A371980 Sophie Germain primes p such that 4*p + 3 is a composite number.

3, 23, 29, 53, 83, 113, 131, 173, 191, 233, 239, 251, 281, 293, 419, 431, 443, 491, 593, 641, 653, 659, 683, 743, 761, 809, 911, 953, 1013, 1049, 1103, 1223, 1289, 1439, 1499, 1559, 1583, 1601, 1733, 1973, 2003, 2039, 2063, 2069, 2129, 2141, 2273, 2339, 2351, 2393, 2399, 2543, 2549, 2693, 2741, 2753

Offset: 1

Author

Alexandre Herrera, Apr 15 2024

Keywords

• nonn

Examples

			a(1) = 3 is prime and 2*3 + 1 = 7 also but not 4*3 + 3 = 15.
		

Crossrefs

Cf. A005384.

Programs

Mathematica

Select[Prime[Range[410]], And[PrimeQ[2 # + 1], CompositeQ[4 # + 3]] &] (* Michael De Vlieger, Apr 19 2024 *)

Python

import sympy as sp
l = []
for i in range(2,2800):
    if sp.isprime(i) and sp.isprime(2*i + 1) and not(sp.isprime(4*i + 3)):
        l.append(i)
print(l)