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

1,1

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

Mathematica

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

Prog

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

Crossrefs

Complement in primes of A007519.

Sequence in context: A105049 A057447 A095074 * A089189 A097375 A007459

Adjacent sequences: A042984 A042985 A042986 * A042988 A042989 A042990

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved