A066179 Primes p such that (p-1)/2 and (p-3)/4 are also prime.

11, 23, 47, 167, 359, 719, 1439, 2039, 2879, 4079, 4127, 4919, 5639, 5807, 5927, 6047, 7247, 7559, 7607, 7727, 9839, 10799, 11279, 13799, 13967, 14159, 15287, 15647, 20327, 21599, 21767, 23399, 24407, 24527, 25799, 28319, 28607, 29399

Offset: 1

Author

Vladeta Jovovic, Dec 14 2001

Keywords

• nonn

Comments

Call p "m-prime" iff (p-(2^i-1))/2^i is prime for i=0..m; sequence gives 2-primes. 0-primes are primes (A000040) and 1-primes are safe primes (A005385). a(n)-1 and a(n) are consecutive terms of the sequence A065966. It is not known if there are infinitely many m-primes for m > 0.

Links

• Harry J. Smith, Table of n, a(n) for n=1,...,1000

Crossrefs

Cf. A000040, A005385, A065966.

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[a=(p-1)/2]&&PrimeQ[(a-1)/2],AppendTo[lst,p]],{n,8!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 27 2009 *)

PARI

{ n=0; default(primelimit, 4294965247); for (m=1, 10^9, p=prime(m); if (frac((p-3)/4), next); if (isprime((p-3)/4) && isprime((p-1)/2), write("b066179.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 05 2010

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 05 2010