François Proth

François Proth (22 March 1852 – 21 January 1879) was a self-taught French mathematician and farmer who lived in Vaux-devant-Damloup near Verdun, France.^[1]

He stated four primality-related theorems.^[2] The most famous of these, Proth's theorem, can be used to test whether a Proth number (a number of the form k × 2ⁿ + 1 with k odd and k < 2ⁿ) is prime. The numbers passing this test are called Proth primes; they continue to be of importance in the computational search for large prime numbers.^[3]

Proth also formulated Gilbreath's conjecture on successive differences of primes, 80 years prior to Gilbreath, but his proof of the conjecture turned out to be erroneous.^[4]

The cause of Proth's death is not known.^[5]

Publications

• Proth, F. (1876), "Énoncés de divers théorèmes sur les nombres", Comptes rendus de l'Académie des Sciences de Paris, 83: 1288–1289.
• Proth, F. (1878), "Sur quelques identités", Nouvelle Correspondance Mathématique de M. E. Catalan, Bruxelles, 4: 377–378.
• Proth, F. (1878), "Théorème relatif à la théorie des nombres", Comptes rendus de l'Académie des Sciences de Paris, 87: 374.
• Proth, F. (1878), "Théorèmes sur les nombres premiers", Comptes rendus de l'Académie des Sciences de Paris, 87: 926.