- 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);
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.
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