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Sophie Germain prime

Any prime number p such that 2p + 1 is also prime; the smallest examples 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 (FLT) is true for such primes. Soon after, Adrien-Marie 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, where k not a multiple of three. Many similar results were also shown, but now that FLT has been proven correct, they are of less interest.

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