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My Factor Collection -- \(a^n\pm1\)


July 5, 2018 -- Lowest exponent (which was 22) for up to base 99999 completed. New lowest exponent is 23.
June 18, 2018 -- New utility added for showing algebraic factors.
June 10, 2018 -- Lowest exponent (which was 40) for up to base 9999 completed. Newest lowest exponent is 41.
June 3, 2018 -- Lowest exponent (which was 38) for up to base 9999 completed. New lowest exponent is 40.
May 28, 2018 -- So I've switched over to developing all Linux stuff using Ubuntu bash under Windows for the last 2 years. This is waaaay more convenient if you're just dealing with non-gui stuff. Here is a guide from Scott Hanselman.
May 23, 2018 -- Nice practical guide on how to factor numbers by Victor de Hollander can be found on mersenneforum here.
Apr. 17, 2018 -- Lowest exponent (which was 19) for up to base 99999 completed. New lowest exponent is 22.
Apr. 7, 2018 -- Lowest exponent (which was 23) for up to base 19999 completed. New lowest exponent is 26.
Apr. 5, 2018 -- Odd-Perfect Style Composite lists ecm'ed to t25 level.
Jan. 9, 2018 -- Due to popular demand (of a singular nature) Odd Perfect Style composite lists are now added. Cheers.
Jan. 1, 2018 -- Happy New Year! So, comps3 (exponent 37) finished. Mooving on (get it?) to exponent 38 for same base range 2 to 9999. All comps ecm'ed to the t35 level at least. Cheers.
Dec. 10, 2017 Part III -- Added a shuffled snapshot option to comps2 and comps3.
Dec. 10, 2017 Part II -- Added comps3 file. This will be the lowest unfinished exponent in the base range 2 to 9999. Composites ecm'ed to t30 level.
Dec. 10, 2017 -- Added comps2 file. This will be the lowest unfinished exponent in the base range 2 to 999. Composites ecm'ed to t40 level.
Oct. 14, 2017 -- Added an expanded LucasCD file which goes from base 2 to base 998.
Aug. 30, 2017 Part II -- Fixed extents for bases and exponents were out of date. Base 8675309 added.
Aug. 30, 2017 -- Fixed phone number format recognition being detected for entries in First Holes and Factorizations.
April 10, 2017 -- Received a report that the "mooo" domain name was not accessible from a certain ISP. Therefore, I'm adding the alternate url "myfactors.cownoise.com". Cheers.
June 30, 2016 -- Removed the pari dependencies from the source files for the Aurifeuillian LMs and Primitive(s) calculators. (By the way, they compile quite easily on linux bash shell for Windows 10 now.
June 9, 2016 -- Tweaked the Lucas CD output (now more human-readable).
May 20, 2016 -- Fiddled with the composites report.
May 18, 2015 -- Modified the SNFS poly generator to output coefficients of 0. Apparently, a newer version of perl causes factMsieve.pl to break. This is a workaround.
Feb. 7, 2014 -- Yay! We broke through the 300 composites level for the Brent composites! Keep them coming! Unfortunately for myself, my reservation is a slow go. Maybe another 2 months.
Jan. 1, 2014 -- Happy New Year to everyone!!!!
Oct. 8, 2013 -- Added degree 6 polynomials for exponents divisible by 3 to the .poly maker. Thanks to Viswam Raman's SNFS polynomial generator.
July 1, 2013 -- Updated the "cyclo.cpp" and "cyclop.cpp" source files for a speed improvement.
May 3, 2013 -- The .poly maker will now compute a value for n if none is given and there is no table entry. Also, small factors less than 8 digits in size will be divided out.
Apr. 30, 2013 -- A few minor updates. Ecm tlevel has been added to the composites query. Full factorizations and composites can now be filtered on prime exponents. Optimal skew calculator is now more accurate and shows nearby skews and MurphyE values. The .poly Maker now shows only one .poly by default with an option to show all candidates. (Still needs more work on how to pick the best .poly between different degrees.)
Mar. 21, 2013 -- Sharp eyes may notice that one factor disappeared from factors.gz this time. This was due to a factor (from \(3785^{66} + 1\)) later determined to be an ultimate (ie. largest factor from the primitive portion) factor which is not supposed to be included.
Mar. 3, 2013 -- Finally got around to implementing the extra polynomials for composite bases in the SNFS Polynomial Generator. Still needs LM's and a lot of tweaking.
Feb. 17, 2013 -- Apparently, there is a bug with the MurphyE's on the older msieve libraries. Now linking with svn 839 of the msieve library and noticing the MurphyE's have changed downwards.
Feb. 13, 2013 -- Added a little utility for optimizing the skew (for maximum MurphyE). Thanks to msieve library!
Feb. 10, 2013 -- Added the SNFS Polynomial Generator. Still needs functionality for composite bases and LM's.
Jan. 26, 2013 -- A big thanks to William Lipp of the Odd Perfect Number Search project. (24171 new factors).
Jan. 23, 2013 -- Adding a filtered list of factors -- "opfactors.gz" -- for data exchange with the oddperfect project.
Jan. 19, 2013 -- The first holes report is finished. Time to work on something more interesting like an SNFS polynomial generator. It's partially completed, so apprx. one week to finish.
Jan. 14, 2013 -- The new comps report is finished. (I suppose the proper terminology is "snapshot", not "live"). Next project is to revisit the "holes.txt" and make it more closely resemble the original.
Jan. 11, 2013 Part II -- A big thanks to Rocke Verser for sharing his private factor collection! 3818 new factors were added including 3 from the "comps" file and quite a few large factors as well!
Jan. 11, 2013 -- comps.gz is produced. The new count is 454 which is a reduction of 219 entries from the May 5, 2011 list or apprx. a 1/3 reduction in size. The next short step for the website will be making the comps list live.
Jan. 9, 2013 -- Ok, the last factors from Prof. Brent arrived yesterday. They are now assimilated into the db. factors.gz is also updated and I've added a delta.gz which is just the new factors since the last update. Next job will be producing the comps.gz file. It shouldn't be too big a job.
Jan. 7, 2013 -- I've agreed to maintain Prof. Richard Brent's "comps.gz", "factors.gz", and "holes.txt" files. Well, at least until "comps.gz" has been completed. For "comps.gz", I'm going to have to do a little coding, since I don't have a report exactly like that yet. That'll take a couple days. Also, I'll need the latest factors from Prof. Brent. For "factors.gz", I've got a report already set up and I'll put it on the website right away. For "holes.txt" my plan is to modify the "First Holes" report to use the "GET" method instead of the "POST" method. This will enable an http link to suffice for showing the first holes.

Gzip Files

factors.gz (8402991 entries -- Sep 30, 2018) delta.gz (Aug 31, 2018 to Sep 30, 2018)
factors.gz (8402697 entries -- Aug 31, 2018) delta.gz (Jul 31, 2018 to Aug 31, 2018)
factors.gz (8402358 entries -- Jul 31, 2018) delta.gz (Jun 30, 2018 to Jul 31, 2018)
factors.gz (8382511 entries -- Jun 30, 2018) delta.gz (May 31, 2018 to Jun 30, 2018)
comps.gz 160 entries -- last updated Oct 20, 2018 (Brent-Montgomery-te Riele composite list) reservations (optional)
comps2.gz 493 entries -- last updated Dec 10, 2017 (lowest exponent (currently 67) for bases <= 999)
comps3.gz 2876 entries -- last updated Sept 1, 2018 (lowest exponent (currently 41) for bases <= 9999)
opfactors.gz (last updated Sep 24, 2015) (factors for \(p^q-1\) where p is an odd prime, q is prime, and \(p^q-1 < 10^{850}\))

Odd-Perfect Style Composite Lists (\(p^q-1\); p is an odd prime, q is a prime, p & q < 10000)

List:

Sorting:

Header: Label: Expression:

Regular Composite Lists

List:

Sorting:

Header: Label: Expression:

Brent-Montgomery-te Riele First Holes

holes.txt (last updated October 20, 2018) First Holes (snapshot)


Other Active Overlapping DB Sites

Cunningham Project \(a^n \pm 1; a \in \{2, 3, 5, 6, 7, 10, 11, 12\}\)
GIMPS Project \(2^p - 1\)
ECMNET Project ecm factors >= 60 digits; Cunningham Project factors
Studio Kamada \(10^n \pm 1\)
FactorDB all factors (but use judgement when x-posting factors as it may be considered spam.)

About The Site

First, a bit of history. This website originally started up around December, 2011. It really wasn't much of anything at first. There was only a basic reporting capability. The title was chosen since most of the factors were found by myself, but that really isn't saying much since they were all relatively easy to find ~20 digits numbers. (The goal is that eventually the "My" part will be the visitor's perspective. To accomplish this, there is still work to be done -- such as adding user logins and streamlining the whole factoring process.) Throughout 2012, small pieces of functionality have slowly been added as time permitted. On Jan, 2013, three of Prof. Brent's lists moved over here.

The site's goal is to successively knock down all the barriers to factoring for anyone no matter their level of expertise. The first barrier is coming up with a composite. The Cunningham Project and Prof. Brent's list give these composites, but from limited sets. If your interest lies outside these sets, then the potential factorer is faced with having to perform a lot of research into algebraic factors and possibly writing their own computer code. Most people would just give up when facing that. Another issue is not repeating work that is already performed. That is one reason factors are locally stored here -- for quick access in computing the minimum size composites. The next barrier is determining the particular factoring method to use. This is highly dependant on the expected size of potential factors, the size of the number, and the "SNFS" polynomials that can be found. To some extent the amount of computer resources (such as memory and hard drive space) available will also play a role. After that, the factoring programs must be located on the internet and installed. (Fortunately, the new yafu program is rapidly combining all the necessary functionality into one program.) Database connectivity and coordination across multiple computers also needs to be addressed.

Progress has been somewhat slow so far. I am however quite excited to see what the next few improvements will bring in terms of who is doing the factoring and the quantity of factoring. Hopefully these improvements will come on stream in the next few months. Time will tell as always.



-- Jonathan Crombie





Misc.


Paul Underwood's probable prime tester version 0.8.4.

Viswam Raman's SNFS Polynomial Generator.


Optimal Skew

             c6: 
             c5: 
             c4: 
             c3: 
             c2: 
             c1: 
             c0: 
             Y1: 
             Y0: 
  


.poly Maker

     (optional) n: 
             Base: 
         Exponent: 
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   (optional) L/M:   (LM only sort of working for bases 2,3,5,6,7,10,11 and 12)
  

All Candidates:


Algebraic Factors for \(a^n\pm1\)

                
a2..99999
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n1..10000
: -/+: Details:

Single Factorization

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Expanded: Separate L,M's: Only Algebraic Factors: Only Table Entries:


Factorizations

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Expanded: Separate L,M's: Only Algebraic Factors: Only Table Entries: Prime Bases: Prime Exponents:


Composites

        From Base: 
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      To Exponent: 
      From Digits: 
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Label: ECM Level: Prime Bases: Prime Exponents: Size Sort:


First Holes

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Expanded: Only Prime Bases:


Factor Submission


Format: base, exponent, +/-, prime factor(s)

  
  


Lucas C,D polynomials

                     
Baseup to 20999
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2-199
2-998


Aurifeuillian LMs

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Source


Primitive(s)

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Source


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Top Downloads Odd Perfect Lists Composite Lists Other Sites History Misc. Skew Optimizer .poly Maker Algebraic Factors Single Entry Multiple Entry Composites First Holes Factor Submission Lucas C,D Aurifeullian LMs Primitives