Classic Math gone wrong...Re: (n!+1)^(1/2)
Frank Vernaillen
Frank.Vernaillen at rug.ac.be
Mon Apr 11 18:01:41 PDT 1994
> Scott Collins:
> (...)
> The classic proof goes:
>
> Is there a largest prime number?
> If there is then collect all primes, p1...pn and multiply them
> together p=p1*p2*...*pn. p+1 is not divisible by p1...pn. Therefore
> p+1 is a prime.
This last step (therefore p+1 is a prime) is not totally
correct. You forgot the posibility p+1 NOT prime, but some prime
number <p+1 but >pn divides p+1. This number is prime and >pn.
So in any case there would exist a prime >pn, which contradicts the
hypothesis, and the conclusion is indeed:
> Therefore there is no largest prime
number.
Frank.Vernaillen at rug.ac.be
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