Our Next Project: 2^811-1

[dleclair]

Hello,

NFSNET has almost finished the sieving stage for 2^757-1. Based on our current estimates, sometime on Monday we will have collected enough relations and will switch to the next project. The relations will be gathered for post-processing and, barring any unforseen problems, we should know the factors of 2^757-1 in a few weeks time.

Our next project is 2^811-1, a Mersenne number. 2^811-1 is a composite number with 245 decimal digits. It has just one known factor, 326023. The remaining composite cofactor has 239 decimal digits. Enough ECM effort has been done on the cofactor to be fairly certain that it has no factors of 50 digits or less.

To date the largest number factored using SNFS is 2^809-1, factored by Franke/Kleinjung/Bahr in early 2003. Assuming we have no challengers (never a safe assumption!) the factorization of 2^811-1 will establish a new worldwide SNFS record.

This project will be much more difficult than the previous projects undertaken by NFSNET. As with 2^757-1 we'll need about 80 million relations but the work required to find them will be substantially more, about six times more.

With that in mind, we need as many contributing users and machines as possible. With our current level of participation the sieving stage could take as long as one year but we will be starting various recruitment activities to attract more participation.

So fire up your machines and spread the word. This is your chance to participate in a record-breaking factorization.

Thanks again for your participation! More details will follow after the switch has been made.

The NFSNET Team
Chris, Don, Jeff, Paul and Richard

[andi314]

how many relations will be needed for M811????

[TauCeti]

Originally posted by andi314
how many relations will be needed for M811????

It's written some lines above. You missed it

As with 2^757-1 we'll need about 80 million relations but the work required to find them will be substantially more, about six times more.

[dsouza123]

The project is 1/4 of the way there (at least the line sieving) with 20+ million relations, and has picked up recently with about a half million relations per day, making better progress.

Does anyone know why the large increase ?

Not in the most literal sense of more machines are running but what has lead to the sudden increase in users and machines ?

[TauCeti]

The increase of users was (in parts) caused by a german press coverage here: RSA-576 broken

The increase in work-units is also caused by one user participating now with a huge number of machines

[dsouza123]

Thanks german press and thanks to the user who has installed NFSNET on a huge number of machines and to all others that are participating.

[Wacky]

Originally posted by dsouza123
The project is 1/4 of the way there (at least the line sieving) with 20+ million relations

Even though we have about 25% of the relations, we have completed only about 15% of the effort.

This is because we start with the lower values of "b" and generally work upward.

As "b" increases, the "yield" (relations per line) steadily decreases. Earlier, we were getting over 2 relations per line. Now, we are below 1.5. By the time we finish, I expect the yield to be around 0.67.

Unfortunately, it takes essentially as much effort to sieve a line that yields 0.67 lines as it did to sieve the line that produced three times as many relations.