A107021 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7 are all primes.

2, 6449, 12119, 19709, 30389, 74699, 107699, 133499, 143609, 167759, 175349, 206369, 210209, 229739, 244589, 254279, 334289, 422069, 528509, 541529, 607319, 641969, 658349, 751529, 810539, 810809, 812849, 926669, 934259, 956909, 968729

Offset: 1

Author

Zak Seidov, May 09 2005

Keywords

• nonn

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A107024: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 all prime; A107023: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 all prime; A107022: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 all prime; A107020: p, 2p+1, 4p+3, 6p+5 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).

Cf. A005384, A007700, A107020, A107022, A107023, A107024.

Programs

Magma

[p: p in PrimesUpTo(1000000)| IsPrime(2*p+1) and IsPrime(4*p+3) and IsPrime(6*p+5) and IsPrime(8*p+7)]; // Vincenzo Librandi, Nov 13 2010

Mathematica

fQ[n_]:=And@@PrimeQ[{2n+1,4n+3,6n+5,8n+7}];Select[Prime@Range@77000,fQ] (* Harvey P. Dale, Dec 16 2010 *)

Extensions

More terms from Vincenzo Librandi, Apr 01 2010