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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A088732 A336446 A129693 * A360041 A360040 A244529

Adjacent sequences: A153587 A153588 A153589 * A153591 A153592 A153593

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 29 2008

Extensions

Edited and extended by Klaus Brockhaus, Jan 01 2009

Status

approved