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A045637 Primes of the form p^2 + 4, where p is prime. 20

%I

%S 13,29,53,173,293,1373,2213,4493,5333,9413,10613,18773,26573,27893,

%T 37253,54293,76733,85853,94253,97973,100493,120413,139133,214373,

%U 237173,253013,299213,332933,351653,368453,375773,458333,552053,619373

%N Primes of the form p^2 + 4, where p is prime.

%C 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

%C Infinite under the Bunyakovsky conjecture. - _Charles R Greathouse IV_, Jul 04 2011

%C All terms > 29 are congruent to 53 mod 120. - _Zak Seidov_, Nov 06 2013

%H T. D. Noe, <a href="/A045637/b045637.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A062324(n)^2 + 4. - _Zak Seidov_, Nov 06 2013

%e 29 belongs to the sequence because it equals 5^2 + 4.

%t Select[Prime[ # ]^2+4&/@Range[140], PrimeQ]

%o (PARI) forprime(p=2,1e4,if(isprime(t=p^2+4),print1(t","))) \\ _Charles R Greathouse IV_, Jul 04 2011

%Y The corresponding primes p are in A062324.

%Y Subsequence of A005473 (and thus A185086).

%Y Cf. A094473-A094479.

%K nonn,easy

%O 1,1

%A _Felice Russo_

%E Edited by _Dean Hickerson_, Dec 10 2002

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Last modified May 26 15:21 EDT 2019. Contains 323597 sequences. (Running on oeis4.)