February 26, 2002
Practical Aspects of Modern Cryptography
47
Finding Primes
nEuclid’s proof of the infinity of primes
nSuppose that the set of all primes were finite.
nLet N be the product of all of the primes.
nConsider N+1.
nThe prime factors of N+1 are not among the finite set of primes multiplied to form N.
nThis contradicts the assumption that the set of all primes is finite.