2LM Table

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
...
2	2314M	C306	108(0.224968)	52(0.0415157)	100(0.00660049)	0(0.000897706)	
119288766558893719789074010033421352139990385060091040788044948113130430659694748048209317677116266733957136434037821506033944095631557976228924929116968991433080257303123194591911325937696826330423332938431507262700314652357530622544186428205887743726915752413130351875502979661858439360644136477019611873
...

Wow!; that was quick. The generic c251-c299s (not 2+ or 2- for n <=1200)
just finished their run to nearly 50% t50; and here's the first pass on
generic c3xx (not ...), and already a condor-xp factor,

p49 = 2611399441339499373329885013353099860731957106781

from the first 500 curves of this 2nd pass, to be added to the 1000 curves
from the 1st pass, expecting a total of three new passes for 2500/7830;
which will bring these up to c. 50% t50 as well. Then back to 2+/2- above
c251, if I have sufficient patience. -Bruce

(that's 3 sentances, only one that runs on for more than 1/4 of a screen.
Semi-colons are almost as good as periods, seems to me? I'll work towards
text-message brevity any day now ...)

[PBMcL]

Bruce, your p49 is missing its final digit: 1

[bdodson]

Originally Posted by PBMcL

Bruce, your p49 is missing its final digit: 1

Ooops, sort-of large for an even prime! Thanks. -Bruce

(Can I quibble about 1-of-3 primes found/reported yesterday? All
complete factorizations. My mouse finger must have gotten fatigued.)

[bdodson]

Originally Posted by bdodson

(Can I quibble about 1-of-3 primes found/reported yesterday? All
complete factorizations. ...)

Wish I was having those mid-Feb problems here at the end of March.
Whining seems to have helped, my no-new-factor stretch ends at
27 days --- a partial, leaving a c193 after

p53 = 47381176963830878991679264698384677605361866148570677

a large p53; bumps CWI's small factor off the top10, for dodson 9 to
CWI 1, except for the note that their p61 remains in first, and that
most of the 7 p54/p53's won't stay in the top10 until December.

As mentioned in my report of CWI's recent p53 in the 12+ list, c234-c250
is nearing t50 --- this p53 was found at/near the 4025th xp curve with
b1=43M, for 89.58% of the t50, with just 900/7830 left to go. This is (just)
the 3rd factor from this run on the 96 Cunninghams in c234-c250, only
one complete --- the other two being p49 and p50. Uhm, that'd be
93*4025 curves that missed, 364K with b1=43M. Likewise, the c3xx's
are finishing 5300/7830 to complete their t50's, the ones still running
with (just) 1300 curves left (queued/running). Uhm, that's without
the 2+/2- for n < 1200, 82 of those left, 38 started running towards
t50, the other 44 in c280-c365 waiting for (one of ) these t50's to
finish. Those 44 Mn/Pn's are now the least tested Cunninghams;
only 2000 of the (last) 6300/7830 done, with the generic (not 2+/2- for
n < 1200) c251-c299's at 2200 ...of the (last) 6300/7830.

So not many factors, but lots of curves, seems like a complete run to
t50 on all c. 800 Cunninghams is within sight, on the (distant) horizon.
As I'd already reported last year, these tail-end t50 ranges on numbers
in c251-c366 (especially now in (t50-2*t45), with two complete t45's)
are quite unproductive for the ecm effort. The main reason they're
getting done is the recent xp grid (with scheduling under condor) on
fast pc's without much RAM available for low-priority background computing
that's prefered to be "cpu-bound"; that is, not heavily disk or
network intensive. I have dropped from running a max of 750 pcs
to aiming for more like 450 pcs (which seems to keep the current
condor installation happier), which drops down to more like 200 pcs
near lunch (when lots of students are browsing, checking their emails,
etc.) and in the early evening.

Anyway, having the xps available for community service (so-to-speak),
the Opterons have been running 2nd t50's on smaller numbers with b1=110M,
with the last of c155-c190 and difficulty < 220 nearly done (last 1000 curves
on last 12 numbers). A 2nd t50 with B1 = 260M (p60-optimal) on the
c190-c233's with difficulty above 220 is about to get started. The
presumption here being that t55's or even 2*t55 won't be sufficient for
many of these, and something more like .7*t60 is a more plausible
ecm-pretest before sieving. -bd

postscript: Uhm, that's with 2*t55 probably being sufficient for the
ones for which snfs is better than gnfs? A c190 that's easier by gnfs
would have difficulty above c. 190+95 = 285. For c230 that would
be 230+115 = 345 ... hmmm, must not be many of those! Maybe a
better description is that the numbers for which 2*t55 is the correct
pretest are being done (somewhat) sub-optimally by searching with
ecm parameters optimal for p60's. A reason being that the performance
of ecm in that more difficult range is nearer current asymptotic interest.
Well. There's also the next snfs record above kilobit = c310 ...

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
...
2	2018L	C300	208(0.25811)	67(0.0463427)	100(0.00689287)	0(0.000897706)
453061695333527845673130419620712632758641724001348754654554627835180228074958538869037550543922932827920119360630284230321098675592092485194822340263074205228759271960538924970294137799906110504256269154273377642069112036288976744944792621805023311522968389023323781284156009711510063050866528133509
...

Another C3xx cut down to size, even if only c300; leaving a c240. Uhm,
so that would be

p61=1291942943772106529500099325194662891337468227487983754043873

finishing t50, last few generic c3xx's left to run. CWI also has a new
p55; sounds like time for an update on the top10 thread, although Paul's
away, so the ECMNET page won't get updated for a bit. -Bruce

[bdodson]

Originally Posted by R.D. Silverman

Do you have any plans to finish the 2+ and 2- above 233 digits to the 50 digit level?

To review, the short answer to this question back in mid-January
was: "no!". Not sure whether I could have done better in one or
more of those replies, but a current short answer might be something
like "ask me again in May" (this being the end of April).

We determined that (if the objective is progress towards completing
the numbers remaining from the 1st Cunningham edition) it's not only
2- and 2+ for n < 1200; but also the 2LM's that are in question.
The two short partial progress reports are that all of the regular
Cunninghams are tested to p50 if they are

(1) below 251-digits; or, (2) above 299-digits.

The 2- and 2+ for n <1200 are actually done to (2a) above 279-digits.
That left some 37 numbers in c251-c279 from 2- or 2+, n < 1200. The
least-tested of those has (at most) 2300/7830 p50-curves left to go to
reach t50. Perhaps the most tested will finish its t50 this weekend. So
"yes", I can now definitively assert that I do plan on finishing t50 on these
last 37 numbers (although they are running at lower priority than several
other ecm search ranges, there being no particular urgency, unless someone
has one of these as a short-term sieving target).

For the "generic" c251-c299's (that is, not 2- or 2+, n < 1200 ... that
is, not the Mn's and Pn's on George's ecmm.txt and ecmp.txt, which are
above), the least-tested needs 4100/7830 more B1 = 43M (p50-optimal)
curves. There are 136 numbers in this range, which includes the last
2LM's not yet at t50. These 136 are now the least tested Cunninghams -
they'd perhaps be regarded as best ecm factoring targets, being most
likely to still have a prime factor under 50-digits. The only reason not
to consider them to be best targets is perhaps more psychological than
mathematically based on the "smallest likely factor size estimates" is
that they're relatively large, so that the ones not likely to have a factor
in ecm range (to p77, say) have a (admittedly small?) chance of being
not just out-of-range, but way-out-of-range (p90 or above, say). Suppose
that would first occur for a _very_ few c180s; happen for a larger slice
of c200's; and we're in c251-c299 (but at least we're done with c3xx).
Probably the ones with smallest prime factor above 120-digits - which
occurs here, but doesn't in c190-c233 (for example) - are relatively few.

Anyway, these generic c251-c299's (c. 136 of them), are currently
getting the full attention of the xp's on our condor grid. So that's
37+136 left to go for full t50 (and not just on the base-2's, but on
the complete Cunningham list). More trouble than it would be worth
to separate out the 2LMs. Ask me again in mid-May (if anyone's still
wondering). -Bruce

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
...
2	2186L	C282	...
2	2186M	C295	0(0.162075)	0(0.0316957)	100(0.0055869)	0(0.000897706)	
1183494302945830533904261409630714950732959499092891540918603058108066557891275648419886132352711691517953005921493860598956356168970751584136548828771702133762329225698155990366774844328484238239028471986146900996913383943458577475663991687899957484981067079048384444301588636087449186577193021
...

As I was saying, ...

p46 = 6929589945942729453900732599945559189623922821

leaving a c249. The previous p4x was a p49 at number 696 on the
ECMNET factor page, this is the 711th, 12 p5x's, a p60 and a p61 ago;
with p6x twice as likely as p4x!? -Bruce (2186M, c295)

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
2	2282L	C264	0(0.267423)	0(0.0522979)	165(0.00921839)	0(0.00148122)	
191761332410463645347416345316499144694796460621946107727798116908634955413055611741054436914956633763222542391677389827336583973359275234057709644152811271376150766650540040518697389123337074272387311804883158655730673939786075782805563415643253453432777634219649
...

That's 2282L, c264, finished with

p52 = 1422354638761439563699438766864657591445804014687977

Looks like in another week-or-so, at the present rate, most of the remaining
Cunninghams not tested to t50 will have no more than 1100/7830 B1=43M
curves to go. -Bruce

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
...
2	1798M	C194	0(1.05135)	40(0.20483)	630(0.0359772)	0(0.00565555)	
17305094793928403298138053181003178436762529201877705702169450453065456198632790916623005806746778567388932947010396122820189838674842614491853488093234558934398364890851973412447360033342622241

Here's a (new) small Cunningham, 2,1798M C194 --> C138 after

p56 = 20078157941325448552726597857286724672278298773354024889

found in step 1 on the new core2 duos (B1=260M), with ATH's new
612 binary. Actually, I was checking -asmredc, which was quicker on
C190, but already slower here in C194 (the p56 found on the "without
-asmredc" run). The p56 would have been 7th on the top10 2006,
but doesn't make the top10 this year (and would also have been
bumped from the 2005 top10, as several p56s were).

Please check with Sam if you're interested in the cofactor. -Bruce

[akruppa]

The cofactor is reserved for GNFS by now. I'm removing the entry.

Alex

[R.D. Silverman]

Originally Posted by akruppa

The cofactor is reserved for GNFS by now. I'm removing the entry.

Alex

Hi,

Why didn't you remove, e.g. 2,1550L, 2,1634L, 2,1658L etc. etc.?
These (and others) have all been done.