Reserve some XYYXF composites


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  First of all, you should choose 1) which composites to factor and 2) which methods to use. After that you should 3) send an e-mail with your decision, then do some factoring work and 4) send your results.

1) Choosing composites.
Every composite has its own name, e.g. C296_149_100, where 296 is the number of decimal digits, 149 and 100 are the values of x and y, respectively. Prime factors are named using the same rule (P43_107_71). The values of x and y may be omitted if they are not needed (e.g., C209_114_79 = P33*P45*C131). The sign after such "short" form means all numbers with number of digits less/greater than or equal to given, e.g. C140+ means composites having 140 or more digits.

You may download a complete list of composites and take some work from it. The composites are sorted by x, then by y; reserved ones are moved to the end of the list and marked as comments.

2) Choosing methods.
First of all, you should know how to factor XYYXF numbers. General information about factoring algorithms will help you to determine which method is more efficient for the composites you are going to reserve.

A few dozens of composites is normal for ECM or P±1. Some work have already been done, please check this list before reservation to avoid wasting your time.

Several composites are usually reserved for NFS or probably QS (if the composite is enough small, say, a C100- cofactor from an ECM effort). When choosing a sieve method, be sure that the composites you want to factor passed enough ECM loops.

There is a good explanation how to use NFS factoring programs, written by Jeff Gilchrist. The smallest composites (roughly, with less than 150 digits) may be factored with GNFS, but sometimes SNFS appears faster. Most of the numbers are good SNFS targets; to build an SNFS polynomial for a given number, feel free to ask our Yahoo! group, or use a program snfspoly.c written by Torbjörn Alm.

Please look through the Records tables, you may have a good chance to occupy some place in them.

3) Sending a choice.
Please take into account some following remarks:

  • all composite cofactors remain reserved as well as the initial composite;
  • be sure that you will be able to obtain some first results within a month;
  • it's unlikely to reserve too many composites at once.
When you have made your decision, please send the list of reservations to our Yahoo! group (if you are not yet a member of the group, use my mailbox). If you are not going to deal with some of your numbers (e.g., large composite cofactors), please let me know which ones you'd like to unreserve and how much ECM work have been done on them.

4) Sending results.
Please send all results of your work to the group or to me as soon as you obtain them. If your factorization fits any of XYYXF Top-20s, you should also report some parameters of the result (e.g., B1 and sigma for an ECM record).

Good luck and happy factoring!

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Andrey Kulsha, Belarus