20030524, 02:57  #1 
May 2003
7×13×17 Posts 
Odd Perfect Numbers
I was just wondering if there is any computer program out there that looks for odd perfect numbers. Currently it has been proven that an odd perfect number must have at least 8 prime factors, but this bound could easily be improved with extensive computations. Anyone out there want to write such a program?

20030528, 19:41  #2 
"Phil"
Sep 2002
Tracktown, U.S.A.
2136_{8} Posts 
I think this would make an interesting project. The Brent, Cohen, and te Riele paper
(reference at http://www.utm.edu/research/primes/references/refs.cgi/BCR91) sketches a proof that any odd perfect number must have at least 8 distinct factors and at least 300 digits. Furthermore, their method of proving this would have discovered such an odd perfect number if one had existed with less than 300 digits. It would be interesting to see how much this bound can be improved with the increase in computing power since then. Since GIMPS can be looked at as the search for even perfect numbers, a search for odd perfect numbers seems a natural complementary project. The beauty of these papers on odd perfect numbers is that they are not extremely technical, and I think most amateur number theorists with only minimal background would be able to understand them. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Is this new formula for Perfect Numbers useful?  mahbel  Miscellaneous Math  20  20170301 22:41 
Right Perfect Prime Numbers  Housemouse  Math  34  20160407 16:29 
Odd Perfect Numbers  davar55  Miscellaneous Math  16  20110129 01:53 
Odd Perfect Number, when will numbers go beyond ecm?  jasong  Factoring  1  20060514 11:28 
Perfect Numbers  MajUSAFRet  Math  3  20031213 03:55 