# 30th June

On this day in 1742, Leonard Euler claimed in a letter to Goldbach that prime numbers of the form 4

He also mentioned that 641 divides $2^{32} + 1$, thereby disproving Fermat's claim that all the so-called numbers Fermat numbers $F_n = 2^{2^n} + 1$ are prime. Years later we have not found another with

*n*+ 1 are represented uniquely as a sum of two squares.He also mentioned that 641 divides $2^{32} + 1$, thereby disproving Fermat's claim that all the so-called numbers Fermat numbers $F_n = 2^{2^n} + 1$ are prime. Years later we have not found another with

*n*> 4 which is prime.