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## #1 2018-06-22 04:58:25

Primenumbers
Member Registered: 2013-01-22
Posts: 147

### Mersenne Number Factors Using Minus 1 Divided By 2

Mersenne numbers are of the form 2^p -1.
If I minus 1 and divide by 2 it will take p goes to get to zero.
Example:

2^11 -1
2^10 -1           First go
2^9 -1            Second go
2^8 -1            Third go
2^7 -1             Fourth go
2^6 -1             Fifth go
2^5 -1             Sixth go
2^4 -1             Seventh go
2^3 -1             Eighth go
2^2 -1             Ninth go
2-1                  Tenth go
1-1=0              Eleventh go

Similarly if 2^p -1 has a factor of the form, n, it should take p goes to get to zero. Only, if minus 1 divided by 2 results in an even number, I should be allowed to add n to the number to continue. As this is what happens to n, as a remainder for 2^p -1, as each go takes place.
Examples:

23
(23-1)/2 = 11                                First go
(11-1)/2 = 5                                  Second go
(5-1)/2 = 2                                   Third go
23+2 = 25, (25-1)/2 = 12           Fourth go
23+12 = 35, (35-1)/2 = 17         Fifth go
(17-1)/2 = 8                                  Sixth go
23+8 = 31, (31-1)/2 = 15            Seventh go
(15-1)/2 = 7                                  Eighth go
(7-1)/2 = 3                                    Ninth go
(3-1)/2 = 1                                    Tenth go
(1-1)/2 = 0                                     Eleventh go

89
(89-1)/2 = 44                                  First go
89+44 = 133, (133-1/2) = 66       Second go
89+66 = 155, (155-1)/2 = 77       Third go
(77-1)/2 = 38                                  Fourth go
89+38 = 127, (127-1)/2 = 63        Fifth go
(63-1)/2 = 31                                  Sixth go
(31-1)/2 = 15                                   Seventh go
(15-1)/2 = 7                                     Eighth go
(7-1)/2 = 3                                       Ninth go
(3-1)/2 = 1                                       Tenth go
(1-1)/2 = 0                                        Eleventh go

Both 23 and 89 take eleven goes to get to zero, as they must do, as they are factors of 2^11 -1, and 2^11 -1 takes eleven goes to get to zero also.

"Time not important. Only life important." - The Fifth Element 1997

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