*What is Mathematics*, the author gives Euclid's proof that there are infinitely many primes by assuming there aren't infinitely many, and taking all the primes, multiplying them together (P1*P2...*Pn), and then adding 1 - showing that this is larger than the largest prime, but not divisible by any of the primes (because of the remainder of 1) thus contradicting the assumption. Does this sexy reductio proof give us a method of find infinitely many primes? If we take all our known primes, multiply them together, and add one, do we always get a new prime and are thus able to find an infinitude of primes with a big enough calculator?