GIMPS factors
 

Yesterday Sep 3rd I ran a script to get all the known factors from the server. There were 35,504,331 factors from 28,300,589 different exponent between p=11 and p=999,999,893. I thought if someone else was interested in the list, they can get it from me. The script ran from ~ 3pm GMT to midnight yesterday Sep 3rd, so future factors can be added by searching known factors found since 2014-09-03.

I concatenated it to one big text file retaining the format: <exponent> comma <factor> like in the known factor list, but without the explaining "Exponent,Factor" line at the top:
[url]http://www.mersenne.org/report_factors/?exp_lo=1&exp_hi=1000&exp_date=&fac_len=&txt=1&B1=Get+Factors[/url]

The text file is 902,512,106 bytes and compressed with 7zip it is a 290,909,226 bytes file. A file this size can only be opened by a non-standard text editor, I use one called Textpad.

This is only for people who are really going to use it for something, otherwise it is just a waste of bandwidth for both of us and a waste of space and time for you:
[URL="http://www.hoegge.dk/mersenne/factors.zip"]factors.zip[/URL] (This is just a small .torrent file that is zipped, otherwise it was blocked)

You can save some more size by storing 'k' (of 2kp+1) instead of the factor.

That is true and I have actually checked the numbers of factors with different k's.

First there is no new examples where k=c*p, so the factor is 2*c*p^2 + 1, still only the one example: p=93077, c=674487.

Here is a list of numbers of factors of each k-value up to k=1024, and a graph of some of the values:
[URL="http://www.hoegge.dk/mersenne/mersennefactors1.txt"]mersennefactors1.txt[/URL] [URL="http://www.hoegge.dk/mersenne/mersennefactors1.png"]mersennefactors1.png[/URL]

For k=2 (mod 4) there is no factors since for those k-values 2kp+1 is not +/- 1 (mod 8) for any prime p.
The number of factors goes down with higher k, but for each k=12*n there seems to be a local peak. The lowest number of factors seems to be at the prime k-values.

Here is a list of all the factors ordered by the length of k in binary, so that is factors where 2[sup]n-1[/sup] <= k < 2[sup]n[/sup]: (note that n=1 is just k=1, n=2: k=3, n=3: k=4,5,7)
[URL="http://www.hoegge.dk/mersenne/mersennefactors2.txt"]mersennefactors2.txt[/URL]
All the missing n-values have 0 factors of that length.

Could you give a summary of count of factors for each digit?

[QUOTE=ATH;382167]Yesterday Sep 3rd I ran a script to get all the known factors from the server.

[/QUOTE]

Purpose?


[QUOTE]

<snip>
A file this size can only be opened by a non-standard text editor, I use one called Textpad.
[/QUOTE]

Please define for us: 'standard' vs. 'non-standard' text editor.

[QUOTE]
This is only for people who are really going to use it for something, otherwise it is just a waste of bandwidth for both of us and a waste of space and time for you:
[/QUOTE]

Teach me. What 'use' do you think there might be for this data?

[QUOTE=wreck;382195]Could you give a summary of count of factors for each digit?[/QUOTE]

Huh? "For each digit"??? What does this mean? Each digit of what?

[QUOTE=ATH;382174]That is true and I have actually checked the numbers of factors with different k's.

First there is no new examples where k=c*p, so the factor is 2*c*p^2 + 1, still only the one example: p=93077, c=674487.

Here is a list of numbers of factors of each k-value up to k=1024, and a graph of some of the values:
[URL="http://www.hoegge.dk/mersenne/mersennefactors1.txt"]mersennefactors1.txt[/URL] [URL="http://www.hoegge.dk/mersenne/mersennefactors1.png"]mersennefactors1.png[/URL]

For k=2 (mod 4) there is no factors since for those k-values 2kp+1 is not +/- 1 (mod 8) for any prime p.
The number of factors goes down with higher k, but for each k=12*n there seems to be a local peak. The lowest number of factors seems to be at the prime k-values.

Here is a list of all the factors ordered by the length of k in binary, so that is factors where 2[sup]n-1[/sup] <= k < 2[sup]n[/sup]: (note that n=1 is just k=1, n=2: k=3, n=3: k=4,5,7)
[URL="http://www.hoegge.dk/mersenne/mersennefactors2.txt"]mersennefactors2.txt[/URL]
All the missing n-values have 0 factors of that length.[/QUOTE]

What is your goal in performing all of this numerology? Is there some
question that you are trying to answer?

[QUOTE=ATH;382167]Yesterday Sep 3rd I ran a script to get all the known factors from the server.[/QUOTE]

Are you aware of [URL="http://www.garlic.com/~wedgingt/mersenne.html"]Will Edgington's Mersenne Page[/URL], which tracks all know factors of Mersenne numbers, including composite exponents? Crosschecking these lists might turn up some new factors for one or the other.

[QUOTE=R.D. Silverman;382199]Huh? "For each digit"??? What does this mean? Each digit of what?[/QUOTE]
I mean the count of factors between 10^x to 10^(x+1).
Just for curious, I have do similar things of sorting all the factors from 10^n - 1.
and the attached file showed the summary of factor counts for each digit, where x is from 1 to 200, and the factor is from number 10^n-1, 1 <= n <= 100000.

[QUOTE=wreck;382213]I mean the count of factors between 10^x to 10^(x+1).[/QUOTE]

I assume you mean the list for the length of the entire factors 2kp+1:
[URL="http://www.hoegge.dk/mersenne/factorlength.txt"]factorlength.txt[/URL]

but here is also the length of the k-values:
[URL="http://www.hoegge.dk/mersenne/klength.txt"]klength.txt[/URL]

To make RDS happy, and to prove that solving a problem usually results in two new problems, I have a good purpose for this list: how to define an algorithm to pack it as tough as possible. Hehe... I already have a way to make it about 1/8 of the original size. Thoughts? You can rearrange the data any way you like, and then use any common packer (like the 7z already mentioned, pkzip, rar, etc) available. Of course, when you pre-arrange the data, you use the special properties of the factors (and this is where the connection with the math is done), the "method" will not have to work for any text file, only for this special file.
:smile:

(p.s. buddy, either your bandwidth sucks, :razz: or you have special settings for Thailand, it crawled all the night with 3 to 5 kilobytes per second and still only 80% completed. I will DLD it and seed it for a while with "normal" speed... hehe)