A123597 Primes of the form p^3 + q^3 + r^3, where p, q and r are primes.

43, 179, 277, 359, 397, 593, 811, 1483, 2017, 2213, 2251, 2447, 2689, 4421, 4519, 4967, 5381, 6271, 7109, 7229, 9181, 9521, 10169, 11897, 12853, 13103, 13841, 14489, 16561, 17107, 20357, 24443, 24677, 25747, 26711, 27917, 30161, 30259, 31193, 31247, 32579, 36161

Offset: 1

Author

Alexander Adamchuk, Nov 14 2006

Keywords

• nonn

Comments

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.

Examples

			a(1) = 43 because 43 = 2^3 + 2^3 + 3^3 is prime and 2^3 + 2^3 + 2^3 = 24 is composite.
		

Crossrefs

Cf. A007490 = Primes of form x^3 + y^3 + z^3.

Programs

Mathematica

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 *)
With[{nn=40},Select[Total/@Tuples[Prime[Range[nn]]^3,3],PrimeQ[#]&&#<= nn^3+ 16&]]//Union (* Harvey P. Dale, Sep 08 2021 *)