A397320 Prime numbers p such that p^2 divides 40^(p-1) - 1.

11, 17, 307, 66431, 7036306088681

Offset

1,1

Comments

a(5) = 7036306088681 is from Fischer's tables. No more terms up to 2*10^14.

Links

Table of n, a(n) for n=1..5.

Richard Fischer, Fermatquotienten von 2 bis 1052, Dec 19 2019.

Wikipedia, Wieferich prime

Prog

(PARI) forprime(p=2, 1e8, if(Mod(40, p^2)^(p-1)==1, print1(p", ")))

Crossrefs

Wieferich primes to base b: A001220 (b=2), A014127 (b=3), A123692 (b=5), A212583 (b=6), A123693 (b=7), A045616 (b=10), A111027 (b=12), A128667 (b=13), A234810 (b=14), A242741 (b=15), A128668 (b=17), A244260 (b=18), A090968 (b=19), A242982 (b=20), A298951 (b=22), A128669 (b=23), A306255 (b=26), A306256 (b=30), A331424 (b=31), A396350 (b=33), A397319 (b=35), A331426 (b=37), this sequence (b=40), A331427 (b=41).

Cf. A039951.

Sequence in context: A286959 A146446 A228055 * A132092 A226258 A056705

Adjacent sequences: A397316 A397317 A397319 * A397321 A397322 A397323

Keyword

nonn,hard,more,new

Author

Daniel Okwor, Jun 20 2026

Status

approved