A214001 Numbers n such that n^2+2, n^3+2, n^4+2 and n^5+2 are all prime.

0, 1, 909, 2055, 11925, 145881, 191079, 254199, 358875, 490215, 614241, 642105, 648261, 689655, 864159, 959595, 1030911, 1047585, 1056981, 1150335, 1366971, 1406571, 1669845, 1746525, 2299485, 2357751, 2491809, 2494329, 2629869, 2876859, 3162159, 3220041, 3257595

Offset: 1

Author

Michel Lagneau, Feb 15 2013

Keywords

• nonn

Comments

n^6+2 is also prime for n = 0, 1, 1746525, 2876859, …

Crossrefs

Cf. A056899, A144953, A182343, A216977, A216979, A216930.

Programs

Mathematica

Select[Range[3500000], And@@PrimeQ/@(Table[n^i+2, {i, 2, 5}]/.n->#)&]
Select[Range[0,33*10^5],AllTrue[#^Range[2,5]+2,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 21 2018 *)