A122131 Numbers n such that n^12 + 488669 is prime.

616980, 764400, 933660, 1051050, 1730820, 1758120, 2467920, 3093090, 3164070, 3461640, 3696420, 3890250, 3923010, 3950310, 4051320, 4075890, 4196010, 4286100, 4324320, 4337970, 4389840, 4556370, 4561830, 4720170, 4793880

Offset

1,1

Comments

When n is odd the polynomial produces even values, so it is trivially composite. When n ends in 2, 4, 6, or 8 then n^12 ends in 6, so the polynomial produces values ending in 5, again composite. Hence all the values in this sequence are divisible by 10. - Dmitry Kamenetsky, Nov 08 2016

By Fermat's Little Theorem the polynomial is divisible by 2, 3, 5, 7 and 13 when n is not divisible by these primes. Hence all the values in the sequence are divisible by the product of these primes, 2730. - Chun Lok Yiu, Mar 14, 2022

References

Paulo Ribenboim, The Little Book of Big Primes, Springer Verlag, 1996.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 138 terms from Vincenzo Librandi)

Eric Weisstein's World of Mathematics, Bouniakowsky Conjecture

Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Mathematica

a = {}; Do[If[PrimeQ[x^12 + 488669], AppendTo[a, x]], {x, 616979, 10000000}]; a (* Artur Jasinski, Dec 31 2006 *)
Select[Range[10^7], PrimeQ[#^12 + 488669] &] (* Vincenzo Librandi, May 03 2014 *)

Prog

(Magma) [n: n in [0..10^7] | IsPrime(n^12+488669)]; // Vincenzo Librandi, May 03 2014
(PARI) is(n)=isprime(n^12+488669) \\ Charles R Greathouse IV, Jun 06 2017

Crossrefs

Cf. A066386, A126893, A126894, A126897.

Sequence in context: A254913 A254906 A257208 * A238053 A254802 A254809

Adjacent sequences: A122128 A122129 A122130 * A122132 A122133 A122134

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 21 2006

Extensions

Edited by N. J. A. Sloane, May 07 2007

Status

approved