As is well known, Fermat couldn't check the primality of $F_{5} = 2^{2^{5}} + 1$. This raises an interesting question : what was the largest prime number that was known to ancients (particularly Greeks) or the mathematicians till Fermat and how much efforts were made to find the larger and larger primes? I couldn't find any authentic answer to this question so far and I would be quite grateful if I get a good answer to this question.
Thanks in advance