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A176983
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Primes p such that smallest prime q > p^2 is of form q = p^2 + k^2.
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5
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2, 5, 7, 13, 17, 37, 47, 67, 73, 97, 103, 137, 163, 167, 193, 233, 277, 281, 293, 307, 313, 317, 347, 373, 389, 421, 439, 461, 463, 487, 499, 503, 547, 571, 577, 593, 607, 613, 661, 677, 691, 701, 739, 743, 769, 787, 821, 823, 827, 829, 853, 883, 953, 967, 983
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OFFSET
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1,1
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COMMENTS
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By Fermat's 4n+1 theorem, q must be congruent to 1 (mod 4).
Corresponding values of k: 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 4, 4, 6, 2, 2, 4, 2. - Zak Seidov, Nov 04 2013
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LINKS
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EXAMPLE
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17 is here because 293 is the first prime after 17^2 and 293 = 17^2 + 2^2.
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MATHEMATICA
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Select[Prime[Range[200]], IntegerQ[Sqrt[NextPrime[ #^2] - #^2]] & ]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2010
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EXTENSIONS
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Edited and extended by T. D. Noe, May 12 2010
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STATUS
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approved
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