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

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

Dec. 29, 2020 -- Add same search functionality to bulk Factor Submission.
Dec. 28, 2020 -- On Submit Factor in Single Factorization query, search all primitives of algebraic factors and add factor to the appropriate one.
Dec. 27, 2020 Part III -- For Factorizations query, show entries where bases are perfect powers.
Dec. 27, 2020 Part II -- Boost max entries in Factorizations Query from 2000 to 20000.
Dec. 27, 2020 -- Added a "Refresh" button to Single Factorization query. Also, added a "Go Back" button to Submit Factor output.
Dec. 22, 2020 -- Added automatic convert of perfect bases in Single Factorization query. Also, added a "Go Back" button and fixed a bug where only one factor could be added at a time.
Nov. 16, 2020 -- The 115 digits level is finished plus all digits below (ie. the DREGs). New ground level is 116 digits. Also, digit levels now extend up to 500 digits (was 134 digits). And also, updates are now instantly/automatically reflected in the digit level lists. (Yay partial indexes!)
Sep. 26, 2020 -- Adding a new collection of composite sets based on number of digits. Will initially run from 115 digits to 134 digits. Just for fun, composites with less than 115 digits will be called "DREG"s which stands for "Digits Reduced by Ecm to less than Ground level".
Aug. 19, 2020 -- The 114 digits list is finished. Moving on to 115 digits.
Jun. 5, 2020 -- The 113 digits list is finished. Moving on to 114 digits.
Mar. 28, 2020 -- Added label selector to Odd-Perfect Style and Regular composite lists.
Mar. 24, 2020 -- The 112 digits list is finished. Moving on to 113 digits.
Mar. 18, 2020 -- Expanded Skew Optimizer to handle octic polynomials.
Feb. 29, 2020 -- The 111 digits list is finished. Moving on to 112 digits.
Feb. 20, 2020 -- Added a shuffled option and a Max Count to Composites Search.
Feb. 12, 2020 -- Added a Quick Composite Search.
Feb. 11, 2020 -- Added t-level filtering to composites search.
Feb. 10, 2020 -- Added filtering for L and M composite types.
Jan. 1, 2020 -- Happy New Year!
Dec. 26, 2019 -- The 110 digits list is finished. Moving on to 111 digits.
Nov. 18, 2019 -- Added Cunningham Project composites list. For the definitive lists visit the official website.
Nov. 13, 2019 -- The 109 digits list is finished. Moving on to 110 digits.
Oct. 26, 2019 -- The 108 digits list is finished. Moving on to 109 digits.
Oct. 9, 2019 -- The 107 digits list is finished. Moving on to 108 digits.
Sep. 26, 2019 -- The 106 digits list is finished. Moving on to 107 digits.
Sep. 18, 2019 -- The 105 digits list is finished. Moving on to 106 digits.
Sep. 6, 2019 -- The 104 digits list is finished. Moving on to 105 digits.
Sep. 5, 2019 -- Lowest exponent for bases up to 9999 finished. New exponent is 43.
Aug. 22, 2019 -- Smallest composites list updated to 104 digits. (Wow, that one went fast.)
Aug. 11, 2019 -- Smallest composites list updated to 103 digits.
July 10, 2019 -- Smallest composites list updated to 102 digits.
May 16, 2019 -- Extended bases 11 to 99 to exponent 100000.
May 13, 2019 -- Extended bases 5 to 7 to exponent 400000.
May 4, 2019 -- Nice...So, thanks largely to outside help the list of smallest composites has gone down to zero entries. To keep things interesting the max number of digits is now boosted to 101.
Apr. 22, 2019 -- Added option to show composites/unknowns as an expression. Renders the gmp-ecm hint hack moot -- therefore deleting it.
Apr. 15, 2019 -- Smarter limits for Algebraic Factors explorer.
Apr. 10, 2019 -- Extended base 3 to exponent 600000.
Apr. 8, 2019 -- Change Composites list to Composites/Unknowns list.
Apr. 7, 2019 -- Lowest exponent (which was 26) for up to base 19999 completed. New lowest exponent is now 28.
Apr. 6, 2019 -- Nice. Just imported ~110K factors from the Wagstaff numbers project.
Apr. 4, 2019 -- Added options to print composites in Wagstaff and gmp-ecm hint hack formats.
Mar. 23, 2019 -- Base 10 expanded to exponent 300000.
Mar. 22, 2019 -- Base 2 expanded to exponent 2000000.
Mar. 21, 2019 -- Base expanded to 1100000.
Feb. 25, 2019 -- Thanks for the factors whoever you are!
Jan. 1, 2019 -- Happy New Year!
Dec. 9, 2018 -- Sync'd the other way (to Factordb) for the lowest exponent (currently 41) for bases 2 to 9999. Should be easier from now on as just have to worry about new factors after today.
Nov. 7, 2018 -- Oops. comps3 was missing 84 entries from before base 2000 due to a higher level of ecm effort and some bad assumptions :-(.
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 "". 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.

Gzip Files

factors.gz 103MB (10753524 entries -- Jan 31, 2021) newfactors.gz 4.4MB (Dec 31, 2020 to Jan 31, 2021)
factors.gz 99MB (10271655 entries -- Dec 31, 2020) newfactors.gz 3.9MB (Nov 30, 2020 to Dec 31, 2020)
factors.gz 95MB (9834313 entries -- Nov 30, 2020) newfactors.gz 2.1MB (Oct 31, 2020 to Nov 30, 2020)
factors.gz 93MB (9601187 entries -- Oct 31, 2020) newfactors.gz 2.3MB (Sep 30, 2020 to Oct 31, 2020)
comps.gz 61 entries -- last updated December 12, 2020 (Brent-Montgomery-te Riele composite list) reservations (optional)
comps2.gz 360 entries -- last updated August 22, 2020 (lowest exponent (currently 67) for bases <= 999)
comps3.gz 5486 entries -- last updated August 22, 2020 (lowest exponent (currently 43) for bases <= 9999)
opfactors.gz 16MB (last updated Feb 4, 2020) (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)


Sorting: Label:

Header: Expression:

Regular Composite Lists


Sorting: Label:

Header: Expression:

Smallest Composites Lists (base < 10000)

Number of Digits (1-500)(Default is DREGs):

Sorting: Label:

Header: Expression:

Brent-Montgomery-te Riele First Holes

holes.txt (last updated December 12, 2020) 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

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:

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

: (if base > 20K, exponent must be <= 20K) -/+: Details:

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:

Quick Search -- Composites


Label: Expression:


        From Base: 
          To Base: 
    From Exponent: 
      To Exponent: 
      From Digits: 
        To Digits: 
     From t-level: 
       To t-level: 
        Max Count: 



Prime Bases: Prime Exponents: Expression:

First Holes

    From Base: 
      To Base: 

Expanded: Only Prime Bases:

Factor Submission

Format: base, exponent, +/-, prime factor(s) eg. something like, "1338 183+ 11522481893233813410187 515423149345314798403"


Lucas C,D polynomials

Baseup to 20999


Aurifeuillian LMs






"Use the force, Luke."

Free DNS

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