18 JUN 2013 by ideonexus
Proof That the Set of Prime Numbers is Infinite
Theorem: There are infinitely many prime numbers.
Proof: Suppose, contrary to the theorem, that there is only a finite number
of primes. Thus, there will be a largest which we can call p. Now
define a number n as 1 plus the product of all the primes:
n = (2 X 3 X 5 X 7 X 11 X...X p) 1
Is n itself prime or composite? If it is prime then our original supposition
is false, since n is larger than the supposed largest prime p. So now
let’s consider it composite. This means that it must be div...There is always one larger.