Reserved for MF - Sequence 4788

[Mini-Geek]

If my math* isn't wrong, at the current size, you can only expect 1/402 downdriver breaking lines per line currently. This would be enough to lower it by about 80 digits, (figuring 5 lines per digit drop) but as you go down, the chance of each line breaking it goes up. Right now, assuming 0.2 digits lowered per line, we have a 50% chance of going 240 lines, to 127 digits on this downdriver run alone. As we go along without losing the downdriver, how low we can expect to go will continue to go down (just like as GIMPS searches farther without a prime, their expected 'next prime' value keeps going up). e.g. if we have the downdriver at size 150, we can expect to go 206 more lines, to 109 digits.

* My math: 402~=log(10^175)=log(10)*175
Explanation: you need a prime to break it, and the chance of a random number n being prime is about 1/log(n), but it must be of the form 4n+1 to break it, which is half of the primes, and the cofactor remaining after the 2 is odd, which doubles the chances, bringing you back to 1/log(n).
Based on this math and the assumption that 5 lines per digit during a downdriver run is a good average, (from my memory and looking at one big downdriver run that looks like a pretty good number - but all things considered, take these results with a grain of salt) I wrote the attached Python script. Run it with the current size as an argument, and it will tell you how far a downdriver run at that size can be expected to go to (it stops when the probability is 50%, not when the expected is 1, but if you want you can tweak the code).

[Batalov]

Let's not rest on laurels, though. Any alpinist will tell you that the way down may be every bit as hard as the way up.

Back to work! back to work!
If I had a cent for every downdriver I've seen, ... ... ...I would probably have had enough for a Two-buck Chuck.

[schickel]

Originally Posted by firejuggler

is it a record?

Yes, this is record territory.

In May 2010, Don LeClair got the downdriver at 158 digits for 3906. (Went from 158 to 131 digits.)

Back in January 2011, I noticed that Paul Zimmerman had captured the downdriver at 164 digits for 1134. (Currently at 158 digits...)

So not only did we break the record, we set the bar higher by 11 digits!

if we manage to 'terminate' 4788 i guess it will be a good news.

It would be fantastic news! Currently the sequence that has gone the highest before terminating is 921232, which hit 127 digits for the peak.

[Syd]

Wow!

I suppose noone is sieving the remaining c121? I'll start it, will take me just a few hours. ecm to t40 is done.

[FactorEyes]

Originally Posted by Syd

Wow!

I suppose noone is sieving the remaining c121? I'll start it, will take me just a few hours. ecm to t40 is done.

Don't sweat it. I have a polynomial, and did t45 ecm.

[FactorEyes]

Originally Posted by FactorEyes

Don't sweat it. I have a polynomial ...

and now a factor:

p60 263383244271008300404438703166546029498860766484450800390909
p62 34139562660572251786716343016790715468655244971318673374913793

Now at iteration 2643, with a C125. I'll run a little ECM, but I have no other plans for this one overnight.

EDIT: Now a C170 at iteration 2644.
EDIT: C170 now a C136.

[Batalov]

c136, u mean?

[Andi47]

Originally Posted by jrk

2639 .   2149411071955720860657336166890905655965824483220064338549598355132035428476407603119480214337905387962490548891054067056757890816363264513247313673869429774079145097281497488 = 2^4 * 7^2 * 36313 * 1586371 * 8912537 * 599792105155937515235840077089871 * 111161303612150687055927860992109312122233326341 * 80090463174488727809679157647738514605828822621791933688597706610570360537
2640 .   2695125631380877120688075316133060454693089119027491140439864162640385444672996877811472864516874780653131908475144601204396797271006125221524885841477163968713595352514710128 = 2^4 * 7^2 * 13^2 * 37 * 23012406055723349992959602849909 * 135829026705324869859041721257513 * 175881396656573732523601134643388090865029684615022498425259778874068454506921441755121344108778897055567
2641 .   4060191761776564175177059510457437381560526099279974065526141757987967817908480035460777708242145782931986876700367614029075549124933548119439790009907188914074930979540271632 = 2^4 * 253761985111035260948566219403589836347532881204998379095383859874247988619280002216298606765134111433249179793772975876817221820308346757464986875619199307129683186221266977
2642 .   3806429776665528914228493291053847545212993218074975686430757898113719829289200033244479101477011671498737696906594638152258327304625201361974803134287989606945247793319004686 = 2 * 9001 * 5424608533 * 19595267390311 * 221223557335948879375904953 * c121

Wonder how low it will go?

(I'll let someone else handle the c121...)

Woooohoooo!!!

[FactorEyes]

2351@3e6 (t40)

800@11e7 (1/4 t50)

I'll run the 11e7 threads for another 2 hours; that will put us at ECM overkill.

[FactorEyes]

We just passed the ECM futility point. Anyone doing a polynomial search?

I just started a polynomial hunt at 20:40 UTC.

If anyone is already on this one, let me know, and I won't bother to continue.

[FactorEyes]

A p54, namely 201905557707743425541689511934123861382714511914540951, takes us onward to 2645, where a C115 sits.

I'm running light ECM. May sieve it tonight if nobody wants the baton.