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.
A more detailed description of the project can be found
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
or as a
Minimum System Requirements:
- Intel/Amd processor.
- At least 128MB of ram free.
- 32MB of free disk space.
- Windows, Linux or Mac (x86) OS.
User of the day
Proud Member of Team [H]ard|OCP and the [H]ard DC Commandos http://hardforum.com/forumdisplay.php?f=32
Bounded App Final Tally of Results
Thank you all for your contributions over the last few years to make the bounded discriminant search a success. Here is a summary of the final results...
The search found all imprimitive decic (degree 10) fields with absolute discriminant less than or equal to 1.2E11. The total compute time (summed over all hosts) was 531 years.
284,410 fields were found within this bound. Among those, the following minimum discriminant fields were of interest (listed by galois group and signature):
About half of these were discovered for the first time. The other half had already been discovered but it was not known until now that they were the minimum.
Although not worthy of a stand alone journal article, the search was an extension of the search discussed in this paper:
20 May 2016, 21:13:30 UTC
The final subfield is almost complete
You may have noticed the bounded app has run dry on work. That is because the last of the WUs have been sent out. We are now just waiting for them to be returned. In a few weeks, after all the results have been returned and processed, I will post the final tally of results.
In the meantime, the regular decics app still has plenty of work, so I hope you all stick around!
14 Apr 2016, 15:09:52 UTC
Subfield 48 of 49 complete.
The subfield with discriminant 8, otherwise know as Q(√2), is now officially complete.
The bounded app has moved on to the final subfield: Q(√5).
14 Mar 2016, 5:55:29 UTC
Subfield 47 of 49 Complete
Subfield 47 (disc 12) is now complete. Subfield 48 (disc 8) has only a couple thousand WUs left and we are just starting to hand out WUs for the final subfield (disc 5).
28 Feb 2016, 6:48:11 UTC
Subfield 46 of 49 Complete
Subfield 46 is now complete. That only leaves 3 more to go (discriminants 12, 8, and 5). Subfield 47 (disc 12) is close behind with only several hundred WUs left and a big dent has already been made in subfield 48 (disc 8). Good work everyone!
22 Feb 2016, 4:45:14 UTC
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