A094490 Primes p such that 2^j+p^j are primes for j=0,2,4,64.

37, 1423, 8537, 61333, 397963, 419927, 699217, 1151603, 1156823, 1210793, 1746923, 1809163, 1915477, 2012113, 2713127, 3617683, 4001567, 4192033, 4760117, 4768133, 5099623, 5432153, 5801737, 5909737, 5924833, 6118157

Offset: 1

Author

Labos Elemer, Jun 01 2004

Keywords

• nonn

Examples

			For j=0 1+1=2 is prime; other conditions are:
because of p^2+4==prime; 3rd and 4th conditions are as
follows: prime=p^4+16 and prime=2^64+p^64.
		

Crossrefs

Cf. A082101, A094473-A094488.

Programs

Mathematica

{ta=Table[0, {100}], u=1}; Do[s0=2;s2=4+Prime[j]^2;s4=16+Prime[j]^4;s64=2^64+Prime[j]^64 If[PrimeQ[s0]&&PrimeQ[s2]&&PrimeQ[s4]&&PrimeQ[s64], Print[{j, Prime[j]}];ta[[u]]=Prime[j];u=u+1], {j, 1, 1000000}]
Select[Prime[Range[500000]],AllTrue[Table[2^j+#^j,{j,{0,2,4,64}}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 29 2015 *)