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→Flaw in proof: comment
: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)
: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)
:: This is only sort of correct. To do it that way makes a proof by contradiction when you would otherwise have a constructive proof. This is suboptimal. [[User:JoshuaZ|JoshuaZ]] 13:58, 23 April 2009 (EDT)
==Why Mathematicians Prefer the Alternative Definition==
==Why Mathematicians Prefer the Alternative Definition==