A105389 Primes of the form x^2 + 32 y^2, also primes p with h(-p) divisible by 8.

41, 113, 137, 257, 313, 337, 353, 409, 457, 521, 569, 577, 593, 761, 809, 857, 881, 953, 1129, 1153, 1201, 1217, 1249, 1321, 1553, 1601, 1657, 1777, 1889, 1993

Offset: 1

Author

John L. Drost, May 01 2005

Keywords

• nonn

Examples

			41 = 9 + 32 * 1, 113 = 81 + 32 *1, 137 = 9 + 32*4
		

References

• Barrucand, P. and Cohn, H. Note on primes of the form x^2 + 32 y^2, class number and residuacity, Journal fur die reine und angewandte Mathematik, v.238, pp. 67-70.

Links

• Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
• S. R. Finch, Powers of Euler's q-Series, arXiv:math/0701251 [math.NT], 2007.
• Steven R. Finch, Class number theory [Cached copy, with permission of the author]
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Programs

Mathematica

QuadPrimes2[1, 0, 32, 10000] (* see A106856 *)
(* Second program: *)
max = 10^4; Table[yy = {y, 1, Floor[Sqrt[(max - x^2)/32]]}; Table[x^2 + 32 y^2, yy // Evaluate], {x, 1, Floor[Sqrt[max]]}] // Flatten // Union // Select[#, # <= max && PrimeQ[#]&]& (* Jean-François Alcover, Oct 04 2018 *)