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Primes p such that (p^2+3)/4 is prime.
4

%I #3 Mar 30 2012 17:22:42

%S 3,5,7,11,13,17,29,31,41,43,67,83,101,109,139,151,157,179,181,199,211,

%T 223,239,263,277,283,307,311,337,347,353,379,389,419,431,463,491,557,

%U 577,587,619,659,673,739,757,797,809,811,829,853,907,911,953,991,1051

%N Primes p such that (p^2+3)/4 is prime.

%C For all primes q>2, we have q=4k+-1 for some k, which makes it easy to show that 4 divides q^2+3. Similar sequences, with p and (p^2+a)/b both prime, are A048161, A062324, A062326, A062718, A109953, A110589, A118915, A118918, A118940, A118941 and A118942.

%t Select[Prime[Range[200]],PrimeQ[(#^2+3)/4]&]

%K nonn

%O 1,1

%A _T. D. Noe_, May 06 2006