3 ms·
Can't wait to use this to prove that are infinite primes. :P
by postit 13y ago
Can't wait to use this to prove that are infinite primes. :P
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- michael_nielsen 13y agoVery amusing. Here's a proof by contradiction, for the record. Assume that there are only a finite number, n, of prime numbers. There are at most n^3 distinct odd numbers that can be formed as a sum of three of those primes. But n^3 is finite, and so the number of odd numbers must be finite, which is, of course, false, and so our original assumption must have been false. QED There are some hilarious variations on this theme (using difficult theorems to prove simple facts) here: http://mathoverflow.net/questions/42512/awfully-sophisticated-proof-for-simple-facts http://mathoverflow.net/questions/42512/awfully-sophisticate...
- SatvikBeri 13y agoAssume there are a finite number of primes. Let p be the largest prime. Then 3p+2 is an odd number > 5, so it must be expressible as the sum of 3 primes. But since p is the largest prime, the sum of 3 primes can never be larger than 3p, contradiction.
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