Missing factors at the 'Known Factors' page

[MatWur-S530113]

Hello,

today I got a litttle bit trouble because at the 'Known Factors' page not all factors are listet. F.e. for M2251 there is only 1 factor listet. I put M2251 to my prp-test proggy, divided out this factor and got: the remaining co-factor is still composite. The Alpertron said it, too (I forgot at that moment that the Alpertron does not ask for known factors of the number from the server, if one factor is given already). I run some small ECM-curves with prime95 and 'found' 2 factors. Then I became startled and asked the Alpertron again only for M2251 and soon I got all factors. I stopped the curves running with prime95, but some are reportet as:
pnErrorResult=40
pnErrorDetail=Factor 1687942505818611032423917201 reported for completely factored M2251

Thus I have 2 questions:
why are not all known factors listet at the status pages?
can I be sure that at least those numbers with remaining composite cofactor have all known factors listet at the status pages?

best regards,

Matthias

[Mr. P-1]

Presumably the cofactors left after all the known small factors are divided out are not listed because they can be easily generated in any particular case, and storing them all would be prohibitive. Many of them will be tens of millions of digits long.

[MatWur-S530113]

Originally Posted by Mr. P-1

Presumably the cofactors left after all the known small factors are divided out are not listed because they can be easily generated in any particular case, and storing them all would be prohibitive. Many of them will be tens of millions of digits long.

Surely the last factor is not listet if it is a prp, that's ok. (That's why I testet it with my proggy). But at least at M2251 there are 3 factors not listet which are needed to get the last factor:
p6 778847
p26 17620954939878356226435007
p34 1687942505818611032423917201
only this factor is listet:
p6 400679
the remainig cofactor of M2251 after dividing out these 4 factors is a p614
If only the first factor of completely factored Mersennenumber is listet, then at least a hint about 'completely factored' is needed at the 'Known Factors' page (and the 'Exponent Status' page).

best regards,

Matthias

[J.F.]

The goal of GIMPS is not to list factors, so why bother storing them. I guess this is just one of many cases only the smallest factor is listed. You are free to submit more, but this just isn't the place for them.

Will Edgington maintains a database with known Mersenne factors and search limits etc.
http://www.garlic.com/~wedgingt/mersenne.html

[MatWur-S530113]

Hello,

of course it is not GIMPS' first wish to list all factors. But the project keeps track of the ECM-curves for already factored M-numbers at least up to exponent 10000. And to prevent myself from finding of already known factors I need to know them (that's about my second question). If a number like M2251 is already completely factored, then the project doesn't need anymore list all factors, one is enough. But then at least a hint about the status of completely factored is needed imho. Or you can get such trouble like I got. Of course I know that such an exponent is not longer listet at the ECM-status page for M-numbers with known factors. But I don't look always at the ECM-page. It is simply a question of time. And btw. there are listet all factors of M29, so why not of M2511. I agree that there must be a limit for the exponent for the storing of all known factors. But this limit must be at least the same as the exponent limit for the ECM-curves with known factors the server keeps track off. And to store all known factors up to exponent 10000 should not need much more space as the list provided at the moment.
How I said, I don't know if there are missing known factors for not completely factored numbers. I will check it, maybe tomorrow. If yes, all who are doing ECM on these numbers will have some problems with finding already known factors. The missing known factors of completely factored M-numbers are less a problem if there is a hint about the status in the 'Known Factors' page. Then one can be sure about the status without looking at the ECM-status page again...

best regards,

Matthias

edit: of course I know Edgington's tables and Wagstaff's and Brent's... but do you look every time at this tables for all known factors if you only want to run some ECM-curves at an exponent?

[cheesehead]

Originally Posted by MatWur-S530113

to prevent myself from finding of already known factors I need to know them (that's about my second question).

There used to be a regularly-updated file named lowm.txt that listed all known factors. I don't know if it's still maintained somewhere on mersenne.org.

Edgington's page has a link to "mersdata.zip: lowM.txt, DATABASE, DB.nf, primeM.txt, factoredM.txt, etc., zipped"

I don't know whether its files are updated regularly. If they are, you could get lowm.txt there.

If a number like M2251 is already completely factored, then the project doesn't need anymore list all factors, one is enough. But then at least a hint about the status of completely factored is needed imho. Or you can get such trouble like I got. Of course I know that such an exponent is not longer listet at the ECM-status page for M-numbers with known factors. But I don't look always at the ECM-page. It is simply a question of time.

So, I presume you're not doing ECM on these exponents, since otherwise how would you decide what B1 to use and how many curves to run?

Then one can be sure about the status without looking at the ECM-status page again...

Why is looking at the ECM-status page such a time-burden for you? How often are factorizations being completed in the range of low exponents you are testing?

Download and store a copy of the page every month or so, so you can refer to that copy quickly offline.

Better yet: sign up for one of those free services that will notify you whenever a particular web page changes, so you can re-download only when it changes.

but do you look every time at this tables for all known factors if you only want to run some ECM-curves at an exponent?

Well ... you'll have to look at some table to get all known factors for that exponent, won't you?

How about downloading and storing a copy of Edgington's table (or the file I mentioned above) once a month or so, whenever you do the same for the ECM-status page? Or put it on your page-change-notification service list.

[Prime95]

Thanks. Let me know if you find other factors missing from the database.

[MatWur-S530113]

Hello,

cheesehead, I will come back to your answer, but atm I have some other problems detectet while finding some more of these factors.

I createt a list with all known factors (for exponents from 1 to 5000) from the GIMPS database and stored it to a text-file. With my own proggy I read out the exponents, createt the M-numbers, divided out the factors and performed a prp-test at the remaining co-factors. The composite cofactors I stored in a table. Then I deletet all those exponents from this table which are still at the ECM-progress page listet with known factors for ECM'ing.
From the remaining exponents in the list I knew this: my proggy says that the last remaing cofactors of these exponents are still composite but the server hasn't listet them anymore at ECM-page, so the server 'thinks' or 'knows' that the last remaining cofactor is prp. It follows that there must be more factors for these exponents. I searched for them (most I got with the Alpertron, some from Brent's, some from Wagstaff's tables etc...). I attached a list with the factors I got.

But there are 3 exponents I have some problem with:
M857 should be deletet from the ECM-page as the last remaining cofactor is prp afaik, 2 factors were added some hours ago (nice to see such long factors found by ECM )

But the real problems are M3259 and M4729
from both numbers 1 factor is known at the GIMPS-database:
M3259: 21926805872270062496819221124452121
M4729: 61944189981415866671112479477273
my proggy says: the remaining cofactors of these M-numbers are still composite. They are not listet for ECM'ing with known factors, thus I have to assume the server 'thinks' or 'knows' that these cofactors are prp. But there are no more factors to find for these 2 exponents. The Alpertron makes a Rabin Miller prp-test at the cofactors, I haven't finished them as they need much time. But the output of my proggy's prp-test that they are composite is a statement for sure...

I already run curves with B1=1e6 (changing to B1=3e6 soon) on the remaining cofactors, but I need a verification of the prp-test. Are the remaining cofactors of M3259 and M4729 composite or prp?
If they are composite they should be added to the ECM-progress page with known factors. If they are prp and my proggy's prp-test is faulty then I will report some senseless work in a few hours.

best regards,

Matthias

 
M1223 c
31799,439191833149903
M1289 c
108817410937,827446666316953,9580889333063599,16055826953448199975207
M1303 c
1140690503
M1307 c
141196558805510033914433414063,161633497146742177992711798481
M1327 c
6363071161
M1361 c
3397057,137450113,30322542339673,15459763525875943,856450061281312036458486309832227737
M1459 c
93377
M1531 c
14661821742553
M1553 c
354271470446427666439,432076532964254217618937,67625467049371226906709645391,169336513704068271013494661928987033
M1693 c
3 361912 
721093432406946778492953,414073707708708359213580367115039,21637859486326546740118800926236362073
M1783 c
59767828889,21991704205191358757046463,60701317462845977755176049,1943163990190458280022304032374692151
M1997 c
2982351597692070261023,342849716969843931264330628335073
M2069 c
1816583,1662927218441,1776510807594595616100267889706057
M2311 c
4514379640917651135021865565129
M2383 c
889865441849036810633962436005361
M2447 c
2771915076094391,459390495235738452861593,24700068031700569654277801,3922634957266302331319319913
M2549 c
5490243876052618831,324013067177330948216089046508086969
M2677 c
81699346406928829474760749455463
M2699 c
307687,1187561,7570504839257,1987104667810711
M2837 c
138871151,336396730297
M2909 c
46174737359,29101424767901148287,2810063687215981074703243943
M3041 c
5565031
M3259 c
???
M3547 c
148823192092809407
M3833 c
340789152474053904109001
M4127 c
2080009
M4729 c
???
M4751 c
3274778783,629530076753,81630665742097,1507074535068001
M4871 c
144558074148074062894378117006327

[J.F.]

Originally Posted by MatWur-S530113

But the real problems are M3259 and M4729
from both numbers 1 factor is known at the GIMPS-database:
M3259: 21926805872270062496819221124452121
M4729: 61944189981415866671112479477273
my proggy says: the remaining cofactors of these M-numbers are still composite.

According to Mathematica (PrimeQ) the cofactors are both prime.
Edgingtons factoredM.txt agrees, which indicates he has primality certificates.
I guess your program contains a bug...

[Prime95]

Prime95 thinks the 2 are PRP:

[Jan 21 12:42] Worker starting
[Jan 21 12:42] Setting affinity to run worker on any logical CPU.
[Jan 21 12:42] Starting PRP test of M4729/61944189981415866671112479477273 using FFT length 224
[Jan 21 12:42] M4729/61944189981415866671112479477273 is a probable prime! Wd1: 24F224F2,00000000
[Jan 21 12:42] Starting PRP test of M3259/21926805872270062496819221124452121 using FFT length 160
[Jan 21 12:42] M3259/21926805872270062496819221124452121 is a probable prime! Wd1: 19761976,00000000

M857 has been removed from the ECM page. It was factored by NFS a day ago.

[bsquared]

Originally Posted by J.F.

According to Mathematica (PrimeQ) the cofactors are both prime.
Edgingtons factoredM.txt agrees, which indicates he has primality certificates.
I guess your program contains a bug...

FWIW, Yafu also agrees that the cofactors are prime. It uses the Rabin-Miller prp test with 20 witnesses (the first 20 primes). I believe Mathematica does MR base 2 and 3, then a lucas test.