- Macintosh Common Lisp Version 4.3.5 (OS9.2)
- CMUCL 19c (MacOS 10.4)
- clisp 2.41 (Windows XP)
- LispWorks (Windows XP)

- to understand himself what science of the last decades has in stock, to reverse the very simple and fundamental operation of multiplying two integers, in spite of having only basic knowledge in number theory
- to have a ready-to-go, easy-to-use and still powerful LISP module for factoring large numbers.

The run time needed to factor a hard (i.e. two large prime factor) integer n can be read off the following plot. To use it, download the source code (a single Lisp file), compile and load it.
To factor the seventh Fermat number F_{7} = 2^{128}+1, evaluate

(setf *default-float-format* 'double-float) ; clisp produces floating overflows ; for (> n 1e40) without this. (load "ulimyhmpqs"); assumes that (compile-file "ulimyhmpqs.lisp") has ; been done once. (factors (+ (expt 2 128) 1) :report t) ; enables the report shown belowwhich produces the following report and the two factors (59649589127497217 5704689200685129054721).

----------------- 340282366920938463463374607431768211457 ---------------- log10(N) (M 24235) (h(x*)) (a_ideal) (a_primes) ( 4950/619 squares) thr 38.53 4.38 23.50 15.03 1.83 3.45 3.84 6.90 d +0.0 16 fctrbase (B 1156) {-1 2 11 13 17 19 ; 31 37 59 61 67 71 89 97 ... 20731} cub a-error #h(x) equ/min new/min #equ #due done% est/min 0.009 1 .25329% 64 4702.04 4702.04 229 1 19.8 0.254 0.057 2 .74957% 128 4848.89 4996.56 471 6 40.7 0.243 0.106 3 .47386% 192 4989.7 5269.02 729 13 63.1 0.236 0.155 4 .88492% 256 4696.65 4028.18 987 22 85.4 0.261 0.219 5 0.9952% 286 4209.07 2035.99 1083 23 93.7 0.302 0.266 #h(x)*2M/equation non/triv #slp 452 due% saved% 1.386d+7 1.28d+4 1 + 5 0.69% 65536 2.1 6.3 16.0s --------------- (59649589127497217 5704689200685129054721) ---------------

I hope those of you who like Mathematics will enjoy this program. A detailed descrption of the algorithm is available both in english and (slightly older) in german.