A176969 Numbers n such that n^2 + 13^2 is prime.

2, 8, 10, 12, 20, 22, 28, 30, 32, 38, 42, 48, 58, 60, 62, 68, 80, 90, 100, 108, 110, 112, 122, 128, 138, 142, 148, 150, 168, 172, 180, 190, 198, 200, 202, 210, 228, 230, 232, 238, 242, 248, 258, 262, 268, 280, 282, 302, 310, 318, 340, 342, 360, 362, 368, 378

Offset

1,1

Comments

The n^2 + d conjecture is a famous and still unsolved problem.

It states that there exist an infinite number of primes whose values are of the form n^2 + d for some integer n.

This is case d = 13^2.

References

J. Matousek, J. Nesetril: Diskrete Mathematik: eine Entdeckungsreise, Springer-Lehrbuch, 2. Aufl., Berlin, 2007

M. du Sautoy: Die Musik der Primzahlen: Auf den Spuren des groessten Raetsels der Mathematik, Deutscher Taschenbuch Verlag, 2006

Links

Table of n, a(n) for n=1..56.

Example

2^2 + 13^2 = 173 = prime(40), 2 is first term.
12^2 + 13^2 = 313 = prime(65) = palprime(11), 12 is 4th term.
310^2 + 13^2 = 96269 = prime(9274) = palprime(106), 310 the 49th term.

Prog

(PARI) isok(n) = isprime(n^2 + 13^2) \\ Michel Marcus, Jun 28 2013

Crossrefs

Cf. A000040, A000290, A056899, A113536, A176371.

Sequence in context: A328559 A328954 A343500 * A303358 A176464 A102278

Adjacent sequences: A176966 A176967 A176968 * A176970 A176971 A176972

Keyword

nonn

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 29 2010

Status

approved