There are infinite prime numbers

supposing , that there are finite prime numbers, p1, p2, ..., p(n-1), pn,
where pn is the hightest prime number. 

this furthermore implies, that a number q would exists, which is defined:
q = p1 * p2 * ... * p(n-1) * pn + 1

q is greater than 1 and cause pn is the highest prime number,

q must have at least one or more divider r from p1, p2, ..., p(n-1), pn

since r|q and r|(p1...pn) => r|1 (what is not possible)

q.e.d.