A154831 -id:A154831 - cp's OEIS frontend

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

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 *)

A216945 Numbers k such that k-2, k^2-2, k^3-2, k^4-2 and k^5-2 are all prime.

Original entry on oeis.org

15331, 289311, 487899, 798385, 1685775, 1790991, 1885261, 1920619, 1967925, 2304805, 2479735, 3049201, 3114439, 3175039, 3692065, 4095531, 4653649, 5606349, 5708235, 6113745, 6143235, 6697425, 7028035, 7461601, 8671585, 8997121, 9260131, 10084915, 10239529

Offset: 1

Michel Lagneau, Sep 20 2012

nonn

k^6-2 is also prime for k = 1685775, 4095531, 4653649, 5606349, 13219339, 13326069, 18439561, ...

Sequence is infinite under Schinzel's Hypothesis H. a(n) >> n log^5 n. - Charles R Greathouse IV, Sep 20 2012

Cf. A052147, A028870, A038599, A154831, A154833, A154935.

Select[Range[20000000], And@@PrimeQ/@(Table[n^i-2, {i, 1, 5}]/.n->#)&]
Select[Prime[Range[680000]]+2,AllTrue[#^Range[2,5]-2,PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 11 2020 *)

Sequence is A052147 intersection A028870 intersection A038599 intersection A154831 intersection A154833.

cp's OEIS Frontend

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

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