A383411 Primes p such that gcd(ord_p(3), ord_p(5)) = 1.

2, 13, 313, 51169, 797161, 3482851, 5096867, 12207031, 162410641, 368385827, 1001523179, 4902814883, 104849105869, 131772143257, 572027881891

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.

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. A062117, A211241, A344202.

Programs

Mathematica

Select[Range[10000], PrimeQ[#] && CoprimeQ[MultiplicativeOrder[3, #], MultiplicativeOrder[5, #]] &]

PARI

forprime(p=13,oo,if(1==gcd(znorder(Mod(5,p)),znorder(Mod(3,p))),print1(p,", "))); \\ Joerg Arndt, Apr 26 2025

Extensions

a(13)-a(15) from Bill McEachen, May 11 2025