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: $2,3,5,11,23,29,41,53,83,89,113,131,173,179,191,233,\dots$

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.

Title Sophie Germain prime SophieGermainPrime 2013-03-22 14:34:23 2013-03-22 14:34:23 yark (2760) yark (2760) 8 yark (2760) Definition msc 11A41 Germain prime