F1797 factored

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Greg

Joined: 26 Jun 08
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Message 1097 - Posted: 6 Mar 2013, 1:43:39 UTC

The Fibonacci number F1797 has been factored. It is the product of 112-digit and 136-digit prime numbers.
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zombie67 [MM]

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Message 1098 - Posted: 6 Mar 2013, 4:47:17 UTC - in response to Message 1097.

The Fibonacci number F1797 has been factored. It is the product of 112-digit and 136-digit prime numbers.

Congratulations...I guess? What does that mean? In what way is it significant? Who will use that data, and to do what with it?
Reno, NV
Team: SETI.USA

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Greg

Joined: 26 Jun 08
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Message 1099 - Posted: 6 Mar 2013, 8:01:50 UTC - in response to Message 1098.

It means different things to different people. The NFS@Home project was started to explore the limits of current publicly available tools for integer factorization. As the saying goes, the purpose is insight, not numbers. With 2,1049+ and other lasievef projects, we are still doing that work. The 14e and 15e projects, though, focus on integer sizes that have now been well characterized.

So why do we continue factoring numbers of these sizes? For me, it is simply because I enjoy it. It's the continuation of a long tradition of constructing factorization tables. The original focus was the Cunningham numbers, a project that has been continuously running since 1925. We have now factored ALL Cunningham numbers in the size range appropriate for the lasieved and lasievee projects. My primary interest has thus shifted to the Fibonacci and Lucas sequences. These sequences have been studied for over 2000 years and have many applications. Factorizations of these numbers started in earnest with Ã‰douard Lucas in 1877, and we are continuing that tradition. Some have likened the effort to stamp collecting, but that's a perfectly fine hobby. I also hope that perhaps a few volunteers who are introduced to integer factorization by this project will become curious about the underlying mathematics, will choose to explore it in depth, and will go on to make new contributions to the field.
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