Difference between revisions of "Euclid's proof of the infinitude of primes"
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Revision as of 18:21, 15 January 2007
This is proved by contradiction. Suppose there is a finite number of primes and let them be . Let
. Then we have
. When divided by any of the primes
,
leaves a remainder of 1 implying that either
is prime or that it has some other prime factors not in the set
. In any case we have it so that
does not contain all prime numbers. Contradiction!