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A042987 Primes congruent to {2, 3, 5, 7} mod 8. 6

%I

%S 2,3,5,7,11,13,19,23,29,31,37,43,47,53,59,61,67,71,79,83,101,103,107,

%T 109,127,131,139,149,151,157,163,167,173,179,181,191,197,199,211,223,

%U 227,229,239,251,263,269,271,277,283,293,307,311,317,331,347,349,359,367,373,379

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

%C Equivalently, primes p not congruent to 1 mod 8.

%C 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.

%H Ray Chandler, <a href="/A042987/b042987.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi)

%H Achava Nakhash, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&amp;threadID=1872454">Irregular Primes and Dedekind Zeta Functions</a>

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

%o (MAGMA) [p: p in PrimesUpTo(1200) | p mod 8 in [2, 3, 5, 7]]; // _Vincenzo Librandi_, Aug 08 2012

%Y Complement in primes of A007519.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.

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Last modified June 15 02:56 EDT 2021. Contains 345042 sequences. (Running on oeis4.)