Are prime numbers infinite?

1 Answer
Apr 4, 2016

There are an infinite number of prime numbers.

Explanation:

To prove this for yourself, suppose you only know a finite number of prime numbers - call them #p_1, p_2, ..., p_n#

Consider the number #q = (p_1 xx p_2 xx ... xx p_n) + 1#

#q# is not divisible by any of the prime numbers you know, so it is either prime itself or there is some other prime #p_(n+1)# which is a factor of #q#.

In either case, your list of primes was incomplete.

So the number of primes is unbounded.