A126112 Prime numbers p such that p^4 + (p-1)^4 + (p+1)^4 is a prime number.

3, 7, 11, 29, 31, 53, 59, 83, 109, 127, 283, 349, 461, 521, 599, 643, 683, 787, 809, 829, 907, 911, 937, 983, 1093, 1117, 1201, 1289, 1301, 1487, 1523, 1613, 1721, 1877, 2017, 2153, 2267, 2281, 2423, 2521, 2579, 2657, 2677, 2699, 2731, 2741, 2797, 2887, 2969

Offset: 1

Author

Tomas Xordan, Mar 05 2007

Keywords

• nonn

Examples

			(3-1)^4 + 3^4 + (3+1)^4 = 2^4 + 3^4 + 4^4 = 16 + 81 + 256 = 353 is prime, hence 3 is a term.
(11-1)^4 + 11^4 + (11+1)^4 = 10^4 + 11^4 + 12^4 = 10000 + 14641 + 20736 = 45377 is prime, hence 11 is a term.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A126657, A126769, A126113.

Programs

Mathematica

f[n_]:=PrimeQ[(n-1)^4+n^4+(n+1)^4];lst={};Do[p=Prime[n];If[f[p],AppendTo[lst,p]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 27 2009 *)
Select[Prime[Range[500]],PrimeQ[Total[(#+{-1,0,1})^4]]&] (* Harvey P. Dale, Dec 07 2012 *)

PARI

forprime(p=2, 3000, if(isprime(q=(p-1)^4+p^4+(p+1)^4), print1(p, ","))) /* Klaus Brockhaus, Mar 09 2007 */

Extensions

Edited, corrected and extended by Klaus Brockhaus, Mar 09 2007