Factor bragging

[jjjjL]

We should have a small thread here dedicated to showing off our discoveries as they come in. They don't belong in the coordination thread and they don't really belong in the client thread either.

So to get the boasting started, here's my latest factor:

276504238660693 | 27653*2^5522829+1

276504238660693-1 = 2 ^ 2 x 3 x 7 x 43 x 577 x 877 x 151279

Just found it. Good thing too considering the next assignment is currently 10223*2^5518457+1. Living on the edge.

Cheers,
Louie

[dmbrubac]

I found

1328735974435881607 | 22699*2^5627854+1 a few days ago and
28195479692754961 | 67607*2^5635211+1 just now.

BTW how do you figure out how the factor expands like that? What makes one smooth and another not? (Hey, I'm not a math guy - so what!)

[hc_grove]

Originally posted by dmbrubac
1328735974435881607 | 22699*2^5627854+1 a few days ago and
28195479692754961 | 67607*2^5635211+1 just now.

BTW how do you figure out how the factor expands like that? What makes one smooth and another not? (Hey, I'm not a math guy - so what!)

I normally use the ifactor function in Maple, for your factors I find:
28195479692754961-1=2^4*3*5*37*41*179*7213*59981
1328735974435881607-1=2*3^2*7^2*17*449*541*11083*32917

These numbers are so small that factoring them is no problem at all (trial division is probably a bad idea though), so you can use almost any program that can handle the numbers. I believe Louie once told what he uses in the 'P-1 factorer' thread.

Smooth just means that all the factors are small. I wouldn't call either of those factors smooth.

[jjjjL]

Originally posted by hc_grove
I believe Louie once told what he uses in the 'P-1 factorer' thread.

Yeah, I use an online java applet at http://www.alpertron.com.ar/ECM.HTM

It's probably overkill for these sized numbers but it's easy to use and if I'm away from my main computer, I can just search google for "ecm java factor" and find it real easily.

So just subtract 1 from your factor, put it in the top text box, and press enter. It will factor the number into it's prime components in a fraction of a second.

Cheers,
Louie

[hc_grove]

Originally posted by hc_grove
These numbers are so small that factoring them is no problem at all (trial division is probably a bad idea though),

I was wrong, I just coded up a quick trialfactorer and it factors both your numbers and Louie's so fast the time command can't measure it (on my 2GHz laptop that does regular factoring in the background).

You can download a UNIX version of the program (called trial) and the source code (trial.c) here (the same place as where you can get my version of the factorer).

You can give the program either p or p-1 as input it will figure that out.

It only works with numbers < 2^64.

[Mystwalker]

Just found:
2186703185472067 | 10223*2^5595929+1

2186703185472067-1 = 2 x 3 x 157 x 907 x 22639 x 113051

[hc_grove]

I just found:
176963110569601 | 28433*2^5691433+1

Unfortunately I found that factor 4 days ago sieving I need to update my results.txt.

The factorization of P-1: 2^7*3*5^2*151*1367*89303

2^7 isn't something we see every day.

[Mystwalker]

Got another one:

62447276586432949 | 28433*2^5598025+1

62447276586432949 - 1 = 2 ^ 2 x 3 x 7 ^ 3 x 17 x 29 x 31 x 15107 x 65713

[hc_grove]

My two newest factors:

677309463913963 | 24737*2^5705071+1
782666928978908543 | 27653*2^5705673+1

677309463913962 = 2*3*11^2*2477*12161*30971
782666928978908542 = 2*19^2*43*97*443*10037*58451

[Mystwalker]

323790238554919 | 24737*2^5599951+1

323790238554918 = 2 x 3 x 251 x 991 x 1609 x 134837

[hc_grove]

295288546740041 | 27653*2^5693433+1

295288546740040 = 2^3*5*7*17*73*12211*69593

[hc_grove]

Once again I found a factor that was already known

19144825376419 | 10223*2^5694269+1

This time the factor is to new to be in results.txt so it would even have helped me to update that (it was a week old so it was about time)

19144825376418 = 2*3^3*7*43*59*1021*19553

[dmbrubac]

32089592427168210307 | 67607*2^5664627+1
=2 * 3 * 241 * 1033 * 13627 * 24103 * 65407

13860049223357177 | 55459*2^5720278+1
=2^3 * 7 * 823 * 1361 * 1657 * 133351

[Nuri]

Originally posted by hc_grove
Once again I found a factor that was already known

19144825376419 | 10223*2^5694269+1

This time the factor is to new to be in results.txt so it would even have helped me to update that (it was a week old so it was about time)

19144825376418 = 2*3^3*7*43*59*1021*19553

That's strange...

This factor was submitted in April 2003 (notice it's a 19T factor).

[jjjjL]

yeah, that should value shouldn't even be in the current .dat file. yours must be old.

[hc_grove]

Originally posted by jjjjL
yeah, that should value shouldn't even be in the current .dat file. yours must be old.

I've replaced it with the one I've used for sieving since we started sieving n=1M to 20M.

[hc_grove]

This time an unknown factor:

6853123410953119 | 4847*2^5707551+1

6853123410953118 = 2*3*13*17*9403*12227*44953

[Frodo42]

finally I'm back in the race with a factor

58266879992975447 | 27653*2^5713017+1
58266879992975446 = 2 x 13 x 509 x 10007 x 16231 x 27107

I was getting woried that I would not find anything anymore, but I guess its my turn for some bad luck, or maybe it's because I'm only using half the CPU of I have used the last couple of months since a working prp-client for this Linux-box appeared.

[Frodo42]

Yiekes I have also started finding factor-duplicates with P-1
18197867605331 | 55459*2^5713714+1
I guess it's time to change from 47 to 48 ...

Weird it's nowhere to be found in the result.txt file, is this one also to old to be in the SoB.dat?

[MikeH]

Weird it's nowhere to be found in the result.txt file

That's 'cause it's too small. At 18T it's in the lowresults.txt file.

You need the latest sob.dat file from which all these canidates are removed, then the latest results.txt file will work fine.

latest sob.dat

[Frodo42]

That's 'cause it's too small. At 18T it's in the lowresults.txt file.

Thanks, I hope I haven't wasted too much CPU rechecking small factors ...

[priwo]

210713652400249 | 33661*2^5737128+1
210713652400248-1 = 2 ^ 3 x 3 ^ 2 x 19 x 541 x 284 714321

210718454330387 | 21181*2^5740772+1
210718454330387-1 = 2 x 2371 x 44436 620483

both found today with the sieve

[Nuri]

762210304266563 | 27653*2^5992989+1

762210304266562 = 2 x 281 x 2797 x 9871 x 49123


I've recently finished two 8000 ranges, and this is the only factor I got out of the 467 k/n pairs within the 16000 range.

So, the question is, do you think this is normal? (I mean, 0.2% hit rate)

PS: May be, it has something to do with the settings I use (48 1.3 160).

[hc_grove]

Just found a new factor:
223648654756363 | 10223*2^5709401+1

223648654756362 = 2*3*11^2*1231*7757*32261

Mystwalker is going to (or might have, but just not reported) find this factor sieving within the next days. As Mystwalker is the next to pass on the scoreboard, this couldn't be better.

[Mystwalker]

Originally posted by Nuri
I've recently finished two 8000 ranges, and this is the only factor I got out of the 467 k/n pairs within the 16000 range.

So, the question is, do you think this is normal? (I mean, 0.2% hit rate)

PS: May be, it has something to do with the settings I use (48 1.3 160).

I also got very few factors lately (none in the last ~7000), although I'm using B1=35000, B2=411250.

Originally posted by hc_grove
Just found a new factor:
223648654756363 | 10223*2^5709401+1

223648654756362 = 2*3*11^2*1231*7757*32261

Mystwalker is going to (or might have, but just not reported) find this factor sieving within the next days.

I'm not that far right now. Chances are that PRP will get there first (well, second )...

As Mystwalker is the next to pass on the scoreboard, this couldn't be better.

That should still take some months. Plus, I still got a neat trick or two left once I have enough time to accomplish them.

[hc_grove]

And once again a new factor

780376430289319 | 10223*2^5733485+1

780376430289318 = 2*3*29*2617*10091*169831

[Mystwalker]

The whole time nothing and then ... 2 ones right after each other!

819201694820819 | 27653*2^5737929+1
819201694820818 = 2 x 239 x 479 x 32251 x 110939

520550137161211 | 33661*2^5738184+1
520550137161210 = 2 x 3 x 5 x 13 x 41 x 439 x 2663 x 27847


What bounds are you guys using?
I'm especially interested in the B2 bound. There have been almost no p-1 factor factors (so to say...) higher than 100,000 and a little...
Maybe I should use lower bounds then.

[hc_grove]

The fifth (and final) factor:
1649427586996001 | 24737*2^5709871+1

1649427586996000 = 2^5*5^3*7*31*73*197*132137

I've used optimal bound (1.5 47 384) giving B1=25000 B2=231250.

[dmbrubac]

52252110283617819719 | 10223*2^5725757+1
52252110283617819718 = 2*11*13*281*353*5981*10711*28751

[Nuri]

Originally posted by Mystwalker
The whole time nothing and then ... 2 ones right after each other!

2 OrkunBanuTST (Nuri) 1731196.94+(10.82) ......
3 Mystwalker 1720152.33+(10.75) .......




I must do something, and do it quickly.

[dmbrubac]

Originally posted by dmbrubac
52252110283617819719 | 10223*2^5725757+1
52252110283617819718 = 2*11*13*281*353*5981*10711*28751

This factor isn't showing up on the stats page. Any ideas why not? The submission page took it OK.

[hc_grove]

Originally posted by dmbrubac
This factor isn't showing up on the stats page. Any ideas why not? The submission page took it OK.

Probably because it's larger than 2"64 and should be submitted via http://www.seventeenorbust.com/largesieve/ to actually end up in results.txt. I think I've seen the ordinary submission form accept large factors without actiing on them before.

[dmbrubac]

Thanks!

[MikeH]

Originally posted by dmbrubac
52252110283617819719 | 10223*2^5725757+1
52252110283617819718 = 2*11*13*281*353*5981*10711*28751

There is something strange here. This factor is less than 2^64 (only just), but when I try to submit it I get

52252110283617819719 10223 5725757 verified. 

Factor table setup returned 1
Test table setup returned 1 

1 of 1 verified in 0.07 secs. 
1 of the results were new results and saved to the database.

And I get the same no matter how many times I try. Strange, is it being added to the DB or not?

EDIT: Not a big problem, one of your attempts to submit the factor obviously worked, it's there in the stats now.

And that makes it the second largest factor found this year.

[hc_grove]

Originally posted by MikeH
There is something strange here. This factor is less than 2^64 (only just), but when I try to submit it I get

18446744073709551616 = 2^64
52252110283617819719 = this factor

Which looks larger to you?

Factor table setup returned 1
Test table setup returned 1 

1 of 1 verified in 0.07 secs. 
1 of the results were new results and saved to the database.

And I get the same no matter how many times I try. Strange, is it being added to the DB or not?

This is exactly what I've seen with factors larger than 2^64 and the ordinary submission page.

[dmbrubac]

well, it is a factor bragging thread!

[Mystwalker]

Then let's brag again!

357737103943831 | 4847*2^5738943+1
357737103943830 = 2 x 3 ^ 3 x 5 x 13 x 601 x 9227 x 18379

Seems like Nuri is 3rd now.

[MikeH]

18446744073709551616 = 2^64
52252110283617819719 = this factor

Which looks larger to you?

Remind me never to use Windows calculator for big math again

Paste the number in decimal, switch to binary, it's <2^64. Guess that's because WinCalc only handles math upto 2^64.

[mklasson]

Originally posted by MikeH
Remind me never to use Windows calculator for big math again

Give http://pari.math.u-bordeaux.fr/ a try -- it's great.

[Nuri]

Seems like Nuri is 3rd now.

Another sieve factor that came just in time.

216379013870543 | 4847*2^5861391+1