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A325086
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Prime numbers congruent to 9, 25 or 57 modulo 112 representable by x^2 + 448*y^2.
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3
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457, 569, 617, 809, 1289, 1801, 1913, 2153, 2297, 2473, 2521, 2633, 3049, 3257, 3929, 4057, 4153, 4201, 4937, 5209, 5273, 5881, 6073, 6553, 6841, 7177, 7193, 7417, 7529, 7673, 7753, 8009, 8521, 8537, 8681, 9769, 10889, 11257, 11321, 11369, 11593, 11657, 11897
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Brink showed that prime numbers congruent to 9, 25 or 57 modulo 112 are representable by exactly one of the quadratic forms x^2 + 14*y^2 or x^2 + 448*y^2. A325085 corresponds to those representable by the first form, and this sequence corresponds to those representable by the second form.
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LINKS
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EXAMPLE
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Regarding 7177:
- 7177 is a prime number,
- 7177 = 64*112 + 9,
- 7177 = 3^2 + 448*4^2,
- hence 7177 belongs to this sequence.
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PROG
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(PARI) See Links section.
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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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