|
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.
|
![[parent]](http://images.planetmath.org:8080/images/uparrow.png)