editing

approved

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 *)

approved

editing

_Labos E. (labos(AT)ana.sote.hu), Elemer_, Jun 01 2004

{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}]

nonn,new

nonn

nonn,new

nonn

Labos E. (labos(AT)ana1ana.sote.hu), Jun 01 2004

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

1,1

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.

{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}]

Cf. A082101, A094473-A094488.

nonn,new

Labos E. (labos(AT)ana1.sote.hu), Jun 01 2004

approved