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
Proof by contradiction.
Assume you have a list containing every single prime number.
Multiple all those numbers together to get a very large number. Add 1 to that number to get a new number we’ll call C.
C cannot be divided by any of the prime numbers on your list, so it must not be composite. But it has to be composite because it isn’t on your list. That’s a contradiction. C can’t be composite but it has to be composite.
Because the assumption created a contradiction, the assumption must be wrong. You cannot in fact have a list of all the prime numbers.
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