A277993 Sophie Germain primes p such that p + 2 and p - 2 are semiprimes.

23, 53, 89, 113, 131, 251, 293, 491, 683, 719, 953, 1439, 1499, 1511, 1733, 2393, 3491, 3779, 5171, 7043, 7151, 7433, 7649, 7901, 8069, 8663, 9689, 10781, 12011, 12653, 13049, 13229, 13451, 13553, 14669, 15569, 16001, 16253, 18899, 19709, 20411, 22469, 22751, 23099

Offset: 1

Author

K. D. Bajpai, Nov 07 2016

Keywords

• nonn

Comments

Intersection of A005384 and A063643.

Examples

			a(1) = 23 is Sophie Germain prime because 2*23 + 1 = 47 is prime. Also, 23 + 2 = 25 =  5*5; 23 - 2 = 21 = 7*3; are both semiprime.
a(2) = 53 is Sophie Germain prime because 2*53 + 1 = 107 is prime. Also, 53 + 2 = 55 =  11*5; 23 - 2 = 51 = 17*3; are both semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A005384, A063637, A063638, A063643.

Programs

Mathematica

Select[Select[Prime[Range[10000]], PrimeQ[2 # + 1] &], PrimeOmega[# - 2] == 2 && PrimeOmega[# + 2] == 2 &]
Select[Prime[Range[3000]],PrimeQ[2#+1]&&PrimeOmega[#+{2,-2}]=={2,2}&] (* Harvey P. Dale, Dec 16 2017 *)

PARI

is(n) = ispseudoprime(n) && ispseudoprime(2*n+1) && bigomega(n+2)==2 && bigomega(n-2)==2 \\ Felix Fröhlich, Nov 07 2016