17 Dec
2003
17 Dec
'03
11:17 p.m.
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@rug.ac.be