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A062326
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Primes p such that p^2 - 2 is also prime.
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43
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2, 3, 5, 7, 13, 19, 29, 37, 43, 47, 61, 71, 89, 103, 107, 127, 131, 139, 173, 191, 211, 223, 233, 239, 257, 293, 313, 337, 359, 421, 443, 449, 467, 491, 523, 541, 569, 587, 607, 653, 677, 719, 727, 733, 743, 751, 757, 761, 797, 811, 863, 881, 1013, 1021
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OFFSET
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1,1
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COMMENTS
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When p and p^2 - 2 are both prime, the fundamental solution of the Pell equation x^2 - n*y^2 = 1, for n = p^2 - 2, is x = p^2 - 1 and y = p. See A109748 for the case of n and x both prime. - T. D. Noe, May 19 2007
3 is the only prime p such that p^2 + 2 and p^2 - 2 are both primes. - Jaroslav Krizek, Nov 25 2013 (note that p^2 + 2 is composite for all primes p >= 5. - Joerg Arndt, Jan 10 2015)
For all primes p except for p = 3, p^2 + 2 is multiple of 3 (see A061725). - Zak Seidov, Feb 19 2015
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LINKS
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MATHEMATICA
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Select[Prime[Range[500]], PrimeQ[#^2 - 2] &] (* Harvey P. Dale, Sep 20 2011 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(1100) | IsPrime(p^2-2) ]; // Klaus Brockhaus, Jan 01 2009
(PARI) { n=0; forprime (p=2, 5*10^5, if (isprime(p^2 - 2), write("b062326.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 05 2009
(Haskell)
import Data.List (elemIndices)
a062326 = a000040 . a137291
a062326_list = map (a000040 . (+ 1)) $
elemIndices 1 $ map a010051' a049001_list
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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