%I #6 Mar 29 2015 14:54:45

%S 37,1423,8537,61333,397963,419927,699217,1151603,1156823,1210793,

%T 1746923,1809163,1915477,2012113,2713127,3617683,4001567,4192033,

%U 4760117,4768133,5099623,5432153,5801737,5909737,5924833,6118157

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

%e For j=0 1+1=2 is prime; other conditions are:

%e because of p^2+4==prime; 3rd and 4th conditions are as

%e follows: prime=p^4+16 and prime=2^64+p^64.

%t {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}]

%t 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 *)

%Y Cf. A082101, A094473-A094488.

%K nonn

%O 1,1

%A _Labos Elemer_, Jun 01 2004