Odd Perfect Number


A perfect number N is one in which the sum of its divisors equal N.   This means that first perfect number is 6, because 1, 2, and 3 are its divisors, and when added up are equal to 6.

The problem is that it has yet to be proven whether or not any odd perfect numbers exist.


  • Chris Kam Suan Khai
    September 21, 2011

    is it 9 an odd perfect number?


  • Moose
    February 9, 2012

    If the definition is changed and supplemented, I can solve this.

    If you do a Summation Notation of n where the upper limit is the Mersenne Prime, you’ll end up with the same values. If the upper limit is 127 the value is 8128 which is factored to 2^6*127, a perect number.

    If you do 4^n/2 in a summation you’ll end up with a 3 in base 4.

    So if you do the first summation with one of my primes (43), you’ll end up with 946 which is 2*11*43. The two is extra, but the 11 is found with my formula -1. If you do another formula you’ll end up with a prime of 174763 which has a summation of 15271140466 and that is factored to 2*43691*174763. Once again the 2 is extra and the 43691 is my -1 function.

    There is a problem with this. For it to get the prime and the prime before it, both have to be prime. Otherwise you’ll get a prime and a factor of the -1 function.

    I have 18 primes so far up to the 99th term. Btw, there is a very distinct pattern to this formula. I’m pretty sure it’s possible to detect every prime if you use a cubic formula. But I could be wrong.

Post a Reply