infinity of primes

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infinity of primes

Postby jjb2011 » Sat Mar 11, 2017 8:55 am

Here is the slickest proof that I have found, it is even more simple than Euclid's proof.
Consider two integers n and the next one n+1 where n>1. Form the product n×(n+1). Now it is true that two consecutive integers have no common factors so the integer nx(n+1) must have at least two different prime factors.Now form the product n x (n+1) x (n+2). By the same argument this integer must have at least three different prime factors. This process can be continued indefinitely so there must be an infinite number of primes.
Nice

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Re: infinity of primes

Postby Gedan » Sat Mar 11, 2017 10:59 am

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Re: infinity of primes

Postby galileo » Sat Mar 11, 2017 1:26 pm

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Re: infinity of primes

Postby jjb2011 » Sun Mar 12, 2017 8:12 pm

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Re: infinity of primes

Postby Gfamily » Sun Mar 12, 2017 10:38 pm

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Re: infinity of primes

Postby jjb2011 » Mon Mar 13, 2017 9:42 am

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Re: infinity of primes

Postby Gfamily » Mon Mar 13, 2017 2:56 pm

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Re: infinity of primes

Postby jjb2011 » Tue Mar 14, 2017 7:25 pm

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