139
edits
Changes
→Flaw in proof
"It is easy to prove that there are an infinite number of primes using Euclid's second theorem. If there were a finite number of primes, you could multiply them all together and add 1. The resulting number would show the existence of a new prime, since it would not be divisible by any smaller prime (it would always have a remainder of 1)." This argument doesn't work. 510511 = 2 * 3 * 5 * 7 * 11 * 13 * 17 + 1, but it's not prime. [[User:Sepura|Sepura]] 13:21, 20 February 2008 (EST)
"It is easy to prove that there are an infinite number of primes using Euclid's second theorem. If there were a finite number of primes, you could multiply them all together and add 1. The resulting number would show the existence of a new prime, since it would not be divisible by any smaller prime (it would always have a remainder of 1)." This argument doesn't work. 510511 = 2 * 3 * 5 * 7 * 11 * 13 * 17 + 1, but it's not prime. [[User:Sepura|Sepura]] 13:21, 20 February 2008 (EST)
:You misunderstand the argument. Since you multiplied only the first 7 primes to get 510510, your hypothesis (the thing to be contradicted in this proof by contradiction) is that those 7 numbers constitute the complete finite set of primes. And in fact, 510511 is not divisible by any of them. Therefore they are not the complete set of primes. And the same argument can be made for any hypothesized finite set. Therefore, no finite set can be the complete set of primes. [[User:Ga ohoyt|Ga ohoyt]] 20:15, 20 February 2008 (EST)