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%I #8 Apr 18 2013 11:12:00
%S 2,3,5,41,89,131,173,293,743,761,911,1559,1583,1811,1931,1973,2129,
%T 2273,2339,2969,3449,3491,4409,4733,5003,5039,5501,6173,6551,6761,
%U 7883,7901,8093,8741,9059,9689,10589,10781,11171,11549,13229,13553,14939,15569
%N Primes p such that both 2*p + 1 and p^2 + p + 1 are primes.
%C Intersection of A005384 and A053182.
%C Note that 2p+1 is the derivative of p^2+p+1 with respect to p. - _T. D. Noe_, Apr 18 2013
%e 5 is a member since 5+6=11 and 5*6+1=31 are both primes.
%t Select[Prime[Range[1850]], PrimeQ[2*# + 1] && PrimeQ[#^2 + # + 1] &]
%Y Cf. A005384, A053182.
%K nonn
%O 1,1
%A _Jayanta Basu_, Apr 17 2013
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