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SOPHIE GERMAIN PRIMES |
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A Sophie Germain Prime is a prime number P for which 2P+1 is also a prime. These prime numbers include: 2, 3, 5, 11, 23, 29, 41, 53, 89, 113, 131... It can be noted that a Sophie Germain prime p > 3 is of the form 6k−1, since adding one to them make them a multiple of six. These primes were named after the French mathematician Marie-Sophie Germain when she (around 1825) proved that Fermat's Last Theorem holds true for these primes. That is, if n is a Sophie Germain prime greater than 2, then there are no whole numbers a, b, c such that an + bn = cn. It has been conjectured that there are infinitely many Sophie Germain primes, however, this conjecture has not yet been proven. The corresponding prime numbers of the form 2P+1, where P is a Sophie Germain prime are called safe primes.
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