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A153590 Primes p such that p^2 + 3p + 1 is also prime. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A000519 A088732 A129693 * A244529 A025019 A140327

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

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)