This page describes some software that I have written, (and some that I didn’t write). And it can be downloaded and used for free! These programs do arithmetic and/or factoring with large integers. (The meaning of “large” varies from one program to another.) These programs run on Windows.

Download (for Windows), version 2.0, last updated on February 6, 2003.

**fact.exe** is a calculator-type program
that runs in a command window on 32-bit or 64-bit Windows.
In addition to calculating,
it can (try to) factor a number using the
“try all divisors” method.

Here is a write-up on how to use this program. There is also an example below showing how the program works.

Version 2.0 of **fact.exe**
includes the “modular inverse” function.
If **e** and **z** are integers, with **gcd(e,z)=1**
(**gcd** = greatest common divisor),
then the modular inverse of **e** mod **z** is the integer **d**
(between 1 and **z**) such that **d * e = 1 mod z**.
**fact.exe** uses the “\” (backslash) character
for the “modular inverse” operator. For example:

e=99,z=1009

d=e\z

d (meaning 99\1009) has the value 265, since 265*99 = 26235 = 1 mod 1009

Note: if **gcd(e,z)>1**, then **e\z** computes **d** such that
**d*e=g mod z**, where **g** is **gcd(e,z)**.
In this case, there is more than one possible value for **d**,
so you get one of the values.
The program also displays a warning message
that the **gcd** is greater than 1.

For example: gcd(6,8) = 2.

6\8 computes the value 7, which works since 7*6 = 42 = 2 mod 8.

The value 3 would also be acceptable, since 3*6 = 18 = 2 mod 8.

fac.exe
is an old 16-bit program similar to **fact.exe**.
However, it is limited to numbers up to about 2400 digits.
This program may be useful if you are still using MS-DOS (without Windows)
or if you are using Windows 3.1.
Otherwise, **fact.exe** is recommended.

Here is a write-up on how to use this program.
It is the same as the write-up for **fact.exe** above.

Shamus has placed **factor.exe** into the public domain,
though I don’t know if it is still available for download.
I downloaded the source code from their website (many years ago),
made a few small changes,
and compiled it
for Windows (32-bit or 64-bit).
Updated on October 7, 1999.

A version of **factor.exe**, which I call
factor2.exe,
works with larger numbers, up to about 280 digits.

Another version of **factor.exe**,
called **factorx.exe**,
tries an additional set of elliptic curves
on numbers larger than 83 digits.
Download it for Windows.

My factoring page has some information on the different factoring methods used by this program.

C:>fact > a=2^99-1? 633825300114114700748351602687=7*23*73*89*199*153649*599479*33057806959 > b=2^127-1 =170141183460469231731687303715884105727 > 3^(b-1)%b =1 > c=2^128+1 =340282366920938463463374607431768211457 > 3^(c-1)%c =47511664169441434718291075092691853899 > x=2^64+1,y=274177,z=x/y =18446744073709551617 =274177 =67280421310721 > y*z=-x =18446744073709551617 =0 > y 274177=PRIME > n=10^29/9 =11111111111111111111111111111 > n 11111111111111111111111111111=3191*16763*43037*62003*77843839397 >

Here are some examples of

You can put the number to be factored on the command line:

C:>factor 12345678910111213141516 first trying brute force division by small primes PRIME FACTOR 2 PRIME FACTOR 2 now trying 1000 iterations of brent's method finally - the multiple polynomial quadratic sieve - with large prime (*) using multiplier k= 1 and 57 small primes as factor base working... 54 trying... working... 55 trying... PRIME FACTOR 2507191691 PRIME FACTOR 1231026625769Or you can use “-f” to indicate a formula. (

(C:\)factor -f 10#41+7 100000000000000000000000000000000000000007 first trying brute force division by small primes PRIME FACTOR 317 now trying 1000 iterations of brent's method PRIME FACTOR 141767 now trying william's (p+1) method phase 1 - trying all primes less than 10000 phase 2 - trying last prime less than 1000000 PRIME FACTOR 1287620401 PRIME FACTOR 1728135292692949031248613And another example:

(C:\)factor -f 10#50+11 100000000000000000000000000000000000000000000000011 first trying brute force division by small primes PRIME FACTOR 3 PRIME FACTOR 37 PRIME FACTOR 47 PRIME FACTOR 1367 now trying 1000 iterations of brent's method now trying william's (p+1) method phase 1 - trying all primes less than 10000 phase 2 - trying last prime less than 1000000 now trying pollard's (p-1) method phase 1 - trying all primes less than 100000 phase 2 - trying last prime less than 5000000 now trying lenstra's method using 10 curves curve 1 phase 1 - trying all primes less than 20000 phase 2 - trying last prime less than 2000000 PRIME FACTOR 82855971825577 PRIME FACTOR 169233693573475517436547188037

Go to my math index page.

Go to my home page.

This page was last updated on: January 30, 2017.