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

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

Author

Michel Lagneau, Sep 20 2012

Keywords

• nonn

Comments

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

Crossrefs

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

Programs

Mathematica

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 *)

Formula

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