GIMPS-2004年9月13日新闻

碧城仙

M971 factored
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On September 13, 2004 David Symcox found a 53-digit factor for M971. This was the smallest Mersenne number for which no factors were known! Visit this page for information on how your computer can help factor these small Mersenne numbers.
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M971   分解因子(Trail Factoring)

2004年9月13日 David Symcox 发现了M971的一个53-数字因子。 这是我们过去尚不知道的最小的梅森素数的最小因子! 查看该页（http://mersenne.org/ecm.htm）可以查看您的计算机怎样才能帮助析因这些小的梅森素数。

[ Last edited by 碧城仙 on 2005-1-1 at 05:37 PM ]

碧城仙

ECM and P-1 Factoring

GIMPS is also involved in trying to factor numbers of the form 2N-1 and 2N+1 using either the P-1 method or the Elliptic Curve Method (ECM). You can win cash awards
for factoring Fermat numbers, or gain a small footnote in math history by finding a new factor for the Cunningham tables, or improve Paul Leyland's table for Mersenne numbers below 10,000, or improve the Mersenne status page by moving an exponent from the "two LL tests" column to the "factored" column.

To help in this factoring effort, you will need version 16.4 or later of the program. Then download the files of known factors lowm.txt and lowp.txt. Finally, pick a few exponents from the tables on the web pages below and run a few curves. When done, email the results.txt file to me and I will add your curves to the counts below. The program was adapted from Richard Crandall's free program and uses an assembly language implementation of his irrational base discrete weighted transforms algorithm for superior performance. Several important improvements came from Paul Zimmermann and Peter Montgomery. Zimmermann's program is ideal for non-PC platforms.

Each web page below contains a table indicating how much ECM factoring has been done on a number. ECM factoring consists of trying a number of random "curves" using a "bound". A complex formula is used to determine the optimal number of curves to run for each bound. For example, the table on the "2N-1 Cunningham numbers" page shows that you will probably find any 45-digit factors if you run 10,600 curves using a bound of 11,000,000. The table also shows that this has been done for 2727-1 and that some of the 19,300 required curves at the 44,000,000 bound have already been run to try and find any 50-digit factors.

Here are the links to the various factoring projects:
Fermat numbers
2N-1 Cunningham numbers
2N+1 Cunningham numbers
2P-1, P P-1, P > 10000, ECM
2P-1, P-1 Factoring

Last updated: August 25, 1999

[ Last edited by 碧城仙 on 2005-1-1 at 05:36 PM ]