# Francois Proth

## (1852 - 1879)

### Francois Proth was a self-taught
farmer, who lived all his short life in the village of

### "Vaux devant Damloup" near
Verdun in France.

### He produced four theorems that can
be used for testing the primality of integers. The most famous one is called *Proth' s theorem.*

*PROTH' S
THEOREM (1878):*

**Let N = k*2**^{n} + 1 with k < 2^{n}

**If there is an integer ***a* such that *a*^{((N-1)/2)}
= -1 (mod N), then N is prime !