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A good concise proof of the infinity of primes

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  • Kermit Rose
    http://www.mathreference.com/num,inf.html impressed me with this concise proof that there are Infinitely Many Primes Suppose there is a finite list of primes.
    Message 1 of 2 , Dec 16, 2007
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      http://www.mathreference.com/num,inf.html


      impressed me with this

      concise proof that there are

      Infinitely Many Primes

      Suppose there is a finite list of primes.
      Multiply them together and add 1, giving n.

      Now n is not prime - it is larger than all the primes on our list,
      which is suppose to be complete.

      So n is composite.

      Let p be a prime in the unique factorization of n.
      Since p is on the list, it divides n-1, as well as n.
      Hence it divides 1, which is impossible.


      There are an infinite number of prime numbers.
    • Jens Kruse Andersen
      ... Good old Euclid has impressed many people. This is one of the most famous proofs in the history of mathematics. I have probably seen it over 100 times. I m
      Message 2 of 2 , Dec 16, 2007
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        Kermit Rose:
        > http://www.mathreference.com/num,inf.html
        > impressed me with this concise proof that there are Infinitely Many Primes

        Good old Euclid has impressed many people.
        This is one of the most famous proofs in the history of mathematics.
        I have probably seen it over 100 times.
        I'm surprised if it's new to a frequent poster to this list.
        If you want to pass 100 in a hurry then try
        http://www.google.com/search?q=Euclid+infinite+primes

        --
        Jens Kruse Andersen
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