A033201 Primes of the form x^2 + 10*y^2.

11, 19, 41, 59, 89, 131, 139, 179, 211, 241, 251, 281, 331, 379, 401, 409, 419, 449, 491, 499, 521, 569, 571, 601, 619, 641, 659, 691, 739, 761, 769, 809, 811, 859, 881, 929, 971, 1009, 1019, 1049, 1051, 1091, 1129, 1171, 1201, 1249, 1259, 1289, 1291, 1321, 1361, 1409, 1451, 1459, 1481

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, p. 36.

Links

• Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 2000 terms from Vincenzo Librandi]
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A139643.

Primes in A020673.

Programs

Magma

[p: p in PrimesUpTo(1500) | NormEquation(10,p) eq true]; // Bruno Berselli, Jul 03 2016

Mathematica

Clear[f,lst,p,x,y]; f[x_,y_]:=x^2+10*y^2; lst={};Do[Do[p=f[x,y];If[PrimeQ[p]&&p<7212,AppendTo[lst,p]],{y,0,6!}],{x,0,6!}];Take[Union[lst],222] (* Vladimir Joseph Stephan Orlovsky, Aug 04 2009 *)
QuadPrimes2[1, 0, 10, 10000] (* see A106856 *)

PARI

select(n->vecsearch([1,9,11,19],n%40), primes(100)) \\ Charles R Greathouse IV, Nov 09 2012

Formula

Same as primes congruent to 1, 9, 11, or 19 mod 40. See, e.g., Cox, p. 36.

a(n) ~ 4n log n. - Charles R Greathouse IV, Nov 09 2012