Updated July 4, 2006

Recent factorizations of divisors of numbers bⁿ±(b-1)

This page collects factorizations of (divisors of) numbers bⁿ±(b-1) obtained during the last month (roughly speeking). They are sorted with respect to date (the newest first). Other sorting keys (by size of a number, by a base, by an exponent etc.) will be included, when my pages will be "fully automatic" and linked to a data base. See some notes below.

After adding the series 17^8k-16 total number of composites is 13056.

Since April 20, 2006 some all numbers (12742) are in a play: 5734 composities left including 213 numbers without known factors.

Since April 10, 2006 some rules of including results have been changed; The file compos.txt is up to date and contains 3158 integers with no known factors. Some new series have been included.

• When a new series of numbers comes into play, there are many small factors/divisors. They are included in this table in a "bunch" (e.g. 30 #'s 3ⁿ-2) without notes about digits and decompositions.
• It is assumed, as for today, that an individual decomposition is included when
  1. A given number is completely factorized;
  2. A factor of one of the most wanted number (with no known factors) has been found (changes in the first five holes will not be included);
  3. A smaller factor has at least 30 digits (about 2⁸⁰) and factorization has not been done by the ECM;
  4. In the case of any ECM program the lower limit is 35 (decimal) digits (about 100 bits) or B1 equal to at least 1e6.
• The following methods/programs are used to decompose numbers:
  1. Sieving and/or trial factoring, identified as Sieve;
  2. Algebraic (Aurifeuillian) factorization for some b and n;
  3. Quadratic sieve (Msieve, PPSIQS, and PPMPQS);
  4. GMP-ECM v. 6.0.1; it is denoted as ECM with a note, when P±1 method was used;
  5. Mprime (Linux) or Prime95 (Windows) for b=2^k;
  6. NFS (GGNFS) factorization.
  Record factorizations for Quadratic Sieve, Number Field Sieve and ECM are listed in files qs100.txt, nfs100.txt, and ecm100.txt, respectively.
• Only a number of digits is presented in this table (Cdd,Cddd - composites, Pdd, Pddd - primes); numbers themselves have to be looked for at the main page with appropriate links. I hope, it will possible to make direct links from this page soon.
• For the overall project status visit the main page, too.
• For recent updates in primes and PRP's visit the Primes & PRP's page.
• Entries in a column Composites left are given as two numbers: the first is the number of composites in a series considered, whereas the second gives the number of composites left in the whole project.

Contributors

• RB - Robert Backstrom
• RG - Robert Gerbicz
• YUJ - Yeong Uk Jo
• DJ - Donovan Johnson
• MK - Makoto Kamada
• MK - Bryan Koen (from M. Kamada's factorization pages)
• AM - Alexander Mkrtychyan (from M. Kamada's factorization pages)
• AR - Alfred Reich (from M. Kamada's factorization pages)
• WS - Wataru Sakai (from M. Kamada's factorization pages)
• SS - Sinkiti Sibata (from M. Kamada's factorization pages)
• su - suberi (from M. Kamada's factorization pages)

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URL of this page http://perta.fizyka.amu.edu.pl/pnq/recfac1.html
Updated July 4, 2006 by Wojciech Florek (WsF).