A397319 - OEIS

%I #9 Jun 26 2026 04:52:26

%S 3,1613,3571

%N Prime numbers p such that p^2 divides 35^(p-1) - 1.

%C There are no further terms up to 2*10^14, according to Fischer's tables.

%H Richard Fischer, <a href="http://www.fermatquotient.com/FermatQuotienten/FermQ_Sort.txt">Fermatquotienten von 2 bis 1052</a>, Dec 19 2019.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Wieferich_prime">Wieferich prime</a>

%o (PARI) forprime(p=2, 1e8, if(Mod(35, p^2)^(p-1)==1, print1(p", ")))

%Y 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), this sequence (b=35), A331426 (b=37), A397320 (b=40), A331427 (b=41).

%Y Cf. A039951.

%K nonn,bref,hard,more

%O 1,1

%A _Daniel Okwor_, Jun 20 2026