20180720, 22:40  #1 
Sep 2003
13×199 Posts 
Someone is reporting orphan factors to FactorDB.
I am doing ECM, looking for additional factors of small Mersenne exponents in the 32.5k range and higher, taking these from t30 to t35.
For each factor found, I report it to FactorDB, only to find in nearly all cases that FactorDB already knew about the factor many months ago... but purely as an "orphan", with no connection to the Mersenne number that it's a factor of. The one exception was for M32611, where the factor I found wasn't known before, and interestingly enough turned out to be the final factor that produced a PRP cofactor. This has only been happening in the 32.5k range, not earlier ranges in the 20k's or even in the 32.0k range. Code:
Primenet discovery FactorDB date the "new" factor 32801 20180720 18:38 20171126 08:31 pm 10941641339708256173010175026136553 32779 20180718 14:03 20170515 03:05 pm 22257124311104189361248843704915279 32647 20180717 22:11 20180209 02:42 pm 1302229651615743519197144966488149289 32603 20180715 23:29 20180205 05:27 am 2949889134479752202380228105050793 32611 20180715 08:26 20180715 07:55 pm 16776537025470371142795572474637384977 Right after I found this factor, initially I didn't report it to FactorDB as a factor of M32801, I just searched for the factor itself (10941641339708256173010175026136553). I got the page in the link as mentioned above, except the first three sections just had " none ", with the same create time of November 26 2017. Those sections didn't get filled in until after I queried FactorDB for its M32801 page, which at the time listed only the two previous factors of lengths 13 and 17 digits respectively, and then reported the new factor in the "Report factors" box. Obviously nobody is systematically entering 35 digit numbers into FactorDB, since these number in the hundreds of decillions. So someone must have already ECM tested these Mersenne numbers, found these specific factors, but didn't for some reason didn't report them to Primenet, and only reported them to FactorDB as isolated prime numbers unconnected to the composite Mersenne numbers that they are factors of. Does this ring a bell to anyone? No doubt there are more of these. Clearly there was a bunch of ECM testing that was done that is basically unrecoverable and the factors have to be rediscovered. If someone knows who this is, maybe that person could look in their log files and recover the work and rereport these factors. 
20180721, 15:39  #3 
Mar 2018
3·43 Posts 
Shouldn't this thread rather be in FactorDB subforum?
I do run some factoring of my own for mersenne numbers with composite exponents that could in theory find something for a prime exponent, but in practice doesn't (as higher B1 ecm/pm1 were run before me). And I always submit it to FactorDB anyway, so those couldn't be "mine". I've checked the logs just in case anyway, nothing from the topic was there. However, I do want to say that since a part of my "project" was (is) making sure FactorDB has all algebraic factorizations of mersenne numbers with composite exponents (currently thoroughly done up to about M320000 + some higher ranges *), I unearthed a lot of factors that were added into the "child" numbers and not the "ancestor" numbers themselves (such as in M(8 × 32801) and not M32801 described above). Basically, I'm cleaning up this mess in FactorDB. __ *  there is a bug in FactorDB though, where a number A has a factor B added and then factor C being added can make it forget about B. I clean that up when I find it, but that means it's possible to find a number under my threashold that won't have full algebraic. 
20180721, 22:15  #4  
Sep 2003
13×199 Posts 
Quote:
Since my last post I also found a factor of M32803, it's a very factorrich environment for some reason, but that one was not previously known to FactorDB. Also there have been factors in the 32.0k to 32.5k range, but all of these have been new and not previously known to FactorDB. Do you have a complete list of factors that were discovered for composite M(8 × n) and M(9 × n)? Are some of the exponents that were mentioned earlier in that list (like 32801 and others)? Were all of your factors submitted to FactorDB, and were they submitted as orphans (just the factors themselves, as simple prime numbers), or were they actually reported as factors of a specific Mersenne number? If so, I can run scripts to recover them from FactorDB and find the ones that are missing for M(n) in FactorDB and in Primenet. Did you only use the multiples 8 and 9, or others as well? However, like I said, the factor of M32801 was not linked to any Mersenne exponent. So if it was you that submitted it, something went wrong and factors like that can't be recovered unless you saved log files. 

20180723, 12:41  #5  
Mar 2018
3·43 Posts 
Quote:
Actully... I can run a comparison of factors to report_factors to make sure. I have my own local copy of all factors of all the numbers that I can query easily. I'll report back about this later. Quote:
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As far, as I'm aware, Primenet doesn't have composite n at all. Quote:
Last fiddled with by DukeBG on 20180723 at 12:49 

20180723, 19:36  #6  
Sep 2003
101000011011_{2} Posts 
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20180724, 19:45  #7 
Mar 2018
3×43 Posts 
I've finished comparing the factors of mersenne numbers with prime exponent in FactorDB and in the factor report of mersenne.org (up to n = 2M, that's where Mersenne numbers have special id treatment in FDB and it's the upper limit I'm using).
There were 0 factors not in the report. I.e. no factors missing. Of course, who knows if there are true orphans like the ones you found. There were a lot of factors not in FDB in the range n > 0.5M. I'm currently submitting them to FDB. (I actually submit the recent finds from the mersenne.org report to FDB about once every few weeks, but I didn't know not all nonrecent were there yet) Just in case. List of currently known factors for n from 1,200 to 2,000,000. For fully factored numbers the last factor is not included. For 0..1M it's from my stuff, but it's identical to the report anyway. For 1M..2M it's from the report. 1.6MB, 7zip archive. 
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