Sophie Germain primes are prime numbers p such that 2p + 1 is also prime. For example, 23 and 2 × 23 + 1 (that is, 47) are both prime numbers, so 23 is a Sophie Germain prime. The French mathematician Sophie Germain (1776–1831) is known for defying the social conventions of the 19th century—women were not supposed to take an interest in mathematics, which was deemed "dangerous" for them because it might jeopardize their reproductive capacity!—and for being the first woman to win a prize from the Paris Academy of Sciences. She introduced the numbers that now bear her name while researching Fermat's Last Theorem. They returned to the spotlight in cryptography in the 1970s.
Fermat's Last Theorem
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Sophie Germain was born in Paris into an educated, liberal, middle-class family. She taught herself mathematics using the family library, despite her parents' initial disapproval. She obtained lecture notes from the École polytechnique, founded in 1794 but closed to women. To do so, she had to use a male pseudonym. She then became acquainted with Joseph-Louis Lagrange, one of the most highly regarded mathematicians of the day. Impressed by her mathematical ability, he enabled her to meet several Parisian scholars, including Adrien-Marie Legendre. From 1804 onward, she also corresponded with the German mathematician Carl Friedrich Gauss.
