Information for cow-orkers

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

2,838- C211
2,838+ C231
3,530- C183
3,646- C169
5,364+ C223
6,319+ C210
6,319- C224
7,293- C182
8,275+ C226
9,260- C226
11,238- C214

The first five holes in each table are

2,838- 2,841- 2,851- 2,852- 2,854- 
2,838+ 2,839+ 2,841+ 2,849+ 2,851+ 
3,530- 3,535- 3,541- 3,542- 3,543- 
3,531+ 3,535+ 3,540+ 3,543+ 3,544+ 
4,421- 4,430- 4,431- 4,433- 4,434- 
4,424+ 4,427+ 4,428+ 4,431+ 4,434+ 
5,367- 5,378- 5,379- 5,380- 5,381- 
5,364+ 5,370+ 5,371+ 5,372+ 5,374+ 
6,319- 6,330- 6,331- 6,333- 6,337- 
6,319+ 6,325+ 6,331+ 6,334+ 6,337+ 
7,293- 7,299- 7,301- 7,303- 7,305- 
7,299+ 7,300+ 7,303+ 7,305+ 7,308+ 
8,280- 8,287- 8,288- 8,290- 8,291- 
8,275+ 8,281+ 8,282+ 8,284+ 8,288+ 
9,260- 9,266- 9,268- 9,269- 9,270- 
9,265+ 9,266+ 9,270+ 9,272+ 9,273+ 
10,253- 10,258- 10,259- 10,261- 10,263- 
10,254+ 10,255+ 10,258+ 10,260+ 10,261+ 
11,238- 11,243- 11,244- 11,245- 11,246- 
11,248+ 11,251+ 11,252+ 11,255+ 11,256+ 
12,235- 12,238- 12,239- 12,240- 12,244- 
12,236+ 12,238+ 12,239+ 12,240+ 12,244+ 

The smallest composite remaining to be factored has 168 digits. There are 32 composites with fewer than 190 digits and 89 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 log10 (n.an) ) for those unfactored numbers which have SNFS-difficulty under 260. There are 53 entries in this table, some of which may have been reserved.

The ECMNet server running at 109.109.168.71:8194 is now loaded with the GCW composites. Curves are being allocated at B1=11M, equivalent to a t45 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 C145 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 250 and 260 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
9,260- C227 Paul Leyland 2017-10-06
6,319+ C210 NFS@Home 2017-10-06
8,291- C168 Paul Leyland 2017-09-30