Sophie Germain prime

A prime number $p$ is called Sophie Germain prime if $2p+1$ is also prime.

The first few Sophie Germain primes are:$2,3,5,11,23,29,41,53,83,89,113,131,173,179,191,233,\mathrm{\dots }$

It is conjectured that there are infinitely many Sophie Germain primes,but (like the Twin Prime Conjecture) this has not been proven.A heuristic estimate for the number of Sophie Germain primes less than $n$ is $\frac{2cn}{{\ln }^{2}n}$, where $c$ is the twin prime constant.