A050265 Primes of the form 2*n^2 + 11.

11, 13, 19, 29, 43, 61, 83, 109, 139, 173, 211, 349, 461, 523, 659, 733, 811, 1069, 1163, 1579, 1693, 1811, 1933, 2749, 3373, 3539, 3709, 4243, 4813, 5011, 5419, 5843, 7211, 7699, 7949, 8461, 9533, 9811, 10093, 11261, 13789, 14461, 15149, 16573

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Comments

The polynomial 2*n^2 + 11 first fails to produce a prime for n = 11, giving 253 = 11 * 23. - Alonso del Arte, Sep 04 2016

Let P(n) = 2*n^2 + 11. The polynomial P(2*n - 10) = 8*n^2 - 80*n + 11 produces prime values (not distinct) for n = 0 to 10. The polynomial P(3*n - 19) = 18*n^2 - 228*n + 733 produces distinct prime values for n = 0 to 9. - Peter Bala, Apr 16 2018

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime-generating Polynomial.

Crossrefs

Cf. A005846, A007641.

Programs

Magma

[a: n in [0..100] | IsPrime(a) where a is 2*n^2+11]; // Vincenzo Librandi, Dec 08 2011

Mathematica

Select[2Range[0, 100]^2 + 11, PrimeQ] (* Harvey P. Dale, May 20 2011 *)

Formula

a(n) = 11 + 2*(A092968(n))^2. - R. J. Mathar, Jan 03 2009

Extensions

11 added by Vincenzo Librandi, Dec 08 2011