A125610 Smallest prime p such that 5^n divides p^4 - 1.

2, 7, 193, 443, 14557, 14557, 735443, 3124999, 7812499, 78124999, 292968749, 853235443, 2441406251, 53834264557, 122070312499, 202513391693, 1118040735443, 3459595983307, 3459595983307, 270488404577057

Offset: 1

Author

Alexander Adamchuk, Nov 28 2006

Keywords

• hard
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..1424
• W. Keller and J. Richstein Fermat quotients that are divisible by p.

Crossrefs

Cf. A125609 = Smallest prime p such that 3^n divides p^2 - 1. Cf. A125611 = Smallest prime p such that 7^n divides p^6 - 1. Cf. A125612 = Smallest prime p such that 11^n divides p^10 - 1. Cf. A125632 = Smallest prime p such that 13^n divides p^12 - 1. Cf. A125633 = Smallest prime p such that 17^n divides p^16 - 1. Cf. A125634 = Smallest prime p such that 19^n divides p^18 - 1. Cf. A125635 = Smallest prime p such that 257^n divides p^256 - 1.

Programs

Maple

f:= proc(n) local k, p2,P,t;
    p2:= numtheory:-msqrt(-1,5^n);
    P:= sort([1,p2,5^n-p2,5^n-1]);
    for k from 0 do
      for t in P do
        if isprime(k*5^n+t) then return k*5^n+t fi
    od od:
end proc:
map(f, [$1..30]); # Robert Israel, Oct 27 2019

PARI

\\ See A125609 - Martin Fuller, Jan 11 2007

Extensions

More terms from Ryan Propper, Jan 02 2007

More terms from Martin Fuller, Jan 11 2007