GermainPrime 2004-09-03 04:46:59 2006-09-01 06:08:02 Definition \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \PMlinkescapeword{estimate} A prime number $p$ is called \emph{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.