

A042987


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


7



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
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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 padically integral, that is has a denominator not divisible by p, where K is the maximal real subfield of the cyclotomic field of pth 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



