Please report any factorizations you find to me by email and inform me of which algorithm you used to find them. Additional information is also welcome: this may include NFS polynomials, factor base and large prime bounds and the size of the matrix or, for ECM, the number of curves run and the B1, B2 and sigma values for the successful curve. Most if not all of this information can be cut and pasted from the output of the factoring software used.

These are the ten Most Wanted Numbers

3,544- | C222 |

3,544+ | C236 |

3,619- | C180 |

4,431- | C214 |

4,431+ | C247 |

5,371+ | C260 |

5,440+ | C188 |

6,333- | C240 |

8,287- | C199 |

9,272+ | C238 |

The first five holes in each table are

2,864- | 2,866- | 2,868- | 2,869- | 2,871- |

2,866+ | 2,867+ | 2,873+ | 2,875+ | 2,883+ |

3,544- | 3,545- | 3,546- | 3,548- | 3,550- |

3,544+ | 3,546+ | 3,548+ | 3,549+ | 3,551+ |

4,431- | 4,433- | 4,434- | 4,436- | 4,437- |

4,431+ | 4,434+ | 4,436+ | 4,439+ | 4,441+ |

5,378- | 5,379- | 5,380- | 5,381- | 5,382- |

5,371+ | 5,372+ | 5,374+ | 5,376+ | 5,380+ |

6,333- | 6,337- | 6,339- | 6,344- | 6,347- |

6,334+ | 6,337+ | 6,340+ | 6,350+ | 6,351+ |

7,310- | 7,312- | 7,315- | 7,318- | 7,320- |

7,308+ | 7,310+ | 7,314+ | 7,315+ | 7,316+ |

8,287- | 8,288- | 8,290- | 8,293- | 8,294- |

8,288+ | 8,291+ | 8,294+ | 8,295+ | 8,296+ |

9,273- | 9,278- | 9,280- | 9,282- | 9,288- |

9,272+ | 9,273+ | 9,275+ | 9,279+ | 9,280+ |

10,261- | 10,263- | 10,265- | 10,266- | 10,281- |

10,260+ | 10,261+ | 10,262+ | 10,264+ | 10,265+ |

11,254- | 11,255- | 11,257- | 11,260- | 11,262- |

11,251+ | 11,255+ | 11,256+ | 11,257+ | 11,260+ |

12,239- | 12,244- | 12,245- | 12,247- | 12,249- |

12,244+ | 12,250+ | 12,256+ | 12,257+ | 12,258+ |

The smallest composite remaining to be factored has 180 digits. There are 6 composites with fewer than 190 digits and 88 with at least 1000 digits.

For those wishing to factor with the SNFS algorithm,
this table contains the *a*
and *n* values sorted by SNFS-difficulty (defined here as
log_{10} (*n.a ^{n}*) ) for those unfactored
numbers which have SNFS-difficulty under 265. There are
42 entries in this table, some of which may have
been reserved.

The
ECMNet server running at 83.217.167.177:8194 is now loaded
with the GCW composites. Curves are being allocated at B1=43M,
equivalent to a t50 test. Please note that this server is still
version 2.x and does *not* work with V3.0 clients.

The following numbers have been reserved. They have been removed from the ECMNet server. Please mail me if you would like to reserve some numbers for yourself. Note that ECM occasionally leaves relatively small "runts". Please assume that anything smaller than a C165 will be reserved and/or factored by me by the time you read this information.

Sam Wagstaff is currently running extensive ECM pre-testing on
all the candidates with SNFS difficulty between 260 and 270
digits with the aim of ultimately completing them by SNFS. They
have *not* been removed from the ECM server and other
workers are welcome to help out with the pre-testing; B1 values
should be at least 110M.

Number |
Size |
Reserved by |
Date |

3,656+ | C184 | Texas State HPC Group | 2019-06-09 |

3,619- | C180 | Paul Leyland | 2022-09-05 |

8,287- | C199 | Oliver Kruse | 2022-12-13 |

6,333- | C240 | Oliver Kruse | 2022-12-13 |

5,371+ | C260 | Oliver Kruse | 2022-12-13 |

2,914+ | C278 | Oliver Kruse | 2023-01-24 |

2,967- | C291 | Oliver Kruse | 2023-01-24 |