A382414 Primes p such that gcd(ord_p(2), ord_p(5)) = 1.

31, 601, 2593, 599479, 204700049, 466344409, 668731841, 11638603429

Offset: 1

Author

Li GAN, Apr 26 2025

Keywords

• nonn
• hard
• more

Comments

'ord_p' here means the multiplicative order modulo p, not to be confused with the p-adic order that is also often denoted by ord_p.

1790799748670521, 58523123221688392679 and 14551915228363037109375001 are also terms. - Giorgos Kalogeropoulos, May 03 2025

Links

• Mathematics Stack Exchange, For all alpha,beta in N, are there only finitely many primes so that gcd(ordp(alpha),ordp(beta))=1?, 2021

Crossrefs

Cf. A014664, A211241, A344202, A383411.

Programs

Mathematica

Select[Range[10000], PrimeQ[#] && CoprimeQ[MultiplicativeOrder[2, #], MultiplicativeOrder[5, #]] &]

PARI

forprime(p=13, oo, if(1==gcd(znorder(Mod(5, p)), znorder(Mod(2, p))), print1(p, ", "))); \\ Joerg Arndt, Apr 26 2025