Q: Are there an infinite number of prime numbers?

Physicist: Yes.  Here’s a proof (there are many):
1) Assume there are a finite number of primes.
2) Multiply them all together and add 1.
3) This new number is not divisible by any of the original primes so it must be a new prime (or be divisible by at least one new prime).

This means that no matter how many primes exist, there must be at least one more.  But that’s a one way trip to infinity.
This is a contradiction, so the assumption that there are a finite number of primes is hereby debunked.
There are actually dozens of different proofs of “the infinitude of primes” but this one is probably the simplest.

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5 Responses to Q: Are there an infinite number of prime numbers?

  1. David says:

    My favorite is Euclid’s proof. It’s a bit longer, but it might satisfy some skeptics out there…

  2. Pingback: Q: How do you talk about the size of infinity? How can one infinity be bigger than another? | Ask a Mathematician / Ask a Physicist

  3. tanuj says:

    dear physicist all the prime nos. are odd and odd*odd = odd and if u add 1 to it it will make it even and non prime respectively ,there is an authentic euclid concept we don`t want yours.

  4. Dylan says:

    tanuj, But when you add one, you’ll notice that one of the factors is two, a prime number you forgot to consider.

  5. Pingback: Q: How do we know that π never repeats? If we find enough digits, isn’t it possible that it will eventually start repeating? | Ask a Mathematician / Ask a Physicist

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