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 2021-02-25, 08:06 #1 bur     Aug 2020 79*6581e-4;3*2539e-3 24616 Posts List of factors on mersenne.ca Take for example 2^1051-1. 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 "co-factor 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?
2021-02-25, 08:26   #2
Viliam Furik

"Viliam Furík"
Jul 2018
Martin, Slovakia

769 Posts

Quote:
 Originally Posted by bur Take for example 2^1051-1. 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)".
I would say it's because it's easier to store and generate the page that way.

Quote:
 Originally Posted by bur The 4th factor is mentioned only as "co-factor is a certified prime". When you follow that link you find the full list of factors.
Yes, that's all you need. If you want the remaining factor for whatever reason, you can simply use some simple code (e.g. in Python) and divide the Mersenne by your 3 known factors.

Quote:
 Originally Posted by bur And out of curiosity, what are the "composite factors" in the table used for?
When any GIMPS-used program finds two factors at once (composite factor in TF, or double factor in P-1), it is shown as one number, a composite factor. This is most probably the correct explanation.

2021-02-25, 08:44   #3
bur

Aug 2020
79*6581e-4;3*2539e-3

58210 Posts

Quote:
 Yes, that's all you need. If you want the remaining factor for whatever reason, you can simply use some simple code (e.g. in Python) and divide the Mersenne by your 3 known factors.
I think I now understand that the layout comes from factorizing the number and every time a factor is found it's added, until only one is left and that isn't show because work is done.

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:
 When any GIMPS-used program finds two factors at once (composite factor in TF, or double factor in P-1), it is shown as one number, a composite factor.
But why would that number needed to be shown on mersenne.ca? Especially since it can simply be calculated, just like you said for the remaining factor. They are also only listed for three of the factors, the fourth is not included.

2021-02-25, 09:41   #4
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

234358 Posts

Quote:
 Originally Posted by bur But why not just list the 4th factor as P180?
It is shown, if you click on "cofactor is..." on the page you linked.

Quote:
 But why would that number [composite factor] needed to be shown on mersenne.ca?
Just because the author chose that way to present the information
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 full-factored 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 2021-02-25 at 09:45

2021-02-25, 09:55   #5
Viliam Furik

"Viliam Furík"
Jul 2018
Martin, Slovakia

11000000012 Posts

Quote:
 Originally Posted by bur Also the sentence about "43.xxx% known" is not correct.
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:
 Originally Posted by bur But why would that number needed to be shown on mersenne.ca? Especially since it can simply be calculated, just like you said for the remaining factor. They are also only listed for three of the factors, the fourth is not included.
Yes, sorry, I forgot to continue the explanation.

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.

2021-02-26, 05:13   #6
James Heinrich

"James Heinrich"
May 2004
ex-Northern Ontario

1110110101002 Posts

Quote:
 Originally Posted by bur Take for example 2^1051-1. 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)".
Thank you for pointing out this oversight on my part. The exponent pages have now been corrected to show an entry in the Known Prime Factors section when the last cofactor is PRP (or proven-prime). As on the PRP page, the decimal representation is not shown by default unless it's really small (less than 80 digits) but a click will get you the decimal version.

2021-02-26, 07:01   #7
bur

Aug 2020
79*6581e-4;3*2539e-3

2×3×97 Posts

Quote:
 Originally Posted by Viliam Furik 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.
Ok, thanks.

Quote:
 Originally Posted by LaurV 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.
I didn't mean that all prime factors have to be shown in their full decimal representation regardless of size. Have a look at the site now (manual reload might be required), that's exactly what I meant.

So thanks for that extremely quick fix.

Last fiddled with by bur on 2021-02-26 at 07:01

2021-02-27, 10:02   #8
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

234358 Posts

Quote:
 Originally Posted by bur that's exactly what I meant. So thanks for that extremely quick fix.
and that's what I said, James is quick to fix things. However, he is still yet to beat Scott, who was fixing Misfit just before we were reported the bugs

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