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A173627
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Primes p such that p^2 + 6, p^2 + 12 and p^2 + 18 are all prime.
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2
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5, 19, 61, 971, 1451, 2711, 3061, 3449, 6011, 15139, 15241, 21821, 27851, 39839, 51749, 62459, 75679, 76081, 82591, 97001, 121039, 121441, 122299, 135581, 161569, 162671, 196681, 196831, 200881, 214741, 217271, 222931, 242069, 243119, 254161
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OFFSET
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1,1
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COMMENTS
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For p > 2, p^2 + 24 is composite (divisible by 5). - Zak Seidov, Sep 07 2018
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LINKS
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MATHEMATICA
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okQ[n_]:=Module[{p2=n^2}, And@@PrimeQ[{p2+6, p2+12, p2+18}]]; Select[Prime[Range[30000]], okQ] (* Harvey P. Dale, Dec 18 2010 *)
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PROG
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(Magma)[p: p in PrimesUpTo(600000)|IsPrime(p^2+6) and IsPrime(p^2+12) and IsPrime(p^2+18)] // Vincenzo Librandi, Dec 13 2010
(PARI) isok(p) = isprime(p) && isprime(p^2+6) && isprime(p^2+12) && isprime(p^2+18); \\ Michel Marcus, Sep 08 2018
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CROSSREFS
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Cf. A062718 (p and p^2 + 6 are both prime).
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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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