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Prove that there are infinite primes

 Jun 5, 2018
 #1
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Euclid's proof:

 

Suppose that \(p_1=2 < p_2 = 3 < ... < p_r\) are all of the primes. Let \(P = p_1\cdotp_2...pr+1\) and let p be a prime dividing P;

 

then p can not be any of \(p_1, p_2, ..., p_r,\) otherwise p would divide the difference \(P-p_1p_2...p_r=1\), which is impossible.

 

So this prime p is still another prime, and \(p_1, p_2, ..., pr\) would not be all of the primes.


laughlaughlaugh

 Jun 5, 2018

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