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A263725
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Smallest prime q > prime(n+3) such that the number p = prime(n)^2 + prime(n+1)^2 + prime(n+2)^2 + prime(n+3)^2 + q^2 is also prime.
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1
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13, 17, 37, 31, 31, 37, 41, 41, 43, 47, 59, 61, 89, 79, 71, 79, 79, 89, 97, 109, 127, 107, 109, 109, 113, 139, 131, 139, 151, 149, 157, 157, 173, 181, 173, 191, 191, 193, 197, 223, 199, 211, 233, 239, 229, 233, 263, 257, 263, 271, 271, 277, 271, 281, 281, 293, 293, 311, 349, 317, 353, 331, 353, 353, 359, 419, 359, 419, 379, 419, 397, 401, 431, 409, 409, 433, 461, 443, 487, 449, 541, 487, 463, 569, 479, 467, 487, 491, 503
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OFFSET
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2,1
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COMMENTS
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The corresponding primes p form A263724.
The prime q exists for all n > 1 under Schinzel's Hypothesis H; see Sierpinski (1988), p. 221.
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REFERENCES
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W. Sierpinski, Elementary Theory of Numbers, 2nd English edition, revised and enlarged by A. Schinzel, Elsevier, 1988.
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LINKS
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EXAMPLE
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The primes 373 = 3^2 + 5^2 + 7^2 + 11^2 + 13^2, 653 = 5^2 + 7^2 + 11^2 + 13^2 + 17^2, and 1997 = 7^2 + 11^2 + 13^2 + 17^2 + 37^2 lead to a(2) = 13, a(3) = 17, and a(4) = 37.
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MATHEMATICA
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Table[k = 4;
While[! PrimeQ[Sum[Prime[n + j]^2, {j, 0, 3}] + Prime[n + k]^2], k++];
Prime[n + k], {n, 2, 90}]
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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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