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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 21 2006
EXTENSIONS
Edited by N. J. A. Sloane, May 07 2007
STATUS
approved