%I
%S 43,179,277,359,397,593,811,1483,2017,2213,2251,2447,2689,4421,4519,
%T 4967,5381,6271,7109,7229,9181,9521,10169,11897,12853,13103,13841,
%U 14489,16561,17107,20357,24443,24677,25747,26711,27917,30161,30259,31193
%N Primes of the form p^3 + q^3 + r^3, where p, q and r are primes.
%C a(n) is a subset of A007490(n) = {3, 17, 29, 43, 73, 127, 179, 197, 251, 277, ...}, i.e., primes of the form x^3 + y^3 + z^3.
%e a(1) = 43 because 43 = 2^3 + 2^3 + 3^3 is prime and 2^3 + 2^3 + 2^3 = 24 is composite.
%t lst={};Do[Do[Do[p=n^3+m^3+k^3;If[PrimeQ[p]&&PrimeQ[n]&&PrimeQ[m]&&PrimeQ[k],AppendTo[lst,p]],{n,4!}],{m,4!}],{k,4!}];Take[Union[lst],16] (* _Vladimir Joseph Stephan Orlovsky_, May 23 2009 *)
%Y Cf. A007490 = Primes of form x^3 + y^3 + z^3.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Nov 14 2006
