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Are there infinitely many prime numbers?

 Jul 30, 2016
 #1
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Yes!! There are.

 Jul 30, 2016
 #2
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Here is [roughly] Euclid's proof of this......

 

Let the greatest known prime = P

 

Now, multiply all the known primes together [including P ] and let this number  = M

 

Now....add 1 to M.......so.....the new number is M + 1

 

If we divide M + 1 by any of the known primes, we get a remainder .......so...........either M + 1 itself is prime, and therefore greater than the greatest prime, P,  or there exists a prime greater than any of the knowm primes which divides  M and which is also greater than P

 

Therefore.......the list of primes is infinite

 

 

 

cool cool cool

 Jul 30, 2016

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