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

(Aug. 30, 2017 Part II) Fixed extents for bases and exponents were out of date.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 "". 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 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.)

factors.gz (8156688 entries -- Sept 19, 2017) delta.gz (June 17, 2017 to Sept 19, 2017)
factors.gz (8105557 entries -- June 17, 2017) delta.gz (August 28, 2016 to June 17, 2017)
factors.gz (8095176 entries -- August 28, 2016) delta.gz (August 8, 2016 to August 28, 2016)
factors.gz (7994109 entries -- August 8, 2016) delta.gz (July 31, 2016 to August 8, 2016)
comps (188 entries -- last updated Sept 11, 2017) comps.gz
comps (snapshot) reservations (optional)
holes.txt (last updated Sept 11, 2017) First Holes (snapshot)

opfactors.gz (last updated Sep 24, 2015) (factors for \(p^q-1\) where p is an odd prime, q is prime, and \(p^q-1 < 10^{850}\))

NOTE: When submitting factors, please also update the relevant projects! A good list is found here .
Also, please update the excellent site , which should always be a superset
of this site. Thanks for your cooperation!

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


Paul Underwood's probable prime tester version 0.8.4.

Viswam Raman's SNFS Polynomial Generator.

Optimal Skew


.poly Maker

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

All Candidates:

Single Factorization


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


        From Base: 
          To Base: 
    From Exponent: 
      To Exponent: 

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


        From Base: 
          To Base: 
    From Exponent: 
      To Exponent: 
      From Digits: 
        To Digits: 

Label: ECM Level: Prime Bases: Prime Exponents: Size Sort:

First Holes

    From Base: 
      To Base: 

Expanded: Only Prime Bases:

Factor Submission

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


Lucas C,D polynomials

         Base (max 20999): 


Aurifeuillian LMs






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