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Re: [PrimeNumbers] Fermat twin prime theorem

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  • Joseph Moore
    Well, I ll take a guess... perhaps (n-1)!+1 is not congruent to 0 mod (n+2)? Joseph. ... __________________________________ Do you Yahoo!? Read only the mail
    Message 1 of 2 , Dec 11, 2004
      Well, I'll take a guess... perhaps (n-1)!+1 is not
      congruent to 0 mod (n+2)?

      Joseph.


      --- "John W. Nicholson" <reddwarf2956@...>
      wrote:

      >
      >
      > == means congruent
      >
      > Wilson's theorem for twins is
      >
      > Let n>=2. The integers n and n+2 form a pair of twin
      > primes iff
      >
      > 4[(n-1)!+1] + n == (mod n(n+2))
      >
      > But,
      >
      > (n-1)!+1 == 0 (mod n)
      >
      > and by a Corollary of Fermat treorem with (a,n)=1,
      >
      > a^(n) - a == 0 (mod n)
      >
      > so,
      >
      > a^(n)-a == (n-1)!+1 == 0 (mod n).
      >
      > Therefore,
      >
      > 4(a^(n)-a) + n == 0 (mod n(n+2))
      > or
      > 4*a^(n) - 4*a + n == 0 (mod n(n+2))
      >
      >
      > If it has not been stated before, I am surprised.
      >
      >
      >
      >




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