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A107142
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Primes of the form x^2 + 36y^2.
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2
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37, 61, 157, 193, 313, 349, 373, 397, 433, 577, 601, 613, 661, 673, 769, 853, 877, 937, 997, 1021, 1069, 1201, 1297, 1321, 1429, 1549, 1657, 1693, 1741, 1789, 1801, 1861, 1933, 1993, 2053, 2137, 2269, 2293, 2389, 2437, 2473, 2521, 2593, 2749
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OFFSET
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1,1
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COMMENTS
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Discriminant = -144. See A107132 for more information.
These appear to be the same as Glaisher's 1889 list of primes == 1 mod 12 that have "positive character". - N. J. A. Sloane, Jul 30 2015
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REFERENCES
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J. W. L. Glaisher, On the square of Euler's series, Proc. London Math. Soc., 21 (1889), 182-194.
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LINKS
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MATHEMATICA
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QuadPrimes2[1, 0, 36, 10000] (* see A106856 *)
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PROG
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(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\1), w=x^2; for(y=1, sqrtint((lim-w)\36), if(isprime(t=w+36*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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