A306255 Wieferich primes to base 26.

3, 5, 71, 486999673, 6695256707

Offset: 1

Author

Jianing Song, Feb 01 2019

Keywords

• nonn
• hard
• more

Comments

Prime numbers p such that p^2 divides 26^(p-1) - 1.

No more terms up to 9.8*10^13.

Links

• Richard Fischer, Fermatquotient B^(P-1) == 1 (mod P^2)
• P. L. Montgomery, New Solutions of a^p-1 == 1 (mod p^2), Mathematics of Computation, Vol. 61, No. 203 (1993), 361-363.
• Wikipedia, Wieferich prime

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), this sequence (b=26), A306256 (b=30).

Programs

Mathematica

Select[Prime[Range[26*10^6]],PowerMod[26,#-1,#^2]==1&] (* The program generates the first 4 terms of the sequence. *) (* Harvey P. Dale, Aug 23 2024 *)

PARI

forprime(p=2, , if(Mod(26, p^2)^(p-1)==1, print1(p, ", ")))