Pascal's OPN roadblock files

[ryanp]

I currently have 1,576 composites left in my local "input.opn" that is {mwrb2100} - {factors found}. I've updated https://cs.stanford.edu/~rpropper/opn.txt with a list of factors found so far. (I also don't seem to have a cert issue).

[RichD]

Originally Posted by ryanp

(I also don't seem to have a cert issue).

Perhaps it is a local cert on my end.

[lavalamp]

I've just submitted a rather large haul of factors to factordb, but I like the look of ryanp's factor reporting format so I processed my factors into the same format and attached them to this post.

I believe many of these factors have already been accounted for in the t2200 file, but at least 130 have not. Unfortunately my script does not currently separate out the two yet.

Here is my progress on the t2200 file:

For the ~13500 composites less than 2^1018 which can be run on GPU, I'm running 1152 curves per candidate @ B1=3e6, B2=14e9. So far 3000 composites have completed stage 1 and 2000 have also completed stage 2. It will be 2-3 more months before this finishes.

For the ~58000 composites larger than 2^1018, all of them have finished 100 curves @ B1=50e3, B2=13.7e6. I'm starting another run of 100 curves now which should take a couple of weeks.

[lavalamp]

Originally Posted by lavalamp

I'm starting another run of 100 curves now which should take a couple of weeks.

Ah ... a minor update to that. As I was plugging in Christmas lights today, the power supply of this machine {censored} exploded.



This will cause a minor delay until I can aquire a replacement and check that the rest of the machine is OK. Progress on the sub 2^1018 composites will be unaffected.

[Pascal Ochem]

The run for \(10^{2200}\) hit this roadblock:
\(11^{18}\) \(6115909044841454629^{16}\) / \(3^4\) / \(5^1\) / \(103^{172}\) / \(227^4\) \(2666986681^{36}\).
It is difficult to circumvent because the abundancy is close to 2.
Without a factor of \(\sigma(6115909044841454629^{16})\), \(\sigma(103^{172})\), or \(\sigma(2666986681^{36})\),
I will have to find a better way to handle roadblocks.
Also, this roadblock prevented the program to produce the file mwrb2200.

http://www.lirmm.fr/~ochem/opn/ropn_comp.txt
These are (probably easier) composites that might simplify the proof in section 6 of this paper.
http://www.lirmm.fr/~ochem/opn/OPNS_Adam_Pace.pdf

[VBCurtis]

Does the first link contain the actual composites you need to factor? I mean, should we throw some ECM firepower at those three large blockers?

Are these three all SNFS difficulty above 320? We can crack some pretty tough numbers these days, but I'm not sure ~330 is within forum firepower.

[henryzz]

Originally Posted by VBCurtis

Does the first link contain the actual composites you need to factor? I mean, should we throw some ECM firepower at those three large blockers?

Are these three all SNFS difficulty above 320? We can crack some pretty tough numbers these days, but I'm not sure ~330 is within forum firepower.

(103^173-1)/102 is 347 digits
(2666986681^37-1)/2666986680 is 340 digits
(6115909044841454629^17-1)/6115909044841454628 is 301 digits


It looks to me like (6115909044841454629^17-1)/6115909044841454628 probably has an octic polynomial at difficulty 301(using the degree halving trick). I am not sure how doable this is.

[VBCurtis]

Thanks! I'll start some ECM on the C301 at B1 = 15e7 tonight.

[henryzz]

Originally Posted by VBCurtis

Thanks! I'll start some ECM on the C301 at B1 = 15e7 tonight.

I would suggest checking that I am correct about the octic before going too crazy on it. Maybe checking whether it would be sane to do as well. While it is large I am fairly sure octic is suboptimal. It could be like doing a quartic in reverse.

[charybdis]

Originally Posted by henryzz

I would suggest checking that I am correct about the octic before going too crazy on it. Maybe checking whether it would be sane to do as well. While it is large I am fairly sure octic is suboptimal. It could be like doing a quartic in reverse.

x^17-1 does produce a reciprocal octic. NFS@home have done a few of these, but looking at the postprocessing logs, I'd guess they're as difficult as sextics at least 30 digits larger? The octic here will still be faster than the difficulty-339 sextic with an enormous coefficient, but I'm not sure it's sane. Lots of ECM is surely the way to go.

[henryzz]

Unless I have made a mistake:

f(x)=x^8+x^7-7x^6-6x^5+15x^4+10x^3-10x^2-4x+1
g(x)=6115909044841454629x-6115909044841454629^2-1


What size have the previous reciprocal octics been?