It will not necessarily be a larger prime. But it will always be divisible by a larger prime. See http://en.wikipedia.org/wiki/Euclids_theorem http://en.wikiped

It will not necessarily be a larger prime. But it will always be divisible by a larger prime. See http://en.wikipedia.org/wiki/Euclids_theorem http://en.wikipedia.org/wiki/Euclids_theorem (Though not necessarily the next largest prime). The problem with this approach is that the product of the first n primes grows exponentially as the number of primes increases.