A339535 Numbers b > 1 such that the smallest six primes, i.e., 2, 3, 5, 7, 11 and 13 are base-b Wieferich primes.

132857, 171793, 261593, 618301, 700993, 997757, 1211201, 1365857, 1388593, 1542293, 1557593, 1681649, 1692557, 1906001, 2086793, 2124757, 2245357, 2293757, 2341349, 2443501, 2822957, 3025457, 3036401, 3435193, 3554657, 3569257, 3814649, 4028093, 4048901

Offset: 1

Author

Felix Fröhlich, Dec 08 2020

Keywords

• nonn

Crossrefs

Cf. A256236. Row 1 of A319063.

Cf. smallest k primes are base-b Wieferich primes: A339531 (k=2), A339532 (k=3), A339533 (k=4), A339534 (k=5), A339536 (k=7), A339537 (k=8).

Programs

Mathematica

Select[Range[2, 4100000], Function[b, AllTrue[{2, 3, 5, 7, 11, 13}, PowerMod[b, (# - 1), #^2] == 1 &]]] (* Michael De Vlieger, Dec 10 2020 *)

PARI

is(n) = forprime(p=1, 13, if(Mod(n, p^2)^(p-1)!=1, return(0))); 1