Fermat's numbers
Fermat's numbers look like:
where n is a nonnegative integer. It was hypothesized that all Fermat's numbers of this kind are prime numbers. This hypothesis was refuted by Euler in 1732, he found the Fermat's number expansion F5:
At the moment, no single Fermat's number is known more than F4. It is known that Fn are composite at 5 <= n <= 32.
