A057604 - OEIS

%I #39 Sep 08 2022 08:45:02

%S 163,167,179,199,227,263,307,359,419,487,563,647,739,839,947,1063,

%T 1187,1319,1459,1607,2099,2467,2663,3079,3299,3527,4007,4259,4519,

%U 4787,5347,5639,5939,6247,6563,7219,7559,7907,8263,8627,8999,9767,10163,10567,10979,11399,11827,12263

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

%C 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

%H Iain Fox, <a href="/A057604/b057604.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi)

%H S. A. Goudsmit, <a href="https://doi.org/10.1038/2141164b0">Unusual Prime Number Sequences</a>, Nature Vol. 214 (1967), 1164.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>

%t Select[Table[4n^2 + 163, {n, 0, 70}], PrimeQ] (* _Vincenzo Librandi_, Jul 15 2012 *)

%o (Magma) [a: n in [0..400] | IsPrime(a) where a is 4*n^2 + 163] // _Vincenzo Librandi_, Aug 07 2010

%o (PARI) lista(nn) = for(n=0, nn, my(p = 4*n^2 + 163); if(isprime(p), print1(p, ", "))) \\ _Iain Fox_, Dec 19 2017

%Y Cf. A005846, A007641, A007635, A057605.

%K nonn,easy

%O 1,1

%A _Tito Piezas III_, Oct 08 2000

%E Sequence corrected by _Vincenzo Librandi_, Jul 15 2012