A237812 Primes p such that 2*p+1 and 2*p+13 are also prime.

2, 3, 5, 23, 29, 83, 89, 113, 173, 233, 239, 293, 509, 653, 719, 743, 1013, 1049, 1223, 1289, 1499, 2003, 2039, 2063, 2129, 2339, 2393, 2459, 2543, 2693, 2753, 2819, 2963, 3389, 3449, 4409, 4733, 4919, 5039, 6053, 6113, 6263, 6323, 6329, 6449, 7433, 7643

Offset: 1

Author

Colin Barker, Feb 13 2014

Keywords

• nonn

Examples

			23 is in the sequence because 23, 2*23+1 = 47 and 2*23+13 = 59 are all prime.
		

Links

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

Crossrefs

Cf. A126107, A237810, A237811, A237813, A237814.

Programs

Magma

[p: p in PrimesUpTo(9200) | IsPrime(2*p+1) and IsPrime(2*p+13)]; // Vincenzo Librandi, Feb 15 2014

Mathematica

Select[Prime[Range[10000]], PrimeQ[2 # + 1] && PrimeQ[2 # + 13] &] (* Vincenzo Librandi, Feb 15 2014 *)
Select[Prime[Range[1000]],AllTrue[2#+{1,13},PrimeQ]&] (* Harvey P. Dale, Jun 27 2023 *)

PARI

s=[]; forprime(p=2, 10000, if(isprime(2*p+1) && isprime(2*p+13), s=concat(s, p))); s