François Proth

François Proth (1852 to 1879) was a self-taught French mathematician and farmer who lived in Vaux-devant-Damloup, near Verdun in France. He died at the age of twenty six, and the cause of his death is not known, yet he stated four theorems concerning primality. The most famous of them, Proth's theorem, gives a test for whether a Proth number is prime. A Proth number has the form k times 2 to the power n plus 1, with k odd and k smaller than 2 to the power n, and the numbers that pass the test are called Proth primes. Proth primes remain important in the computational search for very large prime numbers. Proth also formulated what is now called Gilbreath's conjecture, on the successive differences of the prime numbers, about eighty years before Gilbreath, but the proof of the conjecture that Proth offered turned out to be erroneous.