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Sophie Germain prime (Definition)

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.



"Sophie Germain prime" is owned by yark. [ full author list (2) | owner history (1) ]
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Other names:  Germain prime
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Cross-references: twin prime constant, number, twin prime conjecture, prime number
There are 8 references to this entry.

This is version 5 of Sophie Germain prime, born on 2004-09-03, modified 2006-09-01.
Object id is 6131, canonical name is GermainPrime.
Accessed 3863 times total.

Classification:
AMS MSC: 11A41 (Number theory :: Elementary number theory :: Primes)
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