Definition:Sophie Germain Prime
Jump to navigation
Jump to search
Definition
A Sophie Germain prime is a prime number $p$ such that $2 p + 1$ is also prime.
It follows from this definition that $2 p + 1$ is a safe prime.
Sequence
The sequence of Sophie Germain primes begins:
- $2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, \ldots$
Largest Known
The largest known Sophie Germain primes (as of May 2017) are as follows:
Sophie Germain prime | Number of digits | Date discovered | Discovered by |
---|---|---|---|
$137211941292195 \times 2^{171960} - 1$ | $51780$ | 3rd May 2006 | Zoltán Járai, Gabor Farkas, Timea Csajbok, János Kasza and Antal Járai |
$48047305725 \times 2^{172403} - 1$ | $51910$ | 25th January 2007 | David Underbakke |
$607095 \times 2^{176311} - 1$ | $53081$ | 18th September 2009 | Tom Wu |
$99064503957 \times 2^{200008} - 1$ | $60220$ | April 2016 | S. Urushihata |
$620366307356565 \times 2^{253824} - 1$ | $76424$ | 2nd November 2009 | Zoltán Járai, Gabor Farkas, Timea Csajbok, János Kasza and Antal Járai |
$648621027630345 \times 2^{253824} - 1$ | $76424$ | 2nd November 2009 | Zoltán Járai, Gabor Farkas, Timea Csajbok, János Kasza and Antal Járai |
$183027 \times 2^{265440} - 1$ | $79911$ | 22nd March 2010 | Tom Wu |
$18543637900515 \times 2^{666667} - 1$ | $200701$ | April 2012 | Philipp Bliedung |
$2618163402417 \times 2^{1290000} - 1$ | $388342$ | February 2016 | James Scott Brown |
Also see
- Results about Sophie Germain primes can be found here.
Source of Name
This entry was named for Marie-Sophie Germain.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $89$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $89$
- Weisstein, Eric W. "Sophie Germain Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SophieGermainPrime.html