A153503 Primes p such that 2^(p-1)+3 is prime.

2, 3, 5, 7, 13, 17, 19, 29, 31, 229, 2371, 4003, 33029, 55457, 58313, 205963, 1875553

Offset: 1

Author

Vincenzo Librandi, Dec 28 2008

Keywords

• nonn
• more
• hard

Comments

A prime p is in the sequence if and only if p-1 is in A057732.

Examples

			For p = 2, 2^(p-1)+3 = 5 is prime.
For p = 17, 2^(p-1)+3 = 65539 is prime.
For p = 31, 2^(p-1)+3 = 1073741827 is prime.
		

Crossrefs

Cf. A057732 (numbers k such that 2^k + 3 is prime), A057736 (primes p such that 2^p + 3 is prime), A000043 (primes p such that 2^p - 1 is prime).

Programs

Magma

[p: p in PrimesUpTo(2000) | IsPrime(2^(p-1) + 3)]; // Vincenzo Librandi, Jun 09 2015

Mathematica

Select[Prime[Range[3000]], PrimeQ[2^(# - 1) + 3] &] (* Vincenzo Librandi, Jun 09 2015 *)

Extensions

Edited and a(13)-a(15) (based on A057732) added by Klaus Brockhaus, Jan 06 2009

a(16) from Vincenzo Librandi, Jun 09 2015

a(17) from Amiram Eldar, Aug 01 2024