Seldom has one human being (Archimedes Balonium) written so much and
said so little of value.
There is nothing wrong with the standard proof of the infinitude of
prime. It is a clear proof by contradiction. One assumes one has them
all and then constructs a new number that may or may not actually be
prime, but even if composite, its divisors are not among the assumed
finite set of all primes.
Newbies should not be taken in by this nonsense.
Dr. Michael W. Ecker
Associate Professor of Mathematics
Pennsylvania State University
Wilkes-Barre Campus
Lehman, PA 18627