A154936 -id:A154936 - cp's OEIS frontend

A071351 Numbers n such that both n^4 + 2 and n^4 - 2 are prime.

3, 21, 87, 99, 129, 141, 279, 627, 657, 777, 783, 795, 1653, 1725, 1833, 1959, 2001, 2043, 3039, 3399, 3609, 3861, 3975, 4257, 4371, 4491, 5403, 5541, 5709, 5985, 7371, 7539, 7869, 7917, 8397, 8445, 8547, 8793, 9051, 9057, 9915, 9933, 11067, 12153

Offset: 1

Labos Elemer, May 21 2002

			n=3: n^4 = 81; {79,83} are primes.

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

Cf. A028870, A038599, A154831, A154832, A154833, A154834, A154933, A154934, A154935, A154936. - Vladimir Joseph Stephan Orlovsky, Jan 17 2009

lst={}; Do[p1=n^4-2; p2=n^4+2; If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,n]],{n,0,8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 17 2009 *)
Select[Range[730000], AllTrue[#^4 + {2, -2}, PrimeQ] &] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 02 2018 *)

A154938 Numbers k such that k^6 - 2 and k^6 + 2 are both primes.

Original entry on oeis.org

195, 213, 231, 657, 1563, 1749, 2967, 3597, 3627, 4263, 4887, 6867, 6993, 7257, 7725, 9045, 9201, 9717, 11595, 12579, 13029, 14145, 14259, 14367, 15837, 16131, 16581, 17259, 19905, 19917, 21081, 21711, 23127, 24435, 24921, 28299, 28707

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A154933 and A216978.

Cf. A028870, A038599, A154831, A154832, A154833, A154834, A154934, A154935, A154936, A071351.

[n: n in [1..500] | IsPrime(n^6-2) and IsPrime(n^6+2)]; // Vincenzo Librandi, Nov 26 2010

lst={};Do[p1=n^6-2;p2=n^6+2;If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,n]],{n,0,9!}];lst
Select[Range[30000],AllTrue[#^6+{2,-2},PrimeQ]&] (* Harvey P. Dale, Jun 21 2025 *)

cp's OEIS Frontend

A071351 Numbers n such that both n^4 + 2 and n^4 - 2 are prime.

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