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A045637
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Primes of the form p^2 + 4, where p is prime.
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22
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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
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OFFSET
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1,1
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COMMENTS
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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
All terms > 29 are congruent to 53 mod 120. - Zak Seidov, Nov 06 2013
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LINKS
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FORMULA
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EXAMPLE
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29 belongs to the sequence because it equals 5^2 + 4.
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MATHEMATICA
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Select[Prime[ # ]^2+4&/@Range[140], PrimeQ]
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PROG
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CROSSREFS
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The corresponding primes p are in A062324.
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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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