30th June

On this day in 1742, Leonard Euler claimed in a letter to Goldbach that prime numbers of the form 4n+ 1 are represented uniquely as a sum of two squares.
He also mentioned that 641 divides 232+12^{32} + 1, thereby disproving Fermat's claim that all the so-called numbers Fermat numbers Fn=22n+1F_n = 2^{2^n} + 1 are prime. Years later we have not found another with n > 4 which is prime.