A094491 Primes p such that 2^j+p^j are primes for j=0,4,8,128.

223, 2104547, 2403689, 4268233, 17620457, 21848647, 23487311, 29205821, 42889591, 43458859, 47899487, 48309017, 54666847, 61227457, 73038689, 81742547, 83574457, 85031153, 87285403, 95017003, 100339517, 103136867

Offset: 1

Author

Labos Elemer, Jun 01 2004

Keywords

• nonn

Comments

Primes of 2^j+p^j form are a generalization of Fermat-primes. This is strongly supported by the observation that corresponding j-exponents are apparently powers of 2 like for the 5 known Fermat primes. See A094473-A094490.

Examples

			For j=0 1+1=2 is prime; other conditions are: because of p^4+16==prime; 3rd and 4th conditions are as follows: prime=p^8+256 and prime=2^128+p^128.
		

Crossrefs

Cf. A082101, A094473-A094490.

Programs

Mathematica

{ta=Table[0, {100}], u=1}; Do[s0=2;s4=16+Prime[j]^4;s8=256+Prime[j]^8;s128=2^128+Prime[j]^128 If[PrimeQ[s0]&&PrimeQ[s4]&&PrimeQ[s8]&&PrimeQ[s128], Print[{j, Prime[j]}];ta[[u]]=Prime[j];u=u+1], {j, 1, 1000000}]

Extensions

a(5)-a(22) from Donovan Johnson, Oct 12 2008