“Fermat, Mersenne, factorization and perfect numbers” by Daniel Perrin

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Société Mathématique de France - SMF

Published on Apr 3, 2021
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The presentation is based on two letters from Fermat to Mersenne, both from 1643, both concerning the factorization of large integers: 2027651281 in one and 100895598169 in the other. One of these letters contains a method that allows the first number to be factorized. It does not apply to the second, which refers to the study of perfect numbers (specifically a multi-perfect number suggested, it seems, by Frenicle). These two points will be explained and we will show how these problems remain entirely current in terms of cryptography and RSA code, and the proximity of Fermat's method and modern methods of factorization by the quadratic sieve. Conference of the cycle "A text, a mathematician" of the Mathematical Society of France. March 14, 2018 at the National Library of France.

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