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A154321
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Primes p such that p, p^2 + 2p - 4 and p^2 + 8p - 4 are prime.
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3
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3, 5, 7, 13, 23, 167, 233, 277, 283, 383, 547, 607, 727, 733, 823, 1087, 1427, 1597, 1823, 2297, 3253, 3313, 3533, 3593, 3863, 4027, 4133, 4363, 6257, 6737, 7477, 7577, 7907, 9043, 9227, 11317, 11497, 11833, 11867, 12373, 12503, 12637, 12743, 13367
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OFFSET
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1,1
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LINKS
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EXAMPLE
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For p = 3, p^2 + 2p - 4 = 11, p^2 + 8p - 4 = 29;
for p = 7, p^2 + 2p - 4 = 59, p^2 + 8p - 4 = 101;
for p = 607, p^2 + 2p - 4 = 369659, p^2 + 8p - 4 = 373301.
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MAPLE
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a:= proc(n) if isprime(n) and isprime(n^2+2*n-4) and isprime(n^2+8*n-4) then n end if end proc: seq(a(n), n = 2 .. 15000); # Emeric Deutsch, Jan 20 2009
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MATHEMATICA
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Select[Prime[Range[7000]], And@@PrimeQ/@{#^2 + 2 # - 4, #^2 + 8 # - 4}&] (* Vincenzo Librandi, Apr 18 2013 *)
Select[Prime[Range[2000]], AllTrue[#^2-4+{2#, 8#}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 29 2018 *)
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PROG
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(Magma) [p: p in PrimesUpTo(13500) | IsPrime(p^2+2*p-4) and IsPrime(p^2+8*p-4)]; // Vincenzo Librandi, Apr 18 2013
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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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EXTENSIONS
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STATUS
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approved
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