20210225, 08:06  #1 
Aug 2020
79*6581e4;3*2539e3
110001110_{2} Posts 
List of factors on mersenne.ca
Take for example 2^10511. It's listed as fully factored, yet the website only shows 3 of these factors and says "Known prime factors (3 factors, 456.3 bits, 43.41946160% known)".
The 4th factor is mentioned only as "cofactor is a certified prime". When you follow that link you find the full list of factors. Why is it arranged that way? And out of curiosity, what are the "composite factors" in the table used for? 
20210225, 08:26  #2  
"Viliam Furík"
Jul 2018
Martin, Slovakia
1010101000_{2} Posts 
Quote:
Quote:
When any GIMPSused program finds two factors at once (composite factor in TF, or double factor in P1), it is shown as one number, a composite factor. This is most probably the correct explanation. 

20210225, 08:44  #3  
Aug 2020
79*6581e4;3*2539e3
2·199 Posts 
Quote:
But why not just list the 4th factor as P180? The title of the table "Known prime factors" indicates it contains all known prime factors, while it doesn't. Also the sentence about "43.xxx% known" is not correct. Quote:


20210225, 09:41  #4  
Romulan Interpreter
Jun 2011
Thailand
10011000110000_{2} Posts 
It is shown, if you click on "cofactor is..." on the page you linked.
Quote:
Click "hide" if they bother you. On the other hand, James is very responsive to fix bugs and implement features. I guess he may take "attitude" and add the missing composite factors, or fix the percent to 100%, for the fullfactored numbers, but then what to do with numbers of 20 million digits? Technically, the cofactor times all known prime factors is a composite factor (even a proper one, when more than one prime factor is known). Should he display all of those too? An all their combinations? (it would be a pain in the butt to watch those pages ) There must be a line drawn somewhere. And the best "somewhere", we think, is to ignore the cofactor, regardless of it being prime, composite, or unknown. You can grab the data that you need, and do whatever you like with it. Like decrease 1 from each factor, and verify if it is divisible by p (joking, don't do that, they all are ) Last fiddled with by LaurV on 20210225 at 09:45 

20210225, 09:55  #5  
"Viliam Furík"
Jul 2018
Martin, Slovakia
2^{3}·5·17 Posts 
Yes, that is probably because the cofactor is not included in computation of the percentage. But general GIMPS population doesn't care. They know what it means.
Quote:
If the program finds a factor, which is not a prime factor, thus is not included in the list of prime factors, one could think, without trying to factor the exponent, that it is a new prime factor, while it's only composed of already known factors. If the user notices this sooner than PrimeNet factors it, the user can calm down his ecstasy and drop a tear or two, that he didn't find anything new. At least that's how I think of it. 

20210226, 05:13  #6  
"James Heinrich"
May 2004
exNorthern Ontario
DAC_{16} Posts 
Quote:


20210226, 07:01  #7  
Aug 2020
79*6581e4;3*2539e3
2×199 Posts 
Quote:
Quote:
So thanks for that extremely quick fix. Last fiddled with by bur on 20210226 at 07:01 

20210227, 10:02  #8 
Romulan Interpreter
Jun 2011
Thailand
2^{4}·13·47 Posts 

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