[QUOTE=debrouxl;436658]However, the composite cofactor of [code]1398036042749871729843146160774339503205345274956506531^5-1 (quartic)[/code] is C193, and 14e can cope with this one using 31-bit LPs, so I've started it.[/QUOTE]

Please delete it; the number has already been factored. mersenneforum.org/showthread.php?p=435616

[QUOTE=RichD;436712]Are you sure?
Looking at the first one it is a SNFS(208) or GNFS(155).
NFS@Home uses 29-bit for SNFS(208) and GNFS(155) mostly uses 30-bit.[/QUOTE]

We really don't want to be running anything as easy as a GNFS(155) on nfs@home - it's a complete waste of time and effort compared with running it at home in a week on a quad-core Haswell.

I have screwed up two of these OPN numbers in the past - I assumed that OPN numbers would have no small factors, but these ones are replete with them. I'd really like to see a justification of where the numbers come from and why the factorisations are interesting.

wblipp's outstanding numbers
 

[code]
C153 181^115-1 * reserved fivemack
C186 3237350394808285103075641617594465564146206546711^5-1
C172 3633300011821322527883441762063547117079391973569^5-1
C175 18864198964623859882837445679850969284402949066171^5-1
C188 24772285175707806384099574440402334706455060939751^5-1
C178 2164375781978715114102841584382563299103035038465117^5-1
C177 37424900799714233724027045150234142768618867083668617^5-1
C158 1435130102620557966393278537760156017252441420078670131^5-1
C172 241^125-1 (queued at 15e)
C248 5659^67-1 * sieved by 14e, jyb post-processing
C250 6007^67-1 * sieved by 14e, jyb post-processing
C155 7282882732751770301917311394675342168569930282640579^5-1
C143 37141302977105581064921322418772202338727337015016057^5-1 * done
C151 230605827695659261374183298936900535402657822464812511^5-1
[/code]

None of these have factors in factordb; I would be inclined to queue them as SNFS jobs in descending order of composite size, and will have a go with GNFS starting at the smallest composite myself.

(reserving C143:371...057^5-1) (now completed)

C188_149_78 has got a polynomial: [url]http://mersenneforum.org/showpost.php?p=436689&postcount=643[/url]

A full t60 of ECM was done on it.

To be precise, it's got nine candidate polynomials.

I will do the trial-sieving tonight and queue the best one on 15e in the morning.

14e queue is out of workunits.

[QUOTE=fivemack;436714]We really don't want to be running anything as easy as a GNFS(155) on nfs@home[/QUOTE]

The guidelines in [URL="http://www.mersenneforum.org/showpost.php?p=408161&postcount=167"]post 167[/URL] say that 14e is interested in GFNS 155 to 170. I know that we have been accepting substantially less ECM than that post indicates in order to keep the queues full. I thought the reduced ECM was going to be a temporary measure, but I'm no longer sure. At the time of that post the 15e queue requirements were not discussed because there was no shortage of adequate numbers - that no longer seems to be case. Perhaps we need updated guidelines.

[QUOTE=fivemack;436714]I assumed that OPN numbers would have no small factors, but these ones are replete with them.[/QUOTE]

I like to post the numbers with factordb links so it's easy to find the current residual, but I see that I failed to do that with these. I'll be more careful about posting those links and also an explicit statement of the composite size.

[QUOTE=fivemack;436714]I'd really like to see a justification of where the numbers come from and why the factorisations are interesting.[/QUOTE]

These numbers are from Pascal's "first composite" files. Their factorizations are of interest because they allow factor chains to be built using larger primes, resulting in shorter factor chains. As First Composites, we know these results will always remain of interest - they cannot become obsolete because some earlier composite replaces this branch of the factor chain.

You are more accustomed to seeing RoadBlock numbers instead of First Composite numbers. RoadBlock numbers typically have no known factors - or perhaps tiny factors. You are not currently seeing Roadblock numbers at NFS@Home because Ryan Propper has been factoring the roadblock numbers in the 14e range, 15e range, and higher.

[QUOTE=wblipp;436817]The guidelines in [URL="http://www.mersenneforum.org/showpost.php?p=408161&postcount=167"]post 167[/URL] say that 14e is interested in GFNS 155 to 170. I know that we have been accepting substantially less ECM than that post indicates in order to keep the queues full. I thought the reduced ECM was going to be a temporary measure, but I'm no longer sure. At the time of that post the 15e queue requirements were not discussed because there was no shortage of adequate numbers - that no longer seems to be case. Perhaps we need updated guidelines.
[/QUOTE]

Is this what you're looking for?

[QUOTE=debrouxl;433913]* for 14e, the sweet spot on difficulty is SNFS 236-~250 and GNFS 16x. A SNFS 254 task recently produced decent yield even with 31-bit LPs, but that was a flare.
* for 15e, from what I can see (normally, I'm not taking care of it, though I have access to both the 14e and the 15e management forms), the sweet spot is SNFS 27x and GNFS 18x. GNFS 190-195 work, 195+ stretch 15e to its limits.
[/QUOTE]

C188_149_78 now queued up on 15e.

William or somebody else, could you provide ready-made polynomials for the impending OP numbers posted on the previous page (#550-#599) ? :smile:

Pending improvements to the queue management infrastructure, which shall hopefully eliminate e.g. the recent blunder of me queuing to 14e a number already factored by 15e (measures to prevent this one were already on the todo/wish list at the time I did it), I must say that the validated, ready-made polynomials posted by Sean or Jon are nice to queue managers :blush:

Polynomials for homogeneous Cunningham numbers
 

From Jon Polynomials for homogeneous Cunningham numbers, rest on the attached file.

[CODE]
# 8-3,263
n: 1074220397608063744092456701155722449290119666365802488437623526859160975424802319394559862204759874721680339424141057973064241372305556832686404359799262209821344487053
# 8^263-3^263, difficulty: 238.89, skewness: 1.18, alpha: 0.00
# cost: 3.51489e+18, est. time: 1673.76 GHz days (not accurate yet!)
skew: 1.178
c6: 3
c0: -8
Y1: -984770902183611232881
Y0: 5444517870735015415413993718908291383296
m: 948846335242689185043051815807246334930528758841171544371255697736113038170511956575288886265085139291375316115295849735588039597141802685896968550514902128457299280449
type: snfs


# 5+3,344
n: 50947357611569563899665041936661858420133932467666010404141837622987159151159644790341742059904557155078085087274009047956506693686019417370450122236059032711789321363607489
# 5^344+3^344, difficulty: 240.45, skewness: 0.84, alpha: 0.00
# cost: 3.96943e+18, est. time: 1890.20 GHz days (not accurate yet!)
skew: 0.843
c6: 25
c0: 9
Y1: -1570042899082081611640534563
Y0: 6938893903907228377647697925567626953125
m: 29232390366123976420458996829448819263194918088110616099369889901211728757847643877490814246621681973578055471000687963446283638373524220159411231949389819302777681536280557
type: snfs


# 7+2,283
n: 779356160021698734619124339522489196389911960399415019200624443515246798023068429394986946980171572326396448883333884608123629308155936846255139407706038878031544352406835581
# 7^283+2^283, difficulty: 239.16, skewness: 0.81, alpha: 0.00
# cost: 3.59009e+18, est. time: 1709.57 GHz days (not accurate yet!)
skew: 0.812
c6: 7
c0: 2
Y1: -140737488355328
Y0: 5243338316756303634461458718861951455543
m: 259087587104451103020994232905081544846087250472234975548999965726076326416893905480895358877510761586185171510529067297812977507760802906157551419317512472494134686305611200
type: snfs


# 11+3,232
n: 215891572629251446618183306068419238982167451861393261158220841627610613602312402575359432096810105644562893050898047222779638778182505258475562282901768184857290403847508660887857
# 11^232+3^232, difficulty: 244.64, skewness: 1.54, alpha: 0.00
# cost: 5.50025e+18, est. time: 2619.16 GHz days (not accurate yet!)
skew: 1.542
c6: 9
c0: 121
Y1: -4052555153018976267
Y0: 41144777789250865278081232758997200423491
m: 6284310013250138296491451177346305782146997710098402938764848480638570578926045063670279535599034646051359051352659631632138454351051678471338029684340288071886520727617514634861
type: snfs


# 9+5,254
n: 338768360620111579981546421129315319242241720594161539168276558332777373529709840407292022885094758060826228345875450126199983358548279804119504322074458852002011499823593169432569
# 9^254+5^254, difficulty: 242.38, skewness: 0.82, alpha: 0.00
# cost: 4.61482e+18, est. time: 2197.53 GHz days (not accurate yet!)
skew: 0.822
c6: 81
c0: 25
Y1: -227373675443232059478759765625
Y0: 11972515182562019788602740026717047105681
m: 331490796336612006616409530936621901091140527503423422048189528873255957939825009774789321332315924923279935488854166202617105223720210763280151605362850815409015337021821459986367
type: snfs
[/CODE]