Ok I see what you’re getting at. Maybe a better way to construct this version of the argument is - every integer > 1 is either a prime or a product of primes (

Ok I see what you’re getting at. Maybe a better way to construct this version of the argument is - every integer > 1 is either a prime or a product of primes (this is easy to show by induction) - assume there’s a finite number of primes - then the product of all primes + 1 must be either a prime or a product of primes - but we know that it’s _neither_ (can’t be divided by any of the primes in the list, and not itself in the list), which is a contradiction - it had to be one or the other.