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[parent] table of pseudoprimes below 2000 in bases 2 to 16 (Example)

This table lists pseudoprimes $ p$ of the form $ b^{p - 1} \equiv 1 \mod b$ below 2000.

Base $ b$ Pseudoprimes to base $ b$ OEIS reference
2 341, 561, 645, 1105, 1387, 1729, 1905 A001567
3 91, 121, 286, 671, 703, 949, 1105, 1541, 1729, 1891 A005935
4 15, 85, 91, 341, 435, 451, 561, 645, 703, 1105, 1247, 1271, 1387, 1581, 1695, 1729, 1891, 1905 A020136
5 4, 124, 217, 561, 781, 1541, 1729, 1891 A005936
6 35, 185, 217, 301, 481, 1105, 1111, 1261, 1333, 1729 A005937
7 6, 25, 325, 561, 703, 817, 1105, 1825 A005938
8 9, 21, 45, 63, 65, 105, 117, 133, 153, 231, 273, 341, 481, 511, 561, 585, 645, 651, 861, 949, 1001, 1105, 1281, 1365, 1387, 1417, 1541, 1649, 1661, 1729, 1785, 1905 A020137
9 4, 8, 28, 52, 91, 121, 205, 286, 364, 511, 532, 616, 671, 697, 703, 946, 949, 1036, 1105, 1288, 1387, 1541, 1729, 1891 A020138
10 9, 33, 91, 99, 259, 451, 481, 561, 657, 703, 909, 1233, 1729 A005939
11 10, 15, 70, 133, 190, 259, 305, 481, 645, 703, 793, 1105, 1330, 1729 A020139
12 65, 91, 133, 143, 145, 247, 377, 385, 703, 1045, 1099, 1105, 1649, 1729, 1885, 1891 A020140
13 4, 6, 12, 21, 85, 105, 231, 244, 276, 357, 427, 561, 1099, 1785, 1891 A020141
14 15, 39, 65, 195, 481, 561, 781, 793, 841, 985, 1105, 1111, 1541, 1891 A020142
15 14, 341, 742, 946, 1477, 1541, 1687, 1729, 1891, 1921 A020143
16 15, 51, 85, 91, 255, 341, 435, 451, 561, 595, 645, 703, 1105, 1247, 1261, 1271, 1285, 1387, 1581, 1687, 1695, 1729, 1891, 1905 A020144

As you may have noticed, 1729 appears in all of these except for bases 7, 13 and 14, which share factors 7, 13 and 7, respectively, with 1729.



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Cross-references: factors, bases, OEIS, base

This is version 2 of table of pseudoprimes below 2000 in bases 2 to 16, born on 2007-03-15, modified 2007-03-27.
Object id is 9081, canonical name is TableOfPseudoprimesBelow2000InBases2To16.
Accessed 340 times total.

Classification:
AMS MSC11A51 (Number theory :: Elementary number theory :: Factorization; primality)

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