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Sophie Germain prime (another Prime Pages' Glossary entries) |
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Glossary:
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If both p and 2p+1 are prime, then
p is a Sophie Germain prime.
The first few such primes are
2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113,
and 131. Around 1825 Sophie
Germain proved that the first case of Fermat's last
theorem is true for odd Germain primes.
Soon after Legendre began to
generalize this by showing the
first case of FLT also holds for odd
primes p such that kp+1 is prime,
k=4, 8, 10, 14, and 16. In 1991 Fee and
Granville extended
this to k < 100, k not a multiple
of three. Many similar results were also shown,
but now that Fermat's Last Theorem has been
proven by Wiles, they are of less interest.
Euler and Lagrange
proved the following about Sophie Germain primes:
if p
See Also: CunninghamChain Related pages (outside of this work)
References:
Chris K. Caldwell © 1999-2013 (all rights reserved)
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