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A122131
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Numbers n such that n^12 + 488669 is prime.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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Paulo Ribenboim, The Little Book of Big Primes, Springer Verlag, 1996.
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LINKS
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A066386, A126893, A126894, A126897.
Sequence in context: A254913 A254906 A257208 * A238053 A254802 A254809
Adjacent sequences: A122128 A122129 A122130 * A122132 A122133 A122134
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein, Aug 21 2006
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EXTENSIONS
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Edited by N. J. A. Sloane, May 07 2007
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STATUS
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approved
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