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Osher Doctorow,
I was following you right up until the last
paragraph, where you seem to have some misinformation on Perfect Numbers and
Mersenne Primes.
... Also, any even perfect number has form
2^^(r-1)(2^^r - 2) ...
Nope, perfect numbers have the form 2^^(r - 1)(2^^r
- 1), examples :-
where r = 2 ---> 2^^(1)(2^^2-1) = 2 x 3 =
6
where r = 3 ---> 2^^(2)(2^^3-1) = 4 x 7 =
28
where r = 5 ---> 2^^(4)(2^^5-1) = 16 x 31
= 496
A Perfect Number can only be made (as far as I
know) by taking a Mersenne Prime, and multiplying it by 2 to the power of
the Prime Exponent minus 1. So M(5) = 31, P(5) = 31 * (2^^4).
This is unless someone manages to find an odd
perfect number (which personally I doubt exists).
... if 2^^r and r are prime ... ?
Erm, regardless whether r is prime or composite,
2^^r is always composite (2x2x2x........x2) !
... The Mersenne primes have form 2^^r - 2 for r
prime, of course ...
Of course not, Mersenne primes have form 2^^r - 1
!
Regards
Dave
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