A298951 Wieferich primes to base 22.

13, 673, 1595813, 492366587, 9809862296159

Offset: 1

Author

Tim Johannes Ohrtmann, Jan 30 2018

Keywords

• nonn
• more
• hard

Comments

Prime numbers p such that p^2 divides 22^(p-1) - 1.

Next term, if it exists, is larger than 8.72*10^13.

492366587 was found by Montgomery (cf. Montgomery, 1993). - Felix Fröhlich, Jan 30 2018

Links

• Amir Akbary and Sahar Siavashi, The Largest Known Wieferich Numbers, INTEGERS, 18(2018), A3. See Table 1 p. 5.
• 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), this sequence (b=22), A128669 (b=23), A306255 (b=26), A306256 (b=30).

Programs

PARI

forprime(p=1, , if(Mod(22, p^2)^(p-1)==1, print1(p, ", ")))