This page lists logfiles of some sample applications of FactInt. Approximate runtimes are given for a Pentium 200 under Windows. Please note that these examples have been created in 1999, and that recent versions of the package on today's computers permit performing considerably more difficult factorization tasks.
| F8 = 2^(2^8) + 1 | This is just a small example for the use of ECM. Historical remark: This number was at first factored by Brent and Pollard in 1980. Runtime: 1min 45sec (Version 1.1) |
| p(3489) | This shows the rare occurence of an integer with 3 factors `reaching' the MPQS when using the factorization routine with default parameters. Runtime: 5min 47sec (Version 1.1) |
| 158! + 1 | This example shows that also a special method like Pollard's p-1 can sometimes be very useful. Runtime: 5min 57sec (Version 1.1) |
| 1459^60 - 1 | This is an example of an integer with many `aurifeuillian' factors. Runtime: 13min 19sec (Version 1.1) |
| 1093^28 + 1 | In this example, a 24-digit factor is found by ECM. It shows also the use of options. Runtime: about 1h 10min (Version 1.0) |
| 1093^33 + 1 | This example shows the application of the MPQS to a 61-digit integer with two factors of nearly equal size. Runtime: 1h 37min (Version 1.1) |
| 1093^50 + 1 | In this example, a 27-digit factor is found by ECM. Runtime: about 10h (Version 1.0) |
| 3^157 - 2^157 | A 68-digit number is factored by the MPQS. The factors have 32 resp. 36 digits. Runtime: about 30h (Version 1.0) |
| 3^179 - 2^179 | A 69-digit number is factored by the MPQS. The factors have both 35 digits. Runtime: about 65h (Version 1.0) |
| 1093^40 + 1 | The 75-digit cofactor of this number is the largest integer I factored by the MPQS so far. There was some bad luck that I did not find the 23-digit factor by ECM before invoking the MPQS. Runtime: about 100h (Version 1.0) |
| 3^163 - 2^163 | A 73-digit number is factored by the MPQS. The factors have 34 resp. 39 digits. Runtime: about 115h (Version 1.0) |
Here is a table of factorizations of numbers of the form 3k - 2k for k < 300 (with some gaps), obtained using my package.
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