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A042987 Primes congruent to {2, 3, 5, 7} mod 8. 6
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 (list; graph; refs; listen; history; text; internal format)
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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

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Last modified November 23 09:38 EST 2017. Contains 295115 sequences.