What is NumberFields@home?

NumberFields@home

NumberFields@home is a research project that uses Internet-connected computers to do research in number theory. You can participate by downloading and running a free program on your computer.

NumberFields@home searches for fields with special properties. The primary application of this research is in the realm of algebraic number theory. Number theorists can mine the data for interesting patterns to help them formulate conjectures about number fields. Ultimately, this research will lead to a deeper understanding of the properties of numbers, the basic building blocks of all mathematics. Another application of number fields is in cryptography, where they are used in sophisticated factoring algorithms and as the basis for new cryptosystems. There are also distant applications to mathematical physics, including quantum mechanics and string theory. A more detailed description of the project can be found here.

NumberFields@home is based at the school of mathematics at Arizona State University. The final results of this project will be complete tables of number fields. The results are given in table form or as a searchable database.

Minimum System Requirements:

Intel/Amd processor.
At least 128MB of ram free.
32MB of free disk space.
Windows, Linux or Mac (x86) OS.

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If you have any problems, get help here.

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User of the Day

Steve Hawker* 2M credits (Next badge is at 5M)

I've been crunching since 2012 and the more I do, the more I like it. I try to crunch every project I can find. I don't have a server farm or a...

News

Subfield 3 Officially Complete
I am pleased to report that the search over ℚ(√2), also known affectionately as "subfield 3", is now officially 100% complete.

This search has been in the works, off and on, for several years. It goes without saying that this is a major computational achievement. We couldn't have done it without all the volunteers, so I thank you all!

The batch status tables have been updated accordingly with subfield 3 moved to the archives. The results of the search can be found here.
23 Jun 2023, 6:41:29 UTC · Discuss

Batch Plan
Some of you may have noticed, the search over subfield 7 DS16x11 is coming to an end, and you are probably wondering where we go from here.

We are going to start by making a quick detour to subfield 6 and start the search over DS11x12. The only reason for doing this is to keep the WUs consistent for the BOINC Pentathlon (timing stats for the 2 searches are very similar - WUs average about 2 hours on my CPU)

After that we will go back to subfield 3 and finish that search once and for all.

Then it's back to the final part of subfield 7, and then finally subfield 6.
12 May 2023, 5:18:15 UTC · Discuss

BOINC Pentathlon 2023

Welcome BOINC Pentathlon participants!
12 May 2023, 5:01:15 UTC · Discuss

2022 Year End Summary
2022 was the year of ℚ(√-10) (subfield 7), as most of our time was spent on that search. Many new fields were found and we are now entering the final row of the search. In the next 3 to 6 months we should be at the point where we can say with almost certainty that it is complete.

The goals for 2023 are simple:
1. Get subfield 7 to the point where it is essentially complete.
2. Go back and officially complete subfield 3, so we can say with 100% certainty that it is done.
3. Do more on subfield 7 or move on to subfield 6 (the final search).

Thanks everyone for your contributions and have a wonderful New Year!
1 Jan 2023, 20:20:10 UTC · Discuss

Future of the Project
I've been procrastinating in sharing some news and I finally got around to doing it.

My old thesis advisor who has been backing this project retired in May. I don't actually work for the university, so this means the project has lost is primary benefactor.

The good news is that the university has allowed the project to continue. The bad news is that they will not be supporting any more hardware upgrades. This means when the current hardware fails the project will come to an end.

I'm hoping the current hardware can last several more years. One of the most critical parts is the hard drive, and we just got a new one about 1.5 years ago. Given that the previous hard drive lasted over 4 years, this is a positive.

This news has played into my reasoning on the order of the searches. Given that sf3 is practically guaranteed to be complete, I though it was prudent to use our finite time to first concentrate on sf7. The short term goal is to get sf7 to the same state that sf3 is currently in, which should take us into early next year. At that point, we can either spend the time to finish off sf3 and sf7, or continue on with sf6. Doing sf6 will allow us to find more fields in the finite time we have left, but finishing off sf3 and sf7 will allow us to say with 100% certainty that they are indeed complete. I am leaning towards finishing off sf3 and sf7, but that may change as time goes on.
10 Aug 2022, 17:18:41 UTC · Discuss

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