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A191084
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Primes p that have Kronecker symbol (p|87) = -1.
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2
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5, 19, 23, 31, 37, 43, 53, 59, 61, 71, 73, 79, 83, 97, 107, 127, 149, 157, 163, 167, 173, 179, 193, 197, 211, 227, 229, 233, 239, 257, 271, 281, 307, 331, 337, 347, 353, 367, 379, 383, 401, 409, 419, 421, 431, 433, 509, 521, 541, 557, 577, 587, 593, 601, 607
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OFFSET
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1,1
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COMMENTS
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Originally erroneously named "Primes that are not squares mod 87".
Equivalently, primes p such that kronecker(-87,p) = -1.
Rational primes that remain inert in the field Q(sqrt(-87)).
Primes congruent to 5, 10, 19, 20, 23, 31, 35, 37, 38, 40, 43, 46, 53, 55, 59, 61, 62, 65, 70, 71, 73, 74, 76, 79, 80, 83, 85, 86 modulo 87. (End)
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LINKS
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MATHEMATICA
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Select[Prime[Range[200]], JacobiSymbol[#, 87]==-1&]
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PROG
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(Magma) [p: p in PrimesUpTo(607) | JacobiSymbol(p, 87) eq -1]; // Vincenzo Librandi, Sep 11 2012
(PARI) isA191084(p) == isprime(p) && kronecker(p, 87) == -1 \\ Jianing Song, Oct 13 2022
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CROSSREFS
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Cf. A191052 (rational primes that decompose in the field Q(sqrt(15)))..
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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