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Wilson's Theory and the number 1

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  • paxtontravis
    For those not familiar with Wilson s Theory: P is a prime number if, and only if, (P-1)! + 1 is divisible by P. Now take the number 1, (1-1)! + 1 = 0! + 1 = 2.
    Message 1 of 2 , Mar 1, 2005
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      For those not familiar with Wilson's Theory: P is a prime number if,
      and only if, (P-1)! + 1 is divisible by P.

      Now take the number 1, (1-1)! + 1 = 0! + 1 = 2.
      2 is divisible by 1, so why isn't 1 prime?
    • Hadley, Thomas H (Tom), ALABS
      Here is the definition of Wilson s Theorem from the Prime Pages: http://www.utm.edu/research/primes/notes/proofs/Wilsons.html Wilson s Theorem. Let p be an
      Message 2 of 2 , Mar 1, 2005
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        Here is the definition of Wilson's Theorem from the Prime Pages:
        http://www.utm.edu/research/primes/notes/proofs/Wilsons.html

        Wilson's Theorem.
        Let p be an integer greater than one. p is prime if and only if (p-1)! = -1 (mod p).

        You seem to have left out the first part.

        Tom Hadley

        -----Original Message-----
        From: paxtontravis [mailto:paxtontravis@...]
        Sent: Tuesday, March 01, 2005 11:06 AM
        To: primenumbers@yahoogroups.com
        Subject: [PrimeNumbers] Wilson's Theory and the number 1




        For those not familiar with Wilson's Theory: P is a prime number if,
        and only if, (P-1)! + 1 is divisible by P.

        Now take the number 1, (1-1)! + 1 = 0! + 1 = 2.
        2 is divisible by 1, so why isn't 1 prime?






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