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Old 2018-04-23, 19:28   #12
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Originally Posted by petrw1 View Post
If the smallest factor is actually much larger than 65 digits than the only option is SNFS ... which I know nothing about, but the comments above suggest the world does NOT yet have a computer big enough or fast enough to factor this exponent in our lifetimes.
I didn't get that impression.

My reading was: It's a step up from the exponents in the 1.1K range that were successfully factored in 2014, possibly a bit more than twice as difficult, but if someone really wanted to throw the time, money and resources at it, it could be done before the end of the current decade.
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Old 2018-04-23, 19:32   #13
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Originally Posted by petrw1 View Post
ECM beyond that (i.e. 70 or 75 or 80 digits), which is NOT currently set up in Prime95 but has been attempted a bit by some, would take significantly longer but still with a small chance of finding a factor.

If the smallest factor is actually much larger than 65 digits than the only option is SNFS ... which I know nothing about, but the comments above suggest the world does NOT yet have a computer big enough or fast enough to factor this exponent in our lifetimes.
The standard suggestion for ECM depth is 0.21 or 0.20 * digits (the multiplier shrinks a little as the input grows, 0.22 is used for small jobs); that's 77 to 81 in this case. I'd call half a t80 good. From currently reported ECM depth to t80 is something close to a 20% chance of a factor.

As for SNFS, if by "computer" you mean "single motherboard", we agree. If you mean "computation device", a cluster of the sort frmky and the CADO group use is just fine for solving the matrix, and sieving can be spread over thousands of volunteer cores NFS@home-style. The matrix needs a grant or a sympathetic supercomputer-facility-gatekeeper.
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Old 2018-04-24, 06:09   #14
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Originally Posted by petrw1 View Post
So if I may try to summarize briefly ...
Very good summary. Except for the "our lifetime" thingie, the job could be done in a year or two (or so) with enough motivation, and if we catch Ryan in a dark alley in the night...
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Old 2018-04-24, 06:10   #15
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(oh, didn't see the second page)
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Old 2018-04-24, 07:42   #16
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(oh, didn't see the second page)
How short are your pages? One page for me
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Old 2018-04-24, 08:27   #17
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The default, 11 posts set by Mike (I love eleven, that is why I never changed it!).
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Old 2018-04-24, 08:51   #18
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The default, 11 posts set by Mike (I love eleven, that is why I never changed it!).
I think I get 19 which I thought was the default.
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Old 2018-04-24, 08:56   #19
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I think I get 19 which I thought was the default.
And I set mine up to 97 a while back...
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Old 2018-04-24, 09:01   #20
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Quote:
Originally Posted by VBCurtis View Post

As for SNFS, if by "computer" you mean "single motherboard", we agree. If you mean "computation device", a cluster of the sort frmky and the CADO group use is just fine for solving the matrix, and sieving can be spread over thousands of volunteer cores NFS@home-style. The matrix needs a grant or a sympathetic supercomputer-facility-gatekeeper.
I think you are underestimating the difficulty: you also need about one postdoc-year to get 17e and 18e sieving working adequately (and it will need at least one clever idea to get the memory usage reasonable: 8G or 32G per process are not really feasible for a distributed job), because the yields with the sievers we have at the moment are much too low. More than three large primes would also likely be helpful.

You could probably do it before Christmas 2020 for the price of an average UK house.
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Old 2018-04-24, 13:20   #21
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You could probably do it before Christmas 2020 for the price of an average UK house.
£234,794 as of January 2017 according to
https://www.gov.uk/government/news/u...r-january-2017
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Old 2018-04-24, 15:31   #22
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Originally Posted by fivemack View Post
it will need at least one clever idea to get the memory usage reasonable: 8G or 32G per process are not really feasible for a distributed job
I *think* that a multithreaded siever could share the factor base among all threads instead of each process having it's own copy. Whether that cuts memory use enough is another matter.

Chris
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