A057604 Primes of the form 4*k^2 + 163.

163, 167, 179, 199, 227, 263, 307, 359, 419, 487, 563, 647, 739, 839, 947, 1063, 1187, 1319, 1459, 1607, 2099, 2467, 2663, 3079, 3299, 3527, 4007, 4259, 4519, 4787, 5347, 5639, 5939, 6247, 6563, 7219, 7559, 7907, 8263, 8627, 8999, 9767, 10163, 10567, 10979, 11399, 11827, 12263

Offset: 1

Author

Tito Piezas III, Oct 08 2000

Keywords

• nonn
• easy

Comments

These numbers are not prime in O_Q(sqrt(-163)). If p = n^2 + 163, then (n - sqrt(-163))*(n + sqrt(-163)) = p. - Alonso del Arte, Dec 18 2017

Links

• Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)
• S. A. Goudsmit, Unusual Prime Number Sequences, Nature Vol. 214 (1967), 1164.
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Crossrefs

Cf. A005846, A007641, A007635, A057605.

Programs

Magma

[a: n in [0..400] | IsPrime(a) where a is 4*n^2 + 163] // Vincenzo Librandi, Aug 07 2010

Mathematica

Select[Table[4n^2 + 163, {n, 0, 70}], PrimeQ] (* Vincenzo Librandi, Jul 15 2012 *)

PARI

lista(nn) = for(n=0, nn, my(p = 4*n^2 + 163); if(isprime(p), print1(p, ", "))) \\ Iain Fox, Dec 19 2017

Extensions

Sequence corrected by Vincenzo Librandi, Jul 15 2012