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A062324
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p and p^2 + 4 are both prime.
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25
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3, 5, 7, 13, 17, 37, 47, 67, 73, 97, 103, 137, 163, 167, 193, 233, 277, 293, 307, 313, 317, 347, 373, 463, 487, 503, 547, 577, 593, 607, 613, 677, 743, 787, 823, 827, 853, 883, 953, 967, 983, 997, 1087, 1117, 1123, 1237, 1367, 1423, 1447, 1523, 1543, 1613
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OFFSET
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1,1
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COMMENTS
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Equivalent to the definition: largest absolute dimension of Gaussian primes with prime coordinates. As 2 is the only even prime, the only possibility for a Gaussian prime to have prime coordinates is to be of the form +/-2 +/- I*p or +/-p +/-2*I with p^2+4 a prime, i.e., p is a member of this sequence. - Olivier Gérard, Aug 17 2013
When p > 3, p^2 + 2 is never prime. - Zak Seidov, Nov 04 2013
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 3 because 3^2 + 4 = 13 is prime,
a(4) = 13 because 13^2 + 4 = 173 is prime. - Zak Seidov, Nov 04 2013
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MATHEMATICA
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Select[Prime/@Range[300], PrimeQ[ #^2+4]&]
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PROG
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(PARI) { n=0; forprime (p=2, 5*10^5, if (isprime(p^2 + 4), write("b062324.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 04 2009
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CROSSREFS
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The corresponding primes p^2+4 are in A045637.
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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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More terms from Larry Reeves (larryr(AT)acm.org), Jul 20 2001
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STATUS
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approved
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