Largest known prime number found

[OwlHoot]

Was into number theory when younger. The search for big primes had just started, but conjecture at the time was that there probably was a number which after which no possible primes could exist.

You must be cogging on a bit, over 2000 years old, because Euclid proved in ancient times that there's an infinite number of primes, for the simple reason that if there were only a finite number of primes, and p_1, p_2, ... p_n was a list of all of them, then (p_1 * p_2 * ... * p_n) + 1 exceeds 1 and is thus divisible by at least one prime but is not divisible by any primes in the list, and hence must be a product of prime(s) not in the list, which contradicts the assumption that the list is complete.

(unless you are talking about primes of a certain restricted form, such as Fermat primes 2^2^n + 1 for integer n, of which is it generally believed there are only a finite number, all already found. But it is pretty safe to say that nobody believes there are only a finite number of Mersenne primes (of the form 2^p - 1 with p prime).