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A105389
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Primes of the form x^2 + 32 y^2, also primes p with h(-p) divisible by 8.
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3
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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
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OFFSET
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1,1
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REFERENCES
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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.
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LINKS
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EXAMPLE
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41 = 9 + 32 * 1, 113 = 81 + 32 *1, 137 = 9 + 32*4
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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