A383467 Primes p such that gcd(ord_p(2), ord_p(6)) = 1.

5, 7, 31, 43, 135607, 153649, 270841, 1489441, 1505447, 25781083, 127236649, 558062249, 745988807, 27989941729, 29512739491, 47206579351

Offset: 1

Author

Li GAN, Apr 27 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. A014664, A211242, A344202, A383411, A382414.

Programs

Mathematica

Select[Range[10000], PrimeQ[#] && CoprimeQ[MultiplicativeOrder[2, #], MultiplicativeOrder[6, #]] &]