TITLE: Largest prime known to ancients
QUESTION [6 upvotes]: 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

REPLY [2 votes]: There are, up to Fermat's contemporary Mersenne, many lists in which perfect numbers were listed. Most of them contained the "prime" number $2^{11}-1$, many of them even $2^9 - 1$. It does not make much sense to me to ask for the largest known prime in such a situation.
Also I am surprised to hear that it is well known that Fermat could not check the primality of $F_5$. It is clear that he either did not or that he made a mistake, but there's nothing that would have prevented him to find the divisor 641. Euler verified the primality of $2^{31}-1$, and from then on lists of records do make some sense.