PrimeNet gives same ECM task multiple times?

[Lexicographer]

Issue #1: I've asked PrimeNet for a trial factoring assignment for M1277 on the Manual Testing page and it gave me ECM assignment, which I did not plan to run... But fine.

Issue #2: I think, initially PrimeNet's assignment looked more like this:

150 curves, B1=800000000, B2=80000000000

But in the list of my current assignments it somehow transformed into:

150 curves, B1=999999999, B2=99999999900

Issue #3: After giving that task to my CPU running mprime, I've noticed from the complete exponent status report (with full ECM history) that other people already completed both assignments from above multiple-multiple times over the course of this decade:

2018-03-04 supercat NF-ECM 150 curves, B1=800000000, B2=80000000000
2017-12-04 Yizhe Huang NF-ECM 150 curves, B1=800000000, B2=80000000000
2017-10-11 Terçariol, C. A. S. NF-ECM 150 curves, B1=800000000, B2=80000000000
2017-08-16 Diophantus NF-ECM 150 curves, B1=800000000, B2=80000000000
2017-04-04 Ducho_YYZ NF-ECM 150 curves, B1=800000000, B2=80000000000
2017-01-03 ch3cooh NF-ECM 150 curves, B1=800000000, B2=80000000000
2016-08-24 bayanne NF-ECM 150 curves, B1=800000000, B2=80000000000
2016-06-17 fireredd NF-ECM 150 curves, B1=800000000, B2=80000000000
2016-06-15 Moonwalker89 NF-ECM 150 curves, B1=800000000, B2=80000000000
2016-04-17 dh1 NF-ECM 150 curves, B1=800000000, B2=80000000000
2016-04-04 Mario Tranquillini NF-ECM 150 curves, B1=800000000, B2=80000000000
2016-03-31 cpp1701 NF-ECM 150 curves, B1=800000000, B2=80000000000
2016-02-10 ssateneth NF-ECM 150 curves, B1=800000000, B2=80000000000
2016-02-10 Smoker88 NF-ECM 150 curves, B1=800000000, B2=80000000000
2015-05-15 MadPoo NF-ECM 150 curves, B1=800000000, B2=80000000000
2013-11-11 Oliver Kruse NF-ECM 150 curves, B1=800000000, B2=80000000000
2013-09-26 Aseroberto NF-ECM 150 curves, B1=800000000, B2=80000000000
2013-06-14 yooper NF-ECM 150 curves, B1=800000000, B2=80000000000
2012-12-28 SRJ2877 NF-ECM 150 curves, B1=800000000, B2=80000000000
2011-04-11 Bdot NF-ECM 150 curves, B1=800000000, B2=80000000000
2011-02-14 James Heinrich NF-ECM 150 curves, B1=800000000, B2=80000000000

2018-01-31 Terçariol, C. A. S. NF-ECM 150 curves, B1=999999999, B2=99999999900
2017-02-27 Diophantus NF-ECM 150 curves, B1=999999999, B2=99999999900
2016-02-16 Fastspiky NF-ECM 150 curves, B1=999999999, B2=99999999900
2015-04-28 XZT NF-ECM 150 curves, B1=999999999, B2=99999999900

Isn't it a massive waste of processing power to give the same assignment to multiple users again and again?
I thought, the point of PrimeNet is to coordinate people's effort, not to make them run same task over and over.

[GP2]

Originally Posted by Lexicographer

Issue #1: I've asked PrimeNet for a trial factoring assignment for M1277 on the Manual Testing page and it gave me ECM assignment,

There is no point doing any further trial factoring of this exponent. Indeed, there was no point taking it to 65 bits as someone did last year. That was a wasted effort.

Trial factoring can only search for relatively small factors because the difficulty goes up by a factor of two each time you increment the bit size, so once you hit a certain point you have to try other methods, like P−1 or ECM. And enough ECM has been done on this exponent by now to demonstrate that the smallest factor must be many, many, many, many times too large to be be found by trial-factoring. Here "must" is probabilistic rather than absolutely proven, but the odds are beyond astronomical.

Originally Posted by Lexicographer

Isn't it a massive waste of processing power to give the same assignment to multiple users again and again?
I thought, the point of PrimeNet is to coordinate people's effort, not to make them run same task over and over.

It's not the same task. Each ECM curve has a different (random) sigma. It's like throwing multiple darts at a dartboard, hoping that one will eventually hit a bullseye.

By contrast, redoing P−1 testing with the same B1 and B2 parameters really would be duplicating the same work over again.

[Lexicographer]

Thanks for explaining. I missed the fact that there is a random parameter involved...

Though I still think it would be nice if PrimeNet manual testing page did not assign tasks of different type than I asked for.

As for this exponent, mfaktc, which I planned to use, doesn't even support trial factoring for exponents lower than 100K. As well as non-prime exponents for some reason (I wanted to overcome the 100K limit by trial factoring M163456 = M(2⁷*1277), which is a product of M1277, and looking if there are any new factors between 2113601438322189019 < 2^65 and 2^80 < 1227156720026097481648213, both of which are consecutive factors of M163456).

[ATH]

If you look at this ECM report for M1277:
https://www.mersenne.org/report_ecm/

you can see ECM up to 60 digit level is done and almost half of 65 digit level. That means the chance of a missed 60 digit factor is well below 1/e~37% since the half 65 digit level also further rules out missed 60 digit factors.

The chance of a missed 55 digit factor is much much lower again, and so close to 0% it would be a miracle if one was found. 55 digit factor is ~ 2^183 so you can see why there is no idea trial factoring between 2^65 and 2^80 ?

[Dubslow]

Originally Posted by Lexicographer

Though I still think it would be nice if PrimeNet manual testing page did not assign tasks of different type than I asked for.

PrimeNet also won't assign pointless work, now or in the future. If you want to do pointless work, I suggest setting the nearest bundle of cash on fire.

So it can either 1) assign nothing at all, with an error message, which is admittedly probably the better choice or 2) assign a similar worktype with the same purpose, which is what it did. If you want factors of M1277, that's how you get factors. (Either that or pay several thousand dollars to the right people to run SNFS on it.)

Originally Posted by Lexicographer

As for this exponent, mfaktc, which I planned to use, doesn't even support trial factoring for exponents lower than 100K. As well as non-prime exponents for some reason (I wanted to overcome the 100K limit by trial factoring M163456 = M(2⁷*1277), which is a product of M1277, and looking if there are any new factors between 2113601438322189019 < 2^65 and 2^80 < 1227156720026097481648213, both of which are consecutive factors of M163456).

mfaktc doesn't support nonprime exponents because the basic rules which it relies on don't apply to nonprime exponents (or rather only apply to the parts which are prime exponents), namely that if p is prime, then factors of 2^p-1 are of the form 2kp+1 for some integer k.

[GP2]

Originally Posted by Lexicographer

(I wanted to overcome the 100K limit by trial factoring M163456 = M(2⁷*1277), which is a product of M1277, and looking if there are any new factors between 2113601438322189019 < 2^65 and 2^80 < 1227156720026097481648213, both of which are consecutive factors of M163456).

As ATH mentioned above, enough ECM has been done on M1277 to make us fairly sure that there can be no factors smaller than about 2¹⁸³. The probability that there could be an undiscovered factor of size 2⁸⁰ or smaller is about the same as the odds of winning a hundred million dollars in the lottery not just once but many times in a row.

[kriesel]

Originally Posted by Dubslow

(Either that or pay several thousand dollars to the right people to run SNFS on it.)

Somehow that sounded sort of sinister. Like:

(In the shadows of a dark alley late at night, somewhere in a US midwestern city, wet pavement from the recent rain making it darker, and dimly lit by a shabby warehouse's security illumination, the part that's working, anyway. The sort of neighborhood featuring chain link fence topped by barbed wire, and rebar grilles over dirty windows.) Two shady looking characters in trenchcoats and fedoras approached each other, casting furtive glances in all directions, as if concerned about being followed, and otherwise obviously trying to appear up to nothing in particular, meeting halfway between the security lights. Where it's darkest.

"Hi Slim, thanks for coming. I hear you got connections that can get things done, no-nonsense, for a price. I want you to arrange a factoring hit on M1277 for me. I can make it worth their while. Two grand now to get things rolling, three more when I get proof the deed's done. And a couple g's extra if it's done by the end of next month."

Slim says, "Joe, make it 3, 3 and 2, and M1277's history by Labor Day for sure. We'll need your public PGP key and an email address for sending proof it's done (from an anonymous throwaway account) and that the balance is due. The encrypted message will be in the second least significant bit of each byte of a cat video posted online. We'll send you the URL."

Joe replies, "Deal. Meet back here 11-12 days after the email is sent, same time of day. Wait a sec, I have the down payment now." Joe pulls out from the left inside coat pocket, an envelope stuffed with old worn unmarked non-sequentially numbered small bills, counts out $3000, stuffs the rest in his right coat pocket, and hands Slim the $3000 in the envelope. "I anticipated the key and email request. It's written inside the envelope."

"Make it 7-8 days. Our guys don't like to be kept waiting for their money. It starts tomorrow. You're really on top of the details, almost like you've arranged this sort of thing before. See you by summer's end. Maybe we can, uh, do business again sometime." Slim pockets the envelope and drifts off casually into the developing fog.

Joe heads off in the opposite direction, upbeat. Joe ruminated as he walked back to his car through the lingering puddles. Now it was just a matter of time, and raising a few more grand. No telling what they might do if he couldn't pay the balance promptly, but he was sure he wouldn't like it at all.

The ironic part of dealing with the dark underside of the nearby major college math department, was they certainly didn't need the money. What they made in 100% profit from black market math jobs like this using the free labor of students and grad students, and occasionally assigning academic staff, and with free hardware paid for by alumni, paled in comparison to what they did in their free time, counting cards at casinos for fun, Fourier analysis in the stock market, planted encrypted steganographic leaks in lottery systems, etc. Plus they'd probably publish a paper or two a year subsidized and originated in black market math. Add in legit consulting gigs, and their nominal salaries were in the noise, almost roundoff.

But they had consciously made friends in the criminology department, who knew people who knew people that would do anything for a surprisingly low price, including send people to the ER or morgue. Not the sort of people you want to anger or disappoint.

Nope, don't want to mess with people with tenure and connections. Better tap a few friends with a grudge against M1277 for some contributions, and sell a small asset or two soon. Joe had heard rumors that some of the math guys had rather large botnets, aggressively winning systems over from some of the world's largest spammers (thanks to a friend in the Comp Sci department) and top-shelf highly parallelized distributed computing code for using the bot systems. The CompSci guy had provided extraordinary antitrojan advances, and was rumored to have even better ones that he kept undisclosed for his personal use, and had certainly refused numerous offers from the NSA. So that email from Slim's crowd could be just days away.

M1277 was toast, very soon. That made Joe smile as he reached his car. Until he saw two flat tires. Apparently M1277 had friends, who didn't mind breaking a few rules or laws either, and they were onto him. No cell phone signal. What lighting there was, went out. Joe was shocked to think he might himself soon be "factored".

[Lexicographer]

Thanks guys. I had already found another fresh topic about M1277 which explained most of this to me, but thanks for repeating. And thanks for explaining why mfaktc requires exponents to be prime.

I still think PrimeNet's manual testing page should not assign anything if an assignment of certain type is unavailable or doesn't make sense.

[Mark Rose]

Originally Posted by kriesel

Somehow that sounded sort of sinister. Like:

(In the shadows of a dark alley late at night, somewhere in a US midwestern city, wet pavement from the recent rain making it darker, and dimly lit by a shabby warehouse's security illumination, the part that's working, anyway. The sort of neighborhood featuring chain link fence topped by barbed wire, and rebar grilles over dirty windows.) Two shady looking characters in trenchcoats and fedoras approached each other, casting furtive glances in all directions, as if concerned about being followed, and otherwise obviously trying to appear up to nothing in particular, meeting halfway between the security lights. Where it's darkest.

"Hi Slim, thanks for coming. I hear you got connections that can get things done, no-nonsense, for a price. I want you to arrange a factoring hit on M1277 for me. I can make it worth their while. Two grand now to get things rolling, three more when I get proof the deed's done. And a couple g's extra if it's done by the end of next month."

Slim says, "Joe, make it 3, 3 and 2, and M1277's history by Labor Day for sure. We'll need your public PGP key and an email address for sending proof it's done (from an anonymous throwaway account) and that the balance is due. The encrypted message will be in the second least significant bit of each byte of a cat video posted online. We'll send you the URL."

Joe replies, "Deal. Meet back here 11-12 days after the email is sent, same time of day. Wait a sec, I have the down payment now." Joe pulls out from the left inside coat pocket, an envelope stuffed with old worn unmarked non-sequentially numbered small bills, counts out $3000, stuffs the rest in his right coat pocket, and hands Slim the $3000 in the envelope. "I anticipated the key and email request. It's written inside the envelope."

"Make it 7-8 days. Our guys don't like to be kept waiting for their money. It starts tomorrow. You're really on top of the details, almost like you've arranged this sort of thing before. See you by summer's end. Maybe we can, uh, do business again sometime." Slim pockets the envelope and drifts off casually into the developing fog.

Joe heads off in the opposite direction, upbeat. Joe ruminated as he walked back to his car through the lingering puddles. Now it was just a matter of time, and raising a few more grand. No telling what they might do if he couldn't pay the balance promptly, but he was sure he wouldn't like it at all.

The ironic part of dealing with the dark underside of the nearby major college math department, was they certainly didn't need the money. What they made in 100% profit from black market math jobs like this using the free labor of students and grad students, and occasionally assigning academic staff, and with free hardware paid for by alumni, paled in comparison to what they did in their free time, counting cards at casinos for fun, Fourier analysis in the stock market, planted encrypted steganographic leaks in lottery systems, etc. Plus they'd probably publish a paper or two a year subsidized and originated in black market math. Add in legit consulting gigs, and their nominal salaries were in the noise, almost roundoff.

But they had consciously made friends in the criminology department, who knew people who knew people that would do anything for a surprisingly low price, including send people to the ER or morgue. Not the sort of people you want to anger or disappoint.

Nope, don't want to mess with people with tenure and connections. Better tap a few friends with a grudge against M1277 for some contributions, and sell a small asset or two soon. Joe had heard rumors that some of the math guys had rather large botnets, aggressively winning systems over from some of the world's largest spammers (thanks to a friend in the Comp Sci department) and top-shelf highly parallelized distributed computing code for using the bot systems. The CompSci guy had provided extraordinary antitrojan advances, and was rumored to have even better ones that he kept undisclosed for his personal use, and had certainly refused numerous offers from the NSA. So that email from Slim's crowd could be just days away.

M1277 was toast, very soon. That made Joe smile as he reached his car. Until he saw two flat tires. Apparently M1277 had friends, who didn't mind breaking a few rules or laws either, and they were onto him. No cell phone signal. What lighting there was, went out. Joe was shocked to think he might himself soon be "factored".

Brilliant :D