
#19
Jul2411, 12:06 PM

P: 455

More important, remember that you're assuming that there is no prime greater than p_{n} (which is 13 in the example). Euclid's reasoning shows that no prime <= p_{n} divides q. Under the assumption that there IS no prime greater than p_{n}, there must therefore be no prime that divides q. The example doesn't contradict this, because the smallest prime that divides 30031 is in fact bigger than 13. 



#20
Jul2511, 07:20 PM

P: 69

Euclid's proof shows that if P + 1 is not prime, then P + 1 can not be divided by a prime number in the finite set of prime numbers since when you divide P + 1 by a factor of P, that factor will end up dividing 1. [itex]\frac{(P + 1)}{factor of P}= factor of P\times(something) + \frac{1}{factor of P}[/itex] 


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