A049573 Primes p such that x^41 = 2 has a solution mod p.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Differs from A000040: 83 does not occur.

Examples

			0^41 == 2 (mod 2). 2^41 == 2 (mod 3). 2^41 == 2 (mod 5). 4^41 == 2 (mod 7). 2^41 == 2 (mod 11). 6^41 == 2 (mod 13). 2^41 == 2 (mod 17). 15^41 == 2 (mod 19). 13^41 == 2 (mod 23). 14^41 == 2 (mod 29). 2^41 == 2 (mod 31). 24^41 == 2 (mod 37). 2^41 == 2 (mod 41). 22^41 == 2 (mod 43). - _R. J. Mathar_, Jul 20 2025
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000
• Index entries for related sequences

Crossrefs

Cf. A000040, A059236 for primes not in this sequence.

Programs

Magma

[p: p in PrimesUpTo(300) | exists(t){x : x in ResidueClassRing(p) | x^41 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Mathematica

ok[p_]:= Reduce[Mod[x^41 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 14 2012 *)