20061127, 19:42  #1 
"Jason Goatcher"
Mar 2005
3·7·167 Posts 
How much work would these numbers take?
For those of you familiar with wblipp and his Odd Perfect Number search, you probably know he's searching for factorizations to increase the minimum bounds of what an Odd Perfect Number should be above. He has had the same two numbers in the "Most Wanted" server for what seems like a long time.
The numbers are 3221^731 and 2801^791. I believe one is at the 60digit level and the other is at the 55 or 50 digit level. I haven't run the ecm client in a while, so I'm not sure which is which. I'm wondering how much work it it would take to attempt these factorizations with a method other than ecm. I can't even begin to understand the math involved in these other programs I've heard about, but I have a dualcore 2.8GHz PentiumD to help in whatever way it can. For those of you who want to argue about whether OPNs exist or not, I'm not saying they do or don't. I'm only interested in increasing the lower bounds, which are now around 10^500. Your opinion is appreciated. 
20061127, 20:59  #2 
"Jason Goatcher"
Mar 2005
3×7×167 Posts 
When I wrote the above, it was in reference to what type of factor the ecm curves were expected to find, if they found anything. Sorry for any confusion I may have caused.

20061127, 21:04  #3  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
10101110001001_{2} Posts 
Quote:
3221^731 has 257 digits, so the naive SNFS approach would take, to a quite good approximation, rather a long while. It's smaller than the record holder, but bigger than any others so far reported. The top two, according to Sam Wagstaff's newsletters, have 274 and 248 digits. The other number has 273 digits and so also falls between the record holders. Again, it would be distinctly nontrivial by SNFS but possible  if anyone cared enough about it. I don't immediately see any way of reducing the SNFS difficulty, but that's an admission of ignorance and not a statement of its impossibility. Paul 

20061128, 19:31  #4 
Mar 2004
Belgium
5×13^{2} Posts 
Jasong,
I suggest you do ecm on these numbers first. If you find a factor, it will probably reduce the number. Regards C. 
20061128, 19:52  #5  
Nov 2003
16444_{8} Posts 
Quote:
in this range still leaves the cofactor too big to handle with GNFS. And pulling out a factor does not help SNFS at all. One can only hope that the (resulting) cofactor is prime. 

20061128, 21:03  #6 
Mar 2004
Belgium
845_{10} Posts 
That's true, but if you can reduce the size to decent level, e.g. 150180, it would stand a much better chance to do SNFS on it.
I know, the better approach is to put these number in an ecmnet server, and let several people work on it thus increasing the chance of finding a factor. Crunching alone with that kind of HW, it will be tricky.... My $0.02 
20061128, 21:21  #7 
"Sander"
Oct 2002
52.345322,5.52471
29·41 Posts 

20061129, 01:42  #8  
Nov 2003
2^{2}·5·373 Posts 
Quote:
When I say something, I do so for a reason. Allow me to ask: How many numbers have you factored with SNFS? What qualifies you to contradict an expert on the subject???? Finding a prime factor (that leaves a composite cofactor) of a number that is suitable for SNFS DOES NOT HELP AT ALL. NADA. ZILCH. 

20061129, 02:12  #9  
Tribal Bullet
Oct 2004
3×1,181 Posts 
Quote:
jasonp 

20061129, 05:27  #10  
Mar 2004
Belgium
5·13^{2} Posts 
Quote:
My largest was a c131 with SNFS difficulty of c141. No it would probably won't help for SNFS purposes ... that you are right. Last fiddled with by ValerieVonck on 20061129 at 05:28 

20061129, 10:59  #11  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2B89_{16} Posts 
Quote:
If enough factors are found by ECM to reduce the composite cofactor to, say, 160 digits factoring that residue becomes feasible by GNFS (though still not easy) and easier than SNFS on the full number. Here I confess my laziness. I do not know the size of the unfactored portions of the two numbers and can't be bothered to find out. If you (i.e. CedricVonck) want to do something slightly useful, please find out that information and post it here. Then work out how much ECM effort is likely to be needed before any factors found will reduce the residue to GNFS range. Paul 

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