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A057604 Primes of the form 4*k^2 + 163. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
MATHEMATICA
Select[Table[4n^2 + 163, {n, 0, 70}], PrimeQ] (* Vincenzo Librandi, Jul 15 2012 *)
PROG
(Magma) [a: n in [0..400] | IsPrime(a) where a is 4*n^2 + 163] // Vincenzo Librandi, Aug 07 2010
(PARI) lista(nn) = for(n=0, nn, my(p = 4*n^2 + 163); if(isprime(p), print1(p, ", "))) \\ Iain Fox, Dec 19 2017
CROSSREFS
Sequence in context: A061574 A185444 A217546 * A243532 A272984 A230869
KEYWORD
nonn,easy
AUTHOR
Tito Piezas III, Oct 08 2000
EXTENSIONS
Sequence corrected by Vincenzo Librandi, Jul 15 2012
STATUS
approved

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Last modified April 20 12:25 EDT 2024. Contains 371844 sequences. (Running on oeis4.)