What is the story of M1283?
 

A factor was found for [URL="http://www.mersenne.ca/exponent/1283"]http://www.mersenne.ca/exponent/1283[/URL]. What is the story behind this number? Out of the top of my head, I thought all exponents between 1277 and 1619 were already partially factored? How come so little ECM effort is listed for such a low number?

[QUOTE=tha;454591]A factor was found for [URL]http://www.mersenne.ca/exponent/1283[/URL]. What is the story behind this number? Out of the top of my head, I thought all exponents between 1277 and 1619 were already partially factored? How come so little ECM effort is listed for such a low number?[/QUOTE]

I suspect that that factor has been known for a long while and mersenne.ca just hasn't been told.

[QUOTE=tha;454591]A factor was found for [URL="http://www.mersenne.ca/exponent/1283"]http://www.mersenne.ca/exponent/1283[/URL]. What is the story behind this number? Out of the top of my head, I thought all exponents between 1277 and 1619 were already partially factored? How come so little ECM effort is listed for such a low number?[/QUOTE]

Registered just to say that that my computer found that factor yesterday morning during ECM work. As the mersenne.ca page says, the factor was already discovered in April 2014, but there didn't appear to be a source for it.

I'm trying to fully factor M1283 because I happen to like the number 1283. I'm still not all that familiar with the right way to go about it with Prime95, so if someone wants to let me know what I'm doing right/wrong, that would be great. I have 6 assignments of 1000 curves each queued up, with B1=110000000, B2=11000000000. And I think [url]https://www.mersenne.org/report_ecm/[/url] says another 33,000 curves need to be tested in those bounds?

[QUOTE=tha;454591]A factor was found for [URL="http://www.mersenne.ca/exponent/1283"]http://www.mersenne.ca/exponent/1283[/URL]. What is the story behind this number? Out of the top of my head, I thought all exponents between 1277 and 1619 were already partially factored? How come so little ECM effort is listed for such a low number?[/QUOTE]

Someone rediscovered an old factor and reported it to PrimeNet, and mersenne.ca picked it up from there. This factor is already in the Cunningham project listings and was found before page 129, so the original discovery was before April 28 2014, probably long before.

Mersenne.ca shows a "discovery" date of April 23 2014, but that's likely bogus, a lot of older factors have 2014 dates at Mersenne.ca for some reason. Most likely this factor wasn't originally found by GIMPS, which is why there was no prior log entry for its discovery.

One telltale sign is that there are no LL tests on record for this exponent (see [URL="https://www.mersenne.org/report_exponent/?exp_lo=1283&full=1"]M1283 at mersenne.org[/URL]), by contrast to [URL="https://www.mersenne.org/report_exponent/?exp_lo=1061&exp_hi="]M1061[/URL] which did have LL tests done before its factor was found in 2012.

Maybe the History listing at mersenne.org and mersenne.ca should distinguish rediscovery of old factors from actual new ones, to avoid confusion.

If you want to avoid having this happen to you, don't forget to put the existing factors in your worktodo line, in quotation marks:

[CODE]
ECM2=1,2,1283,-1,110000000,11000000000,100,"4824675346114250541198242904214396192319"
[/CODE]

(comma-separated if there's more than one already-known factor)

[QUOTE=GP2;454608]Someone rediscovered an old factor and reported it to PrimeNet, and mersenne.ca picked it up from there. This factor is already in the Cunningham project listings and was found before page 129, so the original discovery was before April 28 2014, probably long before.[/QUOTE]

On 2007-04-12, at 00:49 [B]Prime95[/B] posted under the heading [URL=http://www.mersenneforum.org/showthread.php?t=7834]2- table[/URL] indicating a C347 cofactor, so the first factor was already known then.

I found another page of similar vintage, [URL=http://members.iinet.net.au/~tmorrow/mathematics/cunningham/cunningham.html]Tim's Cunningham Numbers page[/URL] which was undated, but mentioned updates to the tables in November 2004, so the first factor may already have been found by then.

The listings [URL=http://www.mersennewiki.org/index.php/Remaining_Cunningham_composites_sorted_by_difficulty]here[/URL] last modified 21:36, 2 February 2017 show the C347 apparently yet to be factored.

[update] After a bit more caffeine, it suddenly occurred to me to search for the first factor, which I should have thought of before
:gah:

And I found it, posted Wed Sep 11, 2002 2:55 pm to [URL=https://arstechnica.com/civis/viewtopic.php?f=18&t=760550&start=200]Ars OpenForum[/URL] by [B]garo[/B], reference to August 4 of that year.

My original post is in a moderation queue somewhere at the time I write this, but if this happens to post first...

I guess my next question is: how can I best contribute to fully factoring M1283?

[QUOTE=ZacHFX;454616]I guess my next question is: how can I best contribute to fully factoring M1283?[/QUOTE]

You could use the ECM2= line I posted above, in your worktodo.txt file. Change the 100 to whatever number of curves you want to run. This line incorporates the already-known factor, so you will not rediscover it.

However, for an exponent as small as M1283, you'd probably want to run stage 2 using GMP-ECM instead of mprime, it's much more efficient for small exponents. However, this is somewhat more complicated.

In a nutshell: first you need to [URL="https://gforge.inria.fr/projects/ecm/"]download and compile the GMP-ECM program[/URL], which is relatively straightforward if you use Linux but probably more complicated if you use Windows. Then modify the ECM2= line mentioned above so that the B2 parameter equals B1 instead of being 100 times the B1 parameter (in other words: ECM2=1,2,1283,-1,110000000,110000000,100,"4824675346114250541198242904214396192319"). Then add the line GmpEcmHook=1 to your prime.txt file, and rename your existing results.txt file to something else, then run mprime. When it completes, your new results.txt will consist of a bunch of lines that look like N=0x....; QX=0x....; SIGMA=.... , and the number of lines will equal the number of curves you specified (100, in the above example). Rename the results.txt to, say, ecm_input.txt (or whatever) so that it doesn't get overwritten, then feed that to the GMP-ECM program, which you'd invoke using something like ./ecm -resume ecm_input.txt 110000000 > ecm_output.txt

By the way, if anyone wants to try P−1, I already ran that for this exponent with B1=10[SUP]11[/SUP], B2=10[SUP]17[/SUP].

Thanks! I [I]am[/I] running Windows, so I will stick with Prime95. What about the number of curves to test? Is there any substantive difference in running it in increments of 100 or 1000? How many do I need to test before increasing B1 and B2?

[QUOTE=Dr Sardonicus;454613]And I found it, posted Wed Sep 11, 2002 2:55 pm to [URL=https://arstechnica.com/civis/viewtopic.php?f=18&t=760550&start=200]Ars OpenForum[/URL] by [B]garo[/B], reference to August 4 of that year.[/QUOTE]

But August 4 2002 isn't the actual date of discovery, just an upper bound. A list of known factors was posted on that date, and it included this factor.

Given that no LL test was ever done as far as we know, this factor may well have been discovered prior to the launch of GIMPS in 1996.

[QUOTE=ZacHFX;454622]Thanks! I [I]am[/I] running Windows, so I will stick with Prime95. What about the number of curves to test? Is there any substantive difference in running it in increments of 100 or 1000? How many do I need to test before increasing B1 and B2?[/QUOTE]

It makes no difference whether you use increments of 100 or 1000 or whatever.

See [url]https://www.mersenne.org/report_ecm/?txt=0&ecm_lo=1&ecm_hi=1&ecmnof_lo=1200&ecmnof_hi=1300[/url] , you can see it would need another 33500 curves before bumping B1 to 260000000 and B2 to 26000000000 .

If you have existing assignments in your worktodo.txt file, you can stop Prime95, edit worktodo.txt to add the ,"4824675346114250541198242904214396192319" to each line, then restart Prime95.

By the way, it's entirely possible that the next smallest factor might turn out to be way too large to find with ECM testing. At some point in the next few years, someone will probably [URL="https://en.wikipedia.org/wiki/General_number_field_sieve"]run a sieve[/URL] on it and factor it completely. That approach requires some major-league computing resources though. Take a look at the [URL="http://mersenneforum.org/forumdisplay.php?f=98"]NFS@Home subforum[/URL] here.

[QUOTE=ZacHFX;454622]Thanks! I [I]am[/I] running Windows, so I will stick with Prime95.[/QUOTE]

That's OK, but be aware that using the combination of prime95/GMP-ECM is more that twice as efficient at finding factors.

I guess what I'm saying is it is well worth the effort to get GMP-ECM working.