A193051 Primes p such that 12*p^2-1 and 16*p^3-1 are also primes.

2, 3, 17, 29, 107, 167, 173, 599, 1667, 1889, 2129, 3407, 3539, 3797, 3863, 5189, 6779, 6983, 7529, 8849, 11399, 11519, 11657, 12227, 12437, 12809, 13217, 14153, 15227, 16223, 16607, 17609, 21683, 21863, 22193, 23789, 25127

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 15 2011

Keywords

• nonn
• easy

Comments

Primes p such that 3*(2p)^2-1 (see A089681) and 2*(2p)^3-1 are primes.

Examples

			For p=2, 2 is a prime number, 12*2^2-1=47 is a prime number and 16*2^3-1=127 is a prime number.
For p=3, 3 is a prime number, 12*3^2-1=109 is a prime number and 16*3^3-1=431 is a prime number.
		

Links

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

Crossrefs

Cf. A158463.

Programs

Magma

[p: p in PrimesUpTo(26000)|IsPrime(12*p^2-1) and IsPrime(16*p^3-1)]; // Vincenzo Librandi, Apr 10 2013

Mathematica

fQ[n_] := PrimeQ[12 n^2 - 1] && PrimeQ[16 n^3 - 1]; Select[ Prime@ Range@ 3000, fQ] (* Robert G. Wilson v, Aug 08 2011 *)
Select[Prime[Range[5000]], PrimeQ[12 #^2 - 1] && PrimeQ[16 #^3 - 1]&] (* Vincenzo Librandi, Apr 10 2013 *)