Prime numbers are more than any assigned multitude of prime numbers.
Proof
Given primes p1,…,pn, form N=p1p2⋯pn+1.
By VII.31 N has a prime divisor q. If q were one of the
pi, then q would divide N−p1⋯pn=1 (Common Notion
3), which is impossible. Hence q is a new prime not in the
original list; the list of primes admits no upper bound.