A153590 Primes p such that p^2 + 3p + 1 is also prime.

2, 3, 5, 7, 19, 23, 29, 37, 43, 47, 53, 59, 67, 113, 137, 139, 157, 163, 173, 179, 229, 239, 257, 263, 293, 313, 349, 353, 359, 373, 379, 419, 449, 467, 499, 503, 509, 547, 577, 587, 593, 617, 643, 647, 653, 719, 727, 797, 883, 929, 967, 983, 997, 1013, 1033, 1049

Offset: 1

Author

Vincenzo Librandi, Dec 29 2008

Keywords

• nonn
• easy

Comments

Primes p such that (p*(p+1)) + (p+(p+1)) is prime. Primes p such that sum of product and the sum of p and the nextNumber is prime. - Vladimir Joseph Stephan Orlovsky, Mar 13 2010

Examples

			For p = 2, p^2 + 3p + 1 = 11; p = 67, p^2 + 3p + 1 = 4691; for p = 419, p^2 + 3p + 1 = 176819.
		

Links

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

Crossrefs

Cf. A014574, A174242, A174243, A174244. - Vladimir Joseph Stephan Orlovsky, Mar 13 2010

Programs

Magma

[ p: p in PrimesUpTo(1050) | IsPrime(p^2+3*p+1) ];

Mathematica

Select[Table[Prime[n],{n,6!}], PrimeQ[#^2+3*#+1]&] (* Vladimir Joseph Stephan Orlovsky, Mar 13 2010 *)

Extensions

Edited and extended by Klaus Brockhaus, Jan 01 2009