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Search: id:A139643
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| A139643 |
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Primes of the form x^2+Ny^2, with N=102. |
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54
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| 103, 127, 151, 223, 271, 409, 433, 457, 463, 577, 631, 727, 769, 919, 937, 967, 1033, 1039, 1063, 1087, 1249, 1279, 1327, 1447, 1471, 1543, 1657, 1753, 1759, 1777, 1783, 1801, 1879, 1951, 1993, 2089, 2143, 2161, 2287, 2311, 2473, 2503, 2551
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant=-408. N is an idoneal number (A000926), which means that the quadratic form's genus consists of a single class, which means that the primes of this form are identical to the primes that are congruent to c (mod 4N), where c is a set of numbers less than 4N. The sequence A139642 lists the set c for each idoneal number. That sequence also cross references the sequences for the quadratic forms with N equal to the first 36 idoneal numbers. The remaining quadratic forms are this sequence and the 28 listed in order below. Note that the sequences for N=120 and 240 are the same.
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REFERENCES
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David A. Cox, Primes of Form x^2 + n y^2, Wiley, 1989.
L. E. Dickson, History of the Theory of Numbers, Vol 3, Chelsea, 1923.
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FORMULA
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The primes are congruent to {1, 25, 49, 55, 103, 121, 127, 145, 151, 169, 217, 223, 247, 271, 319, 361} (mod 408).
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CROSSREFS
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Cf. A139644, A139645, A139502, A139646, A139647, A139648, A139506, A139649, A139650, A139651, A139652, A139502, A139653-A139668.
Sequence in context: A095639 A098049 A055628 this_sequence A139957 A077404 A139979
Adjacent sequences: A139640 A139641 A139642 this_sequence A139644 A139645 A139646
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KEYWORD
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nonn,easy
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Apr 29 2008
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