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A225809
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Primes p such that p+q+1 is the square of a prime, where q is the next prime after p.
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1
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3, 11, 59, 139, 179, 419, 919, 1399, 3119, 5099, 6379, 8059, 9377, 16007, 31489, 39461, 60899, 83639, 87767, 92867, 100799, 135719, 161879, 163019, 166457, 179393, 206699, 218459, 229157, 273059, 317599, 338659, 363799, 367219, 389839, 411311, 442733, 491039
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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11+13+1=25=5^2 with 5 a prime.
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MATHEMATICA
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Select[Partition[Prime[Range[41000]], 2, 1], PrimeQ[Sqrt[Total[#]+1]]&][[All, 1]] (* Harvey P. Dale, Apr 17 2022 *)
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PROG
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(PARI) p=2; forprime(q=3, 1e9, if(issquare(p+q+1, &t)&&isprime(t), print1(p", ")); p=q) \\ Charles R Greathouse IV, Aug 27 2013
(Magma) [p: p in PrimesUpTo(5*10^5) | IsSquare(t) and IsPrime(Isqrt(t)) where t is p+NextPrime(p)+1]; // Bruno Berselli, Aug 28 2013
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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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