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Theorem

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  • FILIPPO GIORDANO
    If the respective values of Mersenne p of perfect numbers are known, then the respective last ciphers can be calculated by the following operation: p/4. Such
    Message 1 of 1 , Dec 31, 2001
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      If the respective values of Mersenne p of perfect numbers are known, then the respective last ciphers can be calculated by the following operation: p/4. Such division will give a variable quotient with a constant rest equal to 0,25 or 0,75 (except p=2, unique p pair that has a 0,50 rest). When the rest is equal to 0,25 the last cipher is 6; when the rest is equal to 0,75 the last cipher of the perfect is 8.

      Mersenne p = 3;
      3/4 = 0,75 = last cipher of perfect number = 8 (28);
      Mersenne p = 5;
      5/4 = 1,25 = last cipher of perfect number = 6 (496);
      Mersenne p = 7;
      7/4 = 1,75 = last cipher of perfect number = 8 (8128);
      Mersenne p = 13;
      13/4 =3,25 = last cipher of perfect number =6 (33550336);
      etc.

      Theorem (from my "Primi di Mersenne e numeri perfetti"):
      Look at the value of Mersenne p (except p=2).
      If p/4 = X,25, then the last cipher it's always 6.
      If p/4 = X,75, then the last cipher it's always 8.
      Filippo Giordano


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