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%I #6 Jul 02 2023 18:35:05
%S 5,17,31,43,73,101,197,241,269,283,347,521,599,811,827,829,1019,1049,
%T 1051,1153,1289,1787,2089,2143,2341,2689,2731,2969,3257,3259,3391,
%U 4051,4093,4129,4159,4217,4481,4721,4931,5881,6361,6793,6959,7759,8009,8233
%N Twin prime numbers of the form : i^2+j^3, as sum of square and cube.
%e 31=2^2+3^3; 43=4^2+3^3.
%t lst1={};For[i=1,i<=60,For[j=1,j<=60,c=i^2+j^3;If[((PrimeQ[c]&&PrimeQ[c-2])||(PrimeQ[c]&&PrimeQ[c+2])),AppendTo[lst1,c]];j++ ];i++ ];lst2=Take[Union[lst1],80]
%t Select[Union[Flatten[Table[m^2+n^3,{m,60},{n,60}]]],PrimeQ[#]&&AnyTrue[#+ {2,-2},PrimeQ]&] (* _Harvey P. Dale_, Jul 02 2023 *)
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 01 2008