How do we know there are an infinite number of prime numbers? How do we know that once you get to a certain point, they don’t all end up as composite numbers?
In: Mathematics
Because you can mathematically prove it.
Let’s say there is a finite number of prime numbers.
If you multiple all of them together, then add 1, it would be undividable by any of the prime number used to make that number, which means that number is either prime, or it is dividable by another prime that wasn’t used to make that number up, which means you didn’t have all the prime numbers, which is a contradiction.
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