François Proth

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François Proth (born March 22, 1852 in Vaux-devant-Damloup , † January 21, 1879 ) was a French amateur mathematician.

Proth was a full-time farmer in Vaux-devant-Damloup near Verdun . From 1876 to 1878 he published several theorems about prime numbers, the best known of which is his prime number test (theorem from Proth) for Proth prime numbers (and thus also for Fermat numbers , for example ). The Pépin test is a special case of the Proth theorem and was also published by Proth. Although Proth gave no proof of Proth's theorem in his publications, he wrote in a letter that he had proof. The work on Proth numbers was related to works by Édouard Lucas that appeared around the same time . Proth also formulated Gilbreath's conjecture before the namesake Norman Gilbreath (and gave a flawed proof).

He also claimed to have proven Bertrand's postulate .

Fonts

  • Énoncés de divers théorèmes sur les nombres , Comptes Rendus des Séances de l'Académie des Sciences, Paris, Volume 83, 1876, 1288–1286.
  • Sur quelques identités , Nouvelle Correspondance Mathématique de ME Catalan, Brussels, Volume 4, 1878, 377–378.
  • Sur la série des nombres premiers , Nouv. Corresp. Math., Vol. 4, 1878, 236-240 (Gilbreath's conjecture)
  • Théorème relatif à la théorie des nombres , Comptes Rendus des Séances de l'Académie des Sciences, Paris, Volume 87, 1878, p. 374 (Pépin test, only a brief announcement), Wikisource
  • Théorèmes sur les nombres premiers , Comptes Rendus des Séances de l'Académie des Sciences, Paris, Volume 87, 1878, p. 926 (sentence by Proth, announcement only), wikisource

Individual evidence

  1. ↑ For example Hans Riesel Prime numbers and computer methods for factorization , Birkhäuser, 1994, p. 104
  2. ↑ T. Pépin Comptes Rendus 85, 1877, 329, wikisource
  3. ↑ Hugh C. Williams Édouard Lucas and primality testing , Wiley 1998. Williams considers Proth's claim to be credible. After Chris Caldwell, Top Twenty: Proth
  4. ^ Dickson History of the Theory of Numbers , Volume 1, 435, then in Nouv. Corresp. Math., 4, 1878, 236-240
personal data
SURNAME Proth, François
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH March 22, 1852
PLACE OF BIRTH Vaux-devant-Damloup
DATE OF DEATH January 21, 1879