# Sophie Germain Primes

In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 29 is a Sophie Germain prime and 2 × 29 + 1 = 59 is its associated safe prime. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem.[1] Sophie Germain primes and safe primes have applications in public key cryptography and primality testing. It has been conjectured that there are infinitely many Sophie Germain primes, but this remains unproven.

First 20: 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293

Checkout list of first: 10, 50, 100, 500, 1000 sophie germain primes. You can also check all sophie germain primes.

Checkout sophie germain primes up to: 100, 500, 1000, 10000.

## Visualization#

Every frame counter is increased by one. If it is sophie germain prime then dot appears. Color has no meaning. Video has 25fps.

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## External#

- OEIS: A005384
- Wikipedia: Sophie Germain primes
- Youtube: Visualization up to 1 million

## Tags#

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