Definition:Sophie Germain Prime
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Definition
A Sophie Germain prime is a prime number $p$ such that $2p + 1$ is also prime.
The first few Sophie Germain primes are:
- $2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, \ldots$
This sequence is A005384 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
The largest known Sophie Germain primes (as of March 2010) 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 |
| $620366307356565 \times 2^{253824} - 1$ | $76424$ | 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 |
Source of Name
This entry was named for Sophie Germain.
