Can I borrow some ECM of a friendly CPU?

[fatphil]

Working on something a bit cranky at the moment, where the act of discovery is the main pleasure, hence my secrecy, I'd rather not be spoiled - I'll post here more about it when I've run out of easy ideas, but in order to progress down one of my branches it would be nice if I could get some prime factors from a big number or two...

I've done an hour or so of gmp-ecm on my very ancient celeron (I'm trying to go fanless at home, so have no number crunchers any more), but if someone could run on a punchier box for a few hours, I'd be grateful. The larger the prime factors, the less useful it's likely to be, so there's no desperate need to squeeze until the blood comes out.

2232027714105126816428496408520838343541574716773833234422858719802554161115433284979455602363125877584353560031892174122433028819199338161851711418563679155788334827984879707802194586760032236380533301339398039260132519982610980345662291040085036304200947886685065197112458200057264014024939561484682779714092311963567553241820332104244058889838075512885630103419457958234260809678171117972292268560997359961117264021124933193154972706036460580485672015007550644880805972874512654905555137943723971508484120141668255734453799834345615461799656754596993464424308713463364302328004514033836254716138875402216038222489970056543392748779302754044583602086957893207732343610979066203896281666364562222744443062516699025933511360276131202422714654083269505722655540186872282583773385792650167573211756010416352186314712976030741409505933682844296361336030384873190748192334103858433474918930981694692115809670053438860819719522519400485727410389010472402762612125130999773017467969736471680501015206419372158919496944457986473959477

Spoiler, for the main task at hand: if the list 2, 3, 7, 47, 769, 1087, 127, 119809, 34303, 12289, 6143, ... looks familiar - I'm treading on old ground. Startpage gave me nothing that looked relevant.

[axn]

Have you transcribed the number correctly? This says it has tiny factors

[kriesel]

Alpertron's page finds the tiny factors 3 × 7⁴ × 23 in a flash. Maybe you have an NVIDIA GPU suitable for GPU assisted ECM? https://download.mersenne.ca/GMP-ECM
(And I'm wondering why post one text does not line wrap, like other posts do, but require lateral scrolling. Guessing it's the unformatted 1027-digit number.)

[kruoli]

On the cofactor, I am running t35 and P-1 with B1=200000000, B2=12721007621976 (automatic B2).

[R. Gerbicz]

Originally Posted by fatphil

Spoiler, for the main task at hand: if the list 2, 3, 7, 47, 769, 1087, 127, 119809, 34303, 12289, 6143, ... looks familiar - I'm treading on old ground. Startpage gave me nothing that looked relevant.

Something like Fibonacci stuff, see the comment at https://oeis.org/A319197 .

[fatphil]

Originally Posted by axn

Have you transcribed the number correctly? This says it has tiny factors

Dang, looks like the X clipboard craps out at 4096 characters. I'll stick the next number on a webpage if I need help again.

As I make progress, it looks like I only need 1 factor per term, and that was already a cofactor, so I think I don't need any others from (the non-mangled version of) that one at the moment. Annoyingly, the terms double or treble in size with each step, eventually it will become quite a trudge. gmp-ecm is amazing though, you only really appreciate how good things are when you depend on them!

I'm not sure I understand the OEIS series posted, but there is a very strong sqrt(5) connection, which makes the fib link quite interesting. Fortunately, the sequence I'm working on has a companion sequence, and I will attack that with the most logical approach that I've perversely evolved whilst attacking the first one, so I can put together a more coherent webpage on what I'm doing.

Still continuing, fraction by fraction...

[xilman]

Originally Posted by fatphil

Dang, looks like the X clipboard craps out at 4096 characters. I'll stick the next number on a webpage if I need help again.

As I make progress, it looks like I only need 1 factor per term, and that was already a cofactor, so I think I don't need any others from (the non-mangled version of) that one at the moment. Annoyingly, the terms double or treble in size with each step, eventually it will become quite a trudge. gmp-ecm is amazing though, you only really appreciate how good things are when you depend on them!

I'm not sure I understand the OEIS series posted, but there is a very strong sqrt(5) connection, which makes the fib link quite interesting. Fortunately, the sequence I'm working on has a companion sequence, and I will attack that with the most logical approach that I've perversely evolved whilst attacking the first one, so I can put together a more coherent webpage on what I'm doing.

Still continuing, fraction by fraction...

Hi Phil, how you doing? Long time no see.

You should still have my non-MSFT email address (PM if not) so send me the number and I will see what I can do.

Paul

[fatphil]

Originally Posted by xilman

Hi Phil, how you doing? Long time no see.

You should still have my non-MSFT email address (PM if not) so send me the number and I will see what I can do.

Paul

Life's good, all considering, he says as he runs off to check if the rain has breached the flashing on the roof again, and started to drip into the sauna...

I've pushed forward as far as I can, and have finally hit a number I can't get anything from at all. I'm up to a 80kdigit composite now. Did 100 curves from B1=10k-22k overnight, and pushing forward with 100 more from 22k-50k now. I've stuck the number in a text file here:
http://ircing.org/~fatphil/composites.txt
(Note to internet citizens of the future, that URL won't last, I'm temporarily borrowing a friend's big box to do the ECM work.)

Fortunately, I don't actually *need* to know any factors, this is mostly just trying to optimise the size of what I was searching for - a covering set. There's no shame in throwing a composite in such a set, if it covers, it covers, it's just a neatness thing. It's unsatisfying to not even know one prime at its apparition time.

There are two parts to this hunt, and part 1 had a perfectly neat pattern of removing half the candidates with each factor found. Part 2 has a perfectly neat pattern of absolutely no pattern appearing at all. I presume that part 1 has some algebraic structure, which might imply that my hunt will never terminate, I'll just chop the integers in two forever, and my conjecture is unprovable. I'll put together an HTML page today or tomorrow explaining the whole thing, so some proper mathematical minds can shed some light on the matter. Alas I've got tens of megabytes of Pari/GP output that I need to filter through. It's all a bit of a mess currently. I've been in scatterbrained scientist mode!

[xilman]

Originally Posted by fatphil

I've pushed forward as far as I can, and have finally hit a number I can't get anything from at all. I'm up to a 80kdigit composite now. Did 100 curves from B1=10k-22k overnight, and pushing forward with 100 more from 22k-50k now. I've stuck the number in a text file here:
http://ircing.org/~fatphil/composites.txt

Took a copy and playing with params to get a feel for length of time it takes on this laptop.

Have you run P+1 and/or P-1 and, if so, how far? P-1 with B1=10K, B2= 632208 took 27s and 2214s

I didn't expect to find a factor, just calibrating this machine.

[fatphil]

Originally Posted by xilman

Took a copy and playing with params to get a feel for length of time it takes on this laptop.

Have you run P+1 and/or P-1 and, if so, how far? P-1 with B1=10K, B2= 632208 took 27s and 2214s

I didn't expect to find a factor, just calibrating this machine.

I didn't do P+/-1 because I was prepared to just let ECM run, and with 100 curves, now 125, the Hasse coverage should have pulled out something that was in range of P+/-1. By the time I was hitting this number, I had started looking at the companion sequence, so was happy to just fire and forget.

Run 25 out of 100:
Using B1=25937, B2=25937-6825010, polynomial x^1, sigma=0:13064782877481766227
Step 1 took 890799ms
Step 2 took 167704ms

Anyway, the first 10 minutes of investigation, which got me caught in this rut, is now presented here (I'll try to pull the relevant steps forward out of my GP history tomorrow, no more time today): http://fatphil.org/maths/sqrt_cf/sqrt5.html

[fatphil]

Originally Posted by fatphil

Anyway, the first 10 minutes of investigation, which got me caught in this rut, is now presented here (I'll try to pull the relevant steps forward out of my GP history tomorrow, no more time today): http://fatphil.org/maths/sqrt_cf/sqrt5.html

Just updated with some info about the direction I headed in, so you don't need to reinvent the wheel. It looks like I may have to reinvent some of my factors, as I can't find the window I was working in!

But tonight is sauna night, so I'm happily tucked away there for the rest of the evening.