Difference between revisions of "Any integer bigger than 1 is the multiple of a prime"
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(Created page with "'''Any integer bigger than 1 is the multiple of a prime''' is a basic result in number theory, which can be proved by Reductio ad absurdum. Assume there are integers big...") |
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|Counterclaim=There are integers bigger than 1 that are not multiples of primes | |Counterclaim=There are integers bigger than 1 that are not multiples of primes | ||
|DependentOn1= | |DependentOn1= | ||
| | |DependencyOf1=There are infinitely many primes | ||
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==References== | ==References== | ||
<references/> | <references/> | ||
Revision as of 01:53, 19 January 2022
Any integer bigger than 1 is the multiple of a prime is a basic result in number theory, which can be proved by Reductio ad absurdum.
Assume there are integers bigger than 1 that are not the multiple of a prime, and let a be the smallest of them. Therefore every integer between 1 and a is the multiple of a prime. If a was a multiple of any number between 1 and a it would therefore also be a multiple of a prime, contradictory to our assumption. But a can neither be a multiple of an integer bigger than itself. So a is only divisible by itself and 1, making it prime, again in contradiction to the assumption. So the assumption has to be false.
| Statement of the claim | Any integer bigger than 1 is the multiple of a prime |
| Level of certainty | Proven |
| Nature | Theoretical |
| Counterclaim | There are integers bigger than 1 that are not multiples of primes |
| Dependent on |
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| Dependency of |