505, 45554, 4555C, 455BC, 455C3, 45C04, 488BC, 4B03B, 4B0B5, 4B55C, 4BB0B, 4C003, 4C054, 4C5C4, 50053, 500B1, 5035A, 504B5, 5053A, 50554, 505B4, 50A35, 50B07, 50BBA, 5139B, 519BB, 51BB7, 535AC, 53A5C, 53AC5, 53BAC, 54004, 54035, 5403B, 545C3, 54B05, 54B5C, 54BBC, 54C53, 55357, 5535B, 553AC, 554BC, 55537, 55544, 5554C, 55577, 555A4, 555BB, 55A5C, 55B04, 55B55, 55B77, 55BB5, 55BC4, 55C54, 55C5A, 57403, 591BB, 59443, 59BB7, 5A044, 5AC04, 5AC35, 5B001, 5B007, 5B0AB, 5B0B4, 5B4C5, 5B544, 5B555, 5B5BB, 5B744, 5B777, 5BA0B, 5BB44, 5BB55, 5BBC4, 5BC54, 5C039, 5C35A, 5C53A, 60098, 60964, 60988, 60A63, 66094, 66377, 66692, 66694, 669C2, 669C4, 66A36, 67022, 67099, 67222, 67277, 67772, 68627, 69088, 690C4, 69808, 69994, 6A663, 7007B, 70181, 70222, 70277, 70772, 70808, 70B0B, 70B29, 71113, 71711, 71908, 71999, 7199B, 71BB7, 71BBB, 74035, 74305, 7430B, 74503, 75443, 75454, 75535, 77072, 77108, 77177, 77717, 77BBB, 78011, 79BBB, 7B007, 7B7B7, 7B7BB, 7BBB3, 7BBB7, 80117, 80221, 80771, 80777, 80807, 8084B, 80B7B, 80BBB, 81107, 8400B, 86267, 87107, 87277, 87727, 87B27, 88111, 88201, 88702, 88771, 8888B, 88B77, 88BBB, 8B1BC, 8B727, 90035, 90059, 90088, 90095, 9009B, 90101, 90103, 90305, 90488, 904CC, 90574, 90644, 9064C, 90806, 908B7, 9090B, 90994, 90B09, 90C35, 90C59, 90C64, 91111, 91135, 91315, 9180B, 92008, 92408, 92488, 93359, 93395, 944C2, 944CC, 94505, 9455C, 94804, 94888, 94C0C, 94C33, 94C4C, 95045, 95504, 95573, 955C4, 95C54, 96044, 97BBB, 98066, 98408, 98444, 98804, 98848, 99001, 99005, 9900B, 99074, 990BC, 99113, 99175, 99278, 99335, 99454, 994C3, 99517, 99593, 9984B, 99881, 99904, 99917, 99935, 99955, 99973, 999BB, 999C2, 999C4, 99B99, 9B00B, 9B04B, 9B0B4, 9B1BB, 9BB04, 9C059, 9C244, 9C404, 9C44C, 9C488, 9C503, 9C5C9, 9C644, 9C664, 9CC88, 9CCC2, A00B4, A05BB, A08B2, A08BC, A0BC4, A3336, A3633, A443A, A4443, A50BB, A55C5, A5AAC, A5BBA, A5C53, A5C55, AACC5, AB05B, AB0BB, AB40A, ABBBC, ABC4A, ACC5A, ACCC3, B0053, B0075, B010B, B0455, B0743, B0774, B0909, B0BB4, B2277, B2A2C, B3005, B351B, B37B5, B3A0B, B3ABC, B3B0A, B400A, B4035, B403B, B4053, B4305, B4BC5, B4C0A, B504B, B50BA, B530A, B5454, B54BC, B54C5, B5544, B55B5, B5B44, B5B4C, B5BB5, B7403, B7535, B77BB, B7955, B7B7B, B9207, B9504, B9999, BA055, BA305, BABC5, BAC35, BB054, BB05A, BB207, BB3B5, BB4C3, BB504, BB544, BB54C, BB5B5, BB753, BB7B7, BBABC, BBB04, BBB4C, BBB55, BBBAC, BC035, BC455, C0353, C0359, C03AC, C0904, C0959, C0A5A, C0CC5, C3059, C335C, C5A0A, C5A44, C5AAC, C6692, C69C2, C904C, C9305, C9905, C995C, C99C5, C9C04, C9C59, C9CC2, CA50A, CA5AC, CAA05, CAA5A, CC335, CC544, CC5AA, CC935, CC955, 100039, 100178, 100718, 100903, 101177, 101708, 101711, 101777, 102017, 102071, 103999, 107081, 107777, 108217, 109111, 109151, 110078, 110108, 110717, 111017, 111103, 1111C3, 111301, 111707, 113501, 115103, 117017, 117107, 117181, 117701, 120701, 13C999, 159103, 170717, 177002, 177707, 180002, 187001, 18C002, 19111C, 199903, 1B0007, 1BB077, 1BBB07, 1C0903, 1C8002, 1C9993, 200027, 207107, 217777, 219991, 220027, 222227, 270008, 271007, 277777, 290444, 300059, 300509, 303359, 303995, 309959, 30B50A, 3336AC, 333707, 33395C, 335707, 3360A3, 350009, 36660A, 3666AC, 370007, 377B07, 39001C, 399503, 3BC005, 400366, 400555, 400B3B, 400B53, 400BB5, 400CC3, 4030B5, 40B053, 40B30B, 40B505, 43600A, 450004, 4A088B, 4B0503, 4B5C05, 4BBBB5, 4BC505, 500039, 50045B, 50405B, 504B0B, 50555B, 5055B5, 505B0A, 509003, 50A50B, 50B045, 50B054, 539B01, 550054, 5500BA, 55040B, 553BC5, 5553C5, 55550B, 5555C3, 555C04, 55B00A, 55BB0B, 570007, 5A500B, 5A555B, 5AC505, 5B055B, 5B0B5B, 5B5B5C, 5B5BC5, 5BB05B, 5BBB0B, 5BBB54, 5BBBB4, 5BBC0A, 5BC405, 5C5A5A, 5CA5A5, 600694, 6060A3, 609992, 637777, 6606A3, 6660A3, 667727, 667808, 668777, 669664, 670088, 679988, 696064, 69C064, 6A6333, 700727, 700811, 700909, 70098B, 700B92, 701117, 701171, 701717, 707027, 707111, 707171, 707201, 707801, 70788B, 7080BB, 708101, 70881B, 70887B, 70B227, 710012, 710177, 711002, 711017, 711071, 717707, 718001, 718111, 720077, 722002, 727777, 74BB3B, 74BB53, 770102, 770171, 770801, 777112, 777202, 777727, 777772, 778801, 77B772, 780008, 78087B, 781001, 788B07, 79088B, 794555, 7B000B, 7B0535, 7B077B, 7B2777, 7B4BBB, 7BB4BB, 800021, 800717, 801077, 80BB07, 811117, 870077, 8777B7, 877B77, 880177, 88071B, 88077B, 8808BC, 887017, 88707B, 888227, 88877B, 8887B7, 888821, 888827, 888BB7, 8B001B, 8B00BB, 8BBB77, 8BBBB7, 900097, 900BC9, 901115, 903935, 904033, 90440C, 908008, 908866, 909359, 909C05, 90B944, 90C95C, 90CC95, 91008B, 91115C, 911503, 920888, 930335, 933503, 935903, 940033, 94040C, 940808, 94CCCC, 950005, 950744, 95555C, 9555C5, 95C003, 95C005, 96400C, 96440C, 96664C, 966664, 966994, 969094, 969964, 97008B, 97080B, 975554, 97800B, 97880B, 980006, 980864, 980B07, 984884, 986006, 986606, 986644, 988006, 988088, 988664, 988817, 988886, 988B0B, 98B007, 990115, 990151, 990694, 990B44, 990C5C, 991501, 993059, 99408B, 994555, 995404, 995435, 996694, 9978BB, 998087, 999097, 999103, 99944C, 999503, 9995C3, 999754, 999901, 99990B, 999B09, 99B4C4, 99C0C5, 99C539, 99CC05, 9B9444, 9B9909, 9C0484, 9C0808, 9C2888, 9C400C, 9C4CCC, 9C6994, 9C90C5, 9C9C5C, 9CC008, 9CC5C3, 9CC905, 9CCC08, A0055B, A005AC, A0088B, A00B2C, A00BBB, A0555C, A05CAA, A0A5AC, A0A5CA, A0AC05, A0AC5A, A0B50B, A0BB0B, A0BBB4, A0C5AC, A3660A, A5050B, A555AC, A5B00B, AA0C05, AAA05C, AAA0C5, AAC05C, AB4444, ABB00B, AC050A, AC333A, B0001B, B00099, B0030B, B004B5, B00A35, B00B54, B030BA, B05043, B0555B, B05B0A, B05B5B, B07B53, B09074, B09755, B09975, B09995, B0AB0B, B0B04B, B0B535, B0BB53, B4C055, B50003, B5003A, B500A3, B50504, B50B04, B53BC5, B54BBB, B550BB, B555BC, B55C55, B5B004, B5B0BB, B5B50B, B5B554, 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Last fiddled with by sweety439 on 2021-01-04 at 14:00

 2021-01-04, 08:19 #74 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 233658 Posts Please stop posting all these endless lists of numbers that nobody read nor needs. If you are really interested in studying these minimal sets, make a web page, put them in zip files, provide links, etc. The way you do it, "text mode", and with additional quote to quote to quote to quote, which makes the posts double size, you are only cluttering the forum, and some people believe that you are doing it intentionally (i.e. trolling), which means you are coming very close to a ban (subject already in discussion for a while on moderator threads!). At least, wtf man? if you like your text mode so much, can't you at least use "code" tags? Scrolling down 20 pages of numbers (even more for mobile browsers) is a pain in the butt. Really. Last fiddled with by LaurV on 2021-01-04 at 08:21
2021-01-04, 13:51   #75
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

3,461 Posts

Quote:
 Originally Posted by LaurV Please stop posting all these endless lists of numbers that nobody read nor needs. If you are really interested in studying these minimal sets, make a web page, put them in zip files, provide links, etc. The way you do it, "text mode", and with additional quote to quote to quote to quote, which makes the posts double size, you are only cluttering the forum, and some people believe that you are doing it intentionally (i.e. trolling), which means you are coming very close to a ban (subject already in discussion for a while on moderator threads!). At least, wtf man? if you like your text mode so much, can't you at least use "code" tags? Scrolling down 20 pages of numbers (even more for mobile browsers) is a pain in the butt. Really.
OK, I stopped and going to make a web page about these primes.

Should I delete these posts?

Last fiddled with by sweety439 on 2021-01-04 at 13:52

2021-01-04, 13:57   #76
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

9,973 Posts

Quote:
 Originally Posted by sweety439 Should I delete these posts?
Putting the long text in "code tags" is enough, don't need to delete. You can however delete the quotes to former posts in each (which just duplicate the text). Anyhow, the issue is not the disk space (just some text), but the difficulty in reading through such long strings of numbers.

2021-01-04, 14:02   #77
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

3,461 Posts

Quote:
 Originally Posted by LaurV Putting the long text in "code tags" is enough, don't need to delete. You can however delete the quotes to former posts in each (which just duplicate the text). Anyhow, the issue is not the disk space (just some text), but the difficulty in reading through such long strings of numbers.
Is this OK? I put all my data for bases 13~16 with codes, must I also put data for bases <=12?

(base 13~16 data is much longer)

Last fiddled with by sweety439 on 2021-01-04 at 14:03

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