A042987 Primes congruent to {2, 3, 5, 7} mod 8.

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 79, 83, 101, 103, 107, 109, 127, 131, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 239, 251, 263, 269, 271, 277, 283, 293, 307, 311, 317, 331, 347, 349, 359, 367, 373, 379

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Equivalently, primes p not congruent to 1 (mod 8).

In 1981 D. Weisser proved that a prime not congruent to 1 (mod 8) and >= 7 is irregular if and only if the rational number Zeta_K(-1) is p-adically integral, that is has a denominator not divisible by p, where K is the maximal real subfield of the cyclotomic field of p-th roots of unity. - From Achava Nakhash posting, see Links.

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)
• Achava Nakhash, Irregular Primes and Dedekind Zeta Functions

Crossrefs

Complement in primes of A007519.

Programs

Magma

[p: p in PrimesUpTo(1200) | p mod 8 in [2, 3, 5, 7]]; // Vincenzo Librandi, Aug 08 2012

Mathematica

Select[Prime[Range[100]],MemberQ[{2,3,5,7},Mod[#,8]]&]  (* Harvey P. Dale, Mar 24 2011 *)