cp's OEIS Frontend

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

%I A045637 #37 Aug 25 2021 17:53:58
%S A045637 13,29,53,173,293,1373,2213,4493,5333,9413,10613,18773,26573,27893,
%T A045637 37253,54293,76733,85853,94253,97973,100493,120413,139133,214373,
%U A045637 237173,253013,299213,332933,351653,368453,375773,458333,552053,619373
%N A045637 Primes of the form p^2 + 4, where p is prime.
%C A045637 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 A045637 Infinite under the Bunyakovsky conjecture. - _Charles R Greathouse IV_, Jul 04 2011
%C A045637 All terms > 29 are congruent to 53 mod 120. - _Zak Seidov_, Nov 06 2013
%H A045637 T. D. Noe, <a href="/A045637/b045637.txt">Table of n, a(n) for n = 1..1000</a>
%H A045637 Yang Ji, <a href="https://arxiv.org/abs/2105.05250">Several special cases of a square problem</a>, arXiv:2105.05250 [math.GM], 2021.
%F A045637 a(n) = A062324(n)^2 + 4. - _Zak Seidov_, Nov 06 2013
%e A045637 29 belongs to the sequence because it equals 5^2 + 4.
%t A045637 Select[Prime[ # ]^2+4&/@Range[140], PrimeQ]
%o A045637 (PARI) forprime(p=2,1e4,if(isprime(t=p^2+4),print1(t","))) \\ _Charles R Greathouse IV_, Jul 04 2011
%Y A045637 The corresponding primes p are in A062324.
%Y A045637 Subsequence of A005473 (and thus A185086).
%Y A045637 Cf. A094473-A094479.
%K A045637 nonn,easy
%O A045637 1,1
%A A045637 _Felice Russo_
%E A045637 Edited by _Dean Hickerson_, Dec 10 2002