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.

Title	Sophie Germain prime
Canonical name	SophieGermainPrime
Date of creation	2013-03-22 14:34:23
Last modified on	2013-03-22 14:34:23
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	8
Author	yark (2760)
Entry type	Definition
Classification	msc 11A41
Synonym	Germain prime