A176722 Primes of the form k^3 + 13, k >= 0.

13, 229, 1013, 1741, 39317, 64013, 74101, 157477, 438989, 551381, 830597, 1906637, 2000389, 4096013, 7077901, 9261013, 10941061, 15625013, 16003021, 21024589, 24897101, 27000013, 69934541, 74088013, 79507013, 93576677, 122023949

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 25 2010

Keywords

• nonn

Comments

Necessarily, k = 6 * j or k = 6 * j + 4.

Values of k corresponding to terms of the sequence: 0, 6, 10, 12, 34, 40, 42, 54, 76, 82, 94, 124, 126, 160, 192, 210, 222, 250, 252, 276, 292, 300, 412, 420, 430, 454, 496, 502, 570, 586, 612, 622, 640, 670, 684, 712, 720, 724, 726, 756, 784, 822, 826, 874, 882, 894, 934, 952, 964, 1006, 1056.

Examples

			0^3 + 13 = 13 = prime(6) = a(1);
6^3 + 13 = 229 = prime(50) = a(2);
300^3 + 13 = 27000013 = prime(1683067) = a(22).
		

References

• H. Rademacher, Topics in Analytic Number Theory, Springer-Verlag Berlin, 1973.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• D. R. Heath-Brown and B. Z. Moroz, Primes Represented by Binary Cubic Forms, Proceedings of the London Math. Soc. vol. 84(2), pp. 257-288, 2002; see also.

Crossrefs

Cf. A000040, A000578, A037396, A138375, A144953, A154648, A157772, A168147, A168219, A168327.

Programs

Magma

[a: n in [0..500]|IsPrime(a) where a is n^3+13] // Vincenzo Librandi, Dec 22 2010

Maple

select(isprime,[seq(seq((6*j+m)^3+13,m=[0,4]),j=0..1000)]); # Robert Israel, Jun 28 2018

Mathematica

Select[Range[0,1000]^3+13,PrimeQ]  (* Harvey P. Dale, Mar 12 2011 *)