Has someone tried to tackle the Primo certification of the CF of M82939? Does anyone have an approximation how look it might take (as in: does in take months or years?)?

[QUOTE=kruoli;472528]Has someone tried to tackle the Primo certification of the CF of M82939? Does anyone have an approximation how look it might take (as in: does in take months or years?)?[/QUOTE]
Hmm, a PRP-24938. Based on the following, I'd say months to possibly over a year. From the [url=https://en.wikipedia.org/wiki/Elliptic_curve_primality#cite_note-5]Wikipedia page on ECPP[/url],[quote]As of November 2016, the largest prime that has been proved with ECPP method has 34,093 digits.[url=http://primes.utm.edu/top20/page.php?id=27][sup]5[/sup][/url] The certification by Paul Underwood took 14 months using Marcel Martin's Primo software.[/quote]

And, the latest:

[url=http://www.ellipsa.eu/public/primo/top20.html]Ellipsa > Primo Top-20[/url] Certificate for 2[sup]116224[/sup] - 15905 (34987 decimal digits)[quote]The certification of this number was done by Peter Kaiser with Primo 4.1.1 [°]. The certification process took 694 days for the phase 1 and 58 days for the phase 2 using a Dual Intel E3667 processor (16 cores at 3.2 GHz).
[°] The original format-3 certificate (100.9 MB) was updated to a format-4 certificate in order to get a smaller file (75.5 MB). [/quote]

[This was mentioned in this Forum [url=http://www.mersenneforum.org/showpost.php?p=472097&postcount=17]here[/url]]

Also, one of the other Primo top 20, (2[sup]83339[/sup] + 1)/3, which is only slightly larger than the number currently at issue, took 18 months.

Of course, this does not rule out the possibility of a faster primality proof by some other method...

[QUOTE=Dr Sardonicus;472534]

And, the latest:

[url=http://www.ellipsa.eu/public/primo/top20.html]Ellipsa > Primo Top-20[/url] Certificate for 2[sup]116224[/sup] - 15905 (34987 decimal digits)

[/QUOTE]

I have asked Peter to update the Wiki page with his impressive number.

[QUOTE=kruoli;472528]Has someone tried to tackle the Primo certification of the CF of M82939? Does anyone have an approximation how look it might take (as in: does in take months or years?)?[/QUOTE]

The more cores in one box your throw at it the better. It would top this [URL="http://primes.utm.edu/top20/page.php?id=49"]top20 table[/URL] :smile:

[QUOTE=kruoli;472528]Has someone tried to tackle the Primo certification of the CF of M82939? Does anyone have an approximation how look it might take (as in: does in take months or years?)?[/QUOTE]

If I wanted to tackle this, where would I reserve it? I don't mind spending 6 months on 6 cores to get it done, but I do mind spending 4 months to discover someone else finished it.

[QUOTE=VBCurtis;472640]6 months on 6 cores to get it done...[/QUOTE]
This is off by at least an order of magnitude.

(2^83339 + 1)/3 took Tom Wu 374 days on a 6-core 1090T (3.2GHz) if my memory serves me well. There is little or no advantage to using AVX(2) based machines.

Edit: I see Dr. Sardonicus says it took 18 months. I am taking my timings from the d/l cert at ellipsa.eu

[QUOTE=paulunderwood;472664](2^83339 + 1)/3 took Tom Wu 374 days on a 6-core 1090T (3.2GHz) if my memory serves me well. There is little or no advantage to using AVX(2) based machines.

Edit: I see Dr. Sardonicus says it took 18 months. I am taking my timings from the d/l cert at ellipsa.eu[/QUOTE]

I was merely parroting the user comments I found by following the link to the [url=http://primes.utm.edu/primes/page.php?id=118512]Prime database page for (2[sup]83339[/sup] + 1)/3[/url]:

[quote]The certification process took approximately 18 months on a 6-core AMD Phenom II processor.[/quote]

Thanks for the feedback! I'm not keen on a calculation that would take me 9-10 months on my biggest machine; too much risk of someone Amazon-ing it before I finish.

[QUOTE=VBCurtis;472679]Thanks for the feedback! I'm not keen on a calculation that would take me 9-10 months on my biggest machine; too much risk of someone Amazon-ing it before I finish.[/QUOTE]

Two circumstances make that unlikely:

1. The fact that it is a GUI-only program makes it very inconvenient to run on the cloud, especially with spot instances that can terminate/resume at any time. Is it even possible to start/resume the program automatically without manual intervention?

2. In practice, spot market pricing as observed empirically on AWS makes anything larger than 2-core (c4.xlarge) instances not cost-effective, on a cost-per-hour-per-core basis. (On Google Compute Engine, on the other hand, the cost-per-hour-per-core is always the same fixed amount, regardless of the number of cores on a preemptible virtual machine.)

Do Primo benchmarks scale linearly as you increase the number of cores, or is there a penalty for using multicore, similarly to what is seen with mprime?

[QUOTE=GP2;472684]

Do Primo benchmarks scale linearly as you increase the number of cores, or is there a penalty for using multicore, similarly to what is seen with mprime?[/QUOTE]

It is linear -- Primo is [URL="https://en.wikipedia.org/wiki/Embarrassingly_parallel"]embarrassingly parallel[/URL]