# François Proth

François Proth (1852 – 1879) was a French self-taught mathematician 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 k2n + 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.

## Publications

• Proth, F. (1876), "Énoncés de divers théorèmes sur les nombres", Comptes Rendus des Séances de l'Académie des Sciences, Paris 83: 1288–1286.
• 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 des Séances de l'Académie des Sciences, Paris 87: 347.
• Proth, F. (1878), "Théorèmes sur les nombres premiers", Comptes Rendus des Séances de l'Académie des Sciences, Paris 87: 926.

## References

1. ^ Wells, David (2011), Prime Numbers: The Most Mysterious Figures in Math, John Wiley & Sons, p. 189, ISBN 9781118045718.
2. ^ Mollin, Richard A. (2010), An Introduction to Cryptography, Discrete Mathematics and Its Applications (2nd ed.), CRC Press, p. 192, ISBN 9781420011241.
3. ^ Chaumont, Alain; Leicht, Johannes; Müller, Tom; Reinhart, Andreas (2009), "The continuing search for large elite primes", International Journal of Number Theory 5 (2): 209–218, doi:10.1142/S1793042109002031, MR 2502805.
4. ^ Caldwell, Chris, "The Prime Glossary: Gilbreath's conjecture", The Prime Pages.