There are infinitely many primes
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There are infinitely many primes is a claim of number theory proven through Reductio ad absurdum. The first known instance of a proof dates back to Euclid, c. 300 B.C.[1].
The proof consists in imagining the series of all prime numbers if that series was finite. Multiplying all those prime numbers together and subtracting 1 from the product, one would necessarily arrive at a very large number which would also be co-prime to all other prime numbers. Thus that number would have to be a multiple of some other primes, thus showing that the initial series of prime number was incomplete. Iterated toward infinity, this means that there can be no finite set of all prime numbers.
| Statement of the claim | There are infinitely many primes |
| Level of certainty | Proven |
| Nature | Theoretical |
| Counterclaim | There are a finite amount of prime numbers |
| Dependent on |
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| Dependency of |
References
- ↑ Caldwell, Chris K. (Unknown Publication Date) Euclid's Proof of the Infinitude of Primes (c. 300 BC). Prime Pages, University of Tennessee at Martin. Accessed on January 17, 2022.