>>12332458>why would there be a finite number of primes? Who the fuck told you there was a finite number of primes?
>if natural numbers go to infinity doesn't it follow then there infinite number of primes?These two things are unrelated. But there is an infinite # of primes.
How do we know?
Assume there are a finite number of primes, p(1) through p(n)
Take the product of all those primes, add 1 to it.
What do we know about this number? Well we know it's either prime or composite (all numbers are. So if it's prime, that's a prime that wasn't in our list of primes.
What if it's composite? Well then that means it must be divisible by one of our primes from the list right? But it can't be, because it's 1 off of a multiple of literally every prime we think exists, and there's no integer > 1 that divides both X and X+1. So it must have some prime factor that is not in our list.
