A007490 Primes of form x^3 + y^3 + z^3 where x,y,z > 0.

3, 17, 29, 43, 73, 127, 179, 197, 251, 277, 281, 307, 349, 359, 397, 433, 521, 547, 557, 577, 593, 701, 757, 811, 853, 857, 863, 881, 919, 953, 1009, 1051, 1091, 1217, 1249, 1367, 1459, 1483, 1559, 1583, 1637, 1753, 1801, 1861, 1907, 2017, 2027, 2069, 2087

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

• nonn

Comments

Heath-Brown shows that this sequence is infinite. - Charles R Greathouse IV, Jul 23 2009

The definition implies x, y, z > 0, so the representation (x=0, y=z=1) for the prime 2 or the representation (x=-4, y=-2, z=5) for the prime 53 are not admitted. - R. J. Mathar, Mar 19 2010

References

• W. Sierpiński, A Selection of Problems in the Theory of Numbers. Macmillan, NY, 1964, p. 108.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• D. R. Heath-Brown, Primes represented by x^3 + 2y^3. Acta Mathematica 186 (2001), pp. 1-84.
• R. G. Wilson, V, Note, n.d.

Crossrefs

Cf. A003072 (all numbers).

Programs

Mathematica

nn = 3000; Select[Union[Flatten[Table[x^3 + y^3 + z^3, {x, nn^(1/3)}, {y, x, (nn - x^3)^(1/3)}, {z, y, (nn - x^3 - y^3)^(1/3)}]]], PrimeQ] (* T. D. Noe, Sep 18 2012 *)

PARI

list(lim)=my(v=List(),k,t); lim\=1; for(x=1,sqrtnint(lim-2,3), for(y=1, min(sqrtnint(lim-x^3-1,3),x), k=x^3+y^3; for(z=1,min(sqrtnint(lim-k,3), y), if(isprime(t=k+z^3), listput(v,t))))); Set(v) \\ Charles R Greathouse IV, Sep 14 2015

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Mar 18 2010

Definition clarified by Charles R Greathouse IV, Sep 14 2015