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A045637
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Primes of the form p^2+4, where p is prime.
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12
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13, 29, 53, 173, 293, 1373, 2213, 4493, 5333, 9413, 10613, 18773, 26573, 27893, 37253, 54293, 76733, 85853, 94253, 97973, 100493, 120413, 139133, 214373, 237173, 253013, 299213, 332933, 351653, 368453, 375773, 458333, 552053, 619373
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| These are the only primes that are the sum of two primes squared. 11=3^2+2 is the only prime of the form p^2+2 because all primes greater than 3 can be written as p=6n-1 or p=6n+1, which allows p^2+2 to be factored. - T. D. Noe, May 18 2007
Infinite under the Bunyakovsky conjecture. [Charles R Greathouse IV, Jul 04, 2011]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
| 29 belongs to the sequence because it equals 5^2+4.
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MATHEMATICA
| Select[Prime[ # ]^2+4&/@Range[140], PrimeQ]
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PROG
| (PARI) forprime(p=2, 1e4, if(isprime(t=p^2+4), print1(t", "))) \\ Charles R Greathouse IV, Jul 04, 2011
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CROSSREFS
| The corresponding primes p are in A062324.
Subsequence of A005473 (and thus A185086).
Cf. A094473-A094479.
Sequence in context: A090866 A098062 A094481 * A146743 A065546 A075636
Adjacent sequences: A045634 A045635 A045636 * A045638 A045639 A045640
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KEYWORD
| nonn,easy
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AUTHOR
| Felice Russo (frusso(AT)micron.com)
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 10 2002
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