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-   -   6+ table (https://www.mersenneforum.org/showthread.php?t=3576)

garo 2005-01-18 14:21

6+ table
 
[code]Size Base Index Mod Diff Ratio
261 6 419 + 326 0.798
246 6 421 + 327.6 0.749
331 6 431 + 335.3 0.985
258 6 436 + 339.2 0.758
270 6 439 + 341.6 0.788
282 6 443 + 344.7 0.816
289 6 448 + 298.8 0.965 /7/resvd
283 6 449 + 349.3 0.807
311 6 454 + 353.2 0.878
344 6 457 + 355.6 0.965
336 6 458 + 356.3 0.941
280 6 461 + 358.7 0.8
327 6 463 + 360.2 0.906
311 6 464 + 361 0.859
320 6 466 + 362.6 0.881
312 6 472 + 367.2 0.848
281 6 473 + 334.6 0.838 /11q
338 6 478 + 371.9 0.907
309 6 479 + 372.7 0.827
337 6 481 + 345.4 0.973 /13
268 6 482 + 375 0.713
307 6 484 + 342.3 0.895 /11q
282 6 488 + 379.7 0.741
330 6 493 + 383.6 0.858
316 6 494 + 354.8 0.889 /13
315 6 496 + 385.9 0.814
258 6 497 + 331.4 0.776 /7
294 6 499 + 388.2 0.75
[/code]

jyb 2005-08-18 15:48

GMP-ECM 6.0.1 curves run on 6,762M (with default B2):
4362 curves with B1 = 11e6
6791 curves with B1 = 43e6
15504 curves with B1 = 11e7

-Jon

geoff 2006-02-03 03:02

6,363+ C172 = P75.P98
P75=103373476033477388263515282957106895317857131511194597652434632687520479231

This was done with ggnfs-0.77.1 using polynomial 36x^6-6x^3+1, 28 bit large primes, and algebraic/rational factor base limits of 14.8/16 million.

geoff 2006-02-11 02:08

6,287+ C154 = P66.P88
P66=247859037729470996906245243451923112548845447499779115951590660463

This was by SNFS (difficulty 191.4) with ggnfs-0.77.1, using polynomial x^6-x^5+x^4-x^3+x^2-x+1, 28 bit large primes, and algebraic/rational factor base limits of 14.7/20 million.

Sieving took 66 GHz days on a mix of P2,P3,P4 CPUs, linear algebra took 10 GHz days on a P4, peak RAM usage was 714 MB.

geoff 2006-04-21 22:35

6,798L C140 = P57 * P84
P57 = 286227504202337752215096844369178117421662207554962805489

This was by GNFS with ggnfs CVS 20060310 using 28 bit large primes and algebraic/rational factor base limits of 14.1/14.0 million.

Polynomial search took 9 GHz days on a P4/Celeron, sieving took 93 GHz days on a mix of P2,P3,P4 CPUs, linear algebra (on the third attempt) took 11 GHz days on a P4. Peak RAM usage was about 850 MB.

smh 2006-11-27 18:22

factorization of 6^369+1
 
The factorization of 6^369+1
[CODE]N=1995318523583569410536518710238825992069432091418126270747301312022729565418312904399527685768670754705838744041545211857263269211105325133582097428175392915125238452242062431167 ( 178 digits)
SNFS difficulty: 191 digits.
Divisors found:
r1=13962920965423422985070859383439633233088296131740062300197159 (pp62)
r2=142901225934358910616458334546032475881108357631878872140161426564856550164076857572859982163043154061736815224575913 (pp117)[/CODE]

xilman 2006-11-27 20:53

[QUOTE=smh;92575]The factorization of 6^369+1
[CODE]N=1995318523583569410536518710238825992069432091418126270747301312022729565418312904399527685768670754705838744041545211857263269211105325133582097428175392915125238452242062431167 ( 178 digits)
SNFS difficulty: 191 digits.
Divisors found:
r1=13962920965423422985070859383439633233088296131740062300197159 (pp62)
r2=142901225934358910616458334546032475881108357631878872140161426564856550164076857572859982163043154061736815224575913 (pp117)[/CODE][/QUOTE]
Nice one.

Sam's news letter arrived here this morning. Not sure whether you've received yours yet.


Paul

smh 2006-11-28 12:58

[QUOTE=xilman;92607]Sam's news letter arrived here this morning. Not sure whether you've received yours yet.[/QUOTE]Only a confirmation that he recieved the factors.
I guess i have to ask prof. Wagstaff to be included in this mailing list?

bdodson 2007-01-24 19:21

156=53+103
 
[QUOTE=garo;48285][CODE]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
...
6 337+ C156 0(2.63512) 2160(0.477957) 0(0.0754361) 300(0.0068697)
607055099444498921847583147982450809557514004451282871917948174791099265283291964431544302627498111551020109672026017537034605137651109768044489243175210279
...
[/CODE][/QUOTE]

Not sure that I can give entirely satisfactory reasons, but the Opterons
with first limit 110M (p55-optimal) are running circles around the xp's
and the P3's (and another 80-some xeons that went idle), all with
first limit 43M (p50-optimal). Score: 5-to-2. My intended reason was
that c155-c169's tested to p50 were more likely to factor than the
c234-c299 (as well as some time in c3xx), even though the latter were
only tested to p45. With explanation that too many of the c234-c366's
with factors under p45 removed had (on average) few factors in ecm
range (like lots with smallest factor above p100, say). The first step
limits oughtn't to make that much difference, as the factors being found
are well within range of the smaller limits, given a larger number of
curves. I'm fairly certain that the xp's are spending considerably more
"work units" (without actually checking how these are actually defined);
and with the addition on the xeons there's now a fairly substantial effort
on the c155-c169's of difficulty under 220, that hasn't found anything
at all (this year). Perhaps that's since smaller difficulty numbers had
more ecm (from other users?), or the previous runs used smaller limits,
so were less likely to miss p46-p54 factors (smaller standard deviation?).

Anyway, here's the new one,

p53=84382257093351217403808536729720911956398743537658819

with snfs difficulty 262.24, way harder than the 156-digit gnfs. -Bruce

bdodson 2007-02-19 14:38

New Cunningham C122 (from 6,365+ after p60)
 
[QUOTE=garo;48287][code]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
...
6 365+ C182 0(2.09174) 1500(0.38003) 590(0.0622008) 0(0.00529647)
18277199064023868716464418337366764898392423901374182657841980711016975079192366008607903315073044637550970940888219527035615248207222941096199986090387235389044400550718035078208621
...
[/code][/QUOTE]

Another Opteron factor from the c170-c189's of difficulty 220 and up. One
of the good points about this range is that any factor is likely to be useful.
In this case, even the relatively low snfs difficulty 227 is way-harder than
the cofactor:

p60 = 254856004505238557834753259615355816338030694854500477132141

from c182, leaving a c122. I haven't heard yet from the usual suspects,
but anyone considering polishing off the cofactor (please!) should make
sure that they have a reservation with Sam before starting. -Bruce

PS - this was from the 2nd Opteron pass, which has since finished on
the c182/c122. So it's at 1.66*t50, ready for gnfs (presumably). [2*t50, actually]

akruppa 2007-02-19 15:27

Your p60 isn't prime,

54856004505238557834753259615355816338030694854500477132141 = 3 * 32827965463229429509624429 * 557004815164707788478198263318443

nor do any of the two larger prime factors divide a Cunningham number.

Cut-and-paste error?

Alex

bdodson 2007-02-19 15:38

[QUOTE=akruppa;98948]Your p60 isn't prime,
...
Cut-and-paste error? Alex[/QUOTE]

Also only has 59-digits; missing the leading 2. -bd (fumble-fingers)

bdodson 2007-02-20 05:47

[QUOTE=bdodson;98947] ... leaving a c122.
I haven't heard yet from the usual suspects,
but anyone considering polishing off the cofactor (please!) should make
sure that they have a reservation with Sam before starting. -Bruce
[/QUOTE]

Nevermind, Paul_Z is running it under ggnfs. -Bruce

bdodson 2007-07-20 17:56

c248 --> c196, still snfs
 
[QUOTE=garo;48285][CODE]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
...
6 347+ C248 0(0.267423) 0(0.0522979) 165(0.00921839) 0(0.00148122)
10964338925092426088126948470446380066426543127625758260950563307023836679285462922290667662199737110776460215222333365311710483202526721433806593060755250025989735671706430973854039253697040115169671969414787046146621487945446241359724861879837297
[/CODE][/QUOTE]

2nd p52 today (the other on the 2- discussion thread, this subforum),
but at difficulty 270, the c196 cofactor isn't small enough (yet) for
gnfs to be easier.

p52 = 4254678785395250635090914262464410641424477007559249

-Bruce (that's 6, 347+)

bdodson 2007-07-27 02:26

[QUOTE=garo;48287][code]Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal
...
6 371+ C243 0(0.267423) 0(0.0522979) 165(0.00921839) 0(0.00148122)
708166466456643165057206014273219061287362177418529773038894112079445263158180620536201218854777490094565472668909080513640035584576532631736455633532917590922654920000520013129647589582761390400628750882982003943873373104640036387930965924231
... [/code][/QUOTE]

No need for quibbling about this one,

p52 = 2783700126792688988335822421768098189386895987206391

finishes 6,371+. Remarkably uniform these post t50 factors --- the
Silverman-Wagstaff paragraph about re-estimating the most likely
factor size after a test finishes, which says that the likely size is just
another few digits larger than the previous estimate seems to be well
represented here. So best strategy after p50 is to look for p55; rather
than deciding that most of the p5xs were already swept up, and jumping
to p60. Not that I wouldn't be running B1 = 260M if our pcs had more
RAM installed (as I'm doing with the Opterons), choosing optimal memory
use rather than best strategy. Eight factors so far, a late-ish p49 and
an early p57, then five (!) p52's and a p53. -Bruce

bdodson 2007-10-08 09:19

[QUOTE=bdodson;111221]No need for quibbling about this one,

p52 = 2783700126792688988335822421768098189386895987206391

finishes 6,371+. ...[/QUOTE]

This one also,

p60 = 151634244917416206035101114864937647283016448179107389644473

finishing 6, 292+ One on Bob's remaining 768-bit list of easier snfs
numbers. (Sorry for a double report, not sure whether the nfsnet
list wanted priority.) -Bruce

fivemack 2007-10-08 12:26

6,289+ has been done [page103 of Cunningham tables; Irvine gnfs]

6,283+ has been done [page104 of Cunningham tables; Leyland snfs]

6,353+ has been reduced to a c178 by Dodson [pages 98 and 101 of Cunningham tables]

6,358+ has been reduced to a c163 by Dodson [pages 91 and 101 of Cunningham tables]

6,365+ c122 has been done [Zimmermann, gnfs, page 104 of Cunningham tables]

6,369+ c178 has been done [Hoogendoorn, snfs, page 104 of Cunningham tables]

6,387+ c162 has just been done [Silverman, snfs, page 106 of Cunningham tables]

Batalov 2009-05-29 03:24

6,762M = p78 . p82
 
1 Attachment(s)
The log is attached.

Because it was a quartic, the FB limits were lop-sided and it worked out nicely. Interestingly, the sqrt was done modulo 53, because "no irreducible prime found, switching to small primes". Now, that was the last 6L/M number and the last one in all tables with difficulty under 200. There are some quartics left slightly above diff.200 (single "home"-computer type projects).

--Serge

R. Gerbicz 2009-05-29 10:45

That was 6,762M.

bdodson 2009-08-12 12:10

6, 304+ C216 = p78*p138
 
[QUOTE=bdodson;184267] ...an "appalling" collection of seven
new first holes set by Serge. -Bruce
[/QUOTE]

(from over on the (non-sticky) 2+ discussion). Here's the first
of the seven, 6, 304+ C216 = p78*p138, Batalov+Dodson snfs.

A Most wanted number from page 106. The other early wanted
numbers that are now first holes:
[code]
page 106:

3,509+ c171 B+D snfs
6,304+ c216 done
11,229- c217 Edwards
12,233- c215 251.45 0.855 (snfs difficulty, sb ratio)
12,232+ c181 250.37 0.723

page 107:

10,241+ c175 running [/code]
-Bruce

Andi47 2009-08-12 12:35

[QUOTE=bdodson;185107](from over on the (non-sticky) 2+ discussion). Here's the first
of the seven, 6, 304+ C216 = p78*p138, Batalov+Dodson snfs.
[/QUOTE]

What are the factors?

kar_bon 2009-08-12 12:46

BTW:

what about a link in the first post like this:

[url=http://factordb.com/search.php?query=6%5En%2B1&v=n&n=300&EC=1&E=1&Prp=1&C=1&CF=1&of=H&pp=100&se=Update]Fatoring Database Composites for 6+ beginning at n=300[/url]

and if so, for the other subthreads, too.

bdodson 2009-08-12 13:44

[QUOTE=kar_bon;185116]BTW:

what about a link in the first post like this:

[url=http://factordb.com/search.php?query=6%5En%2B1&v=n&n=300&EC=1&E=1&Prp=1&C=1&CF=1&of=H&pp=100&se=Update]Fatoring Database Composites for 6+ beginning at n=300[/url]

and if so, for the other subthreads, too.[/QUOTE]

We already have a link, displayed with the main "Factoring Projects"
entry for Cunningham Tables:

[url]http://homes.cerias.purdue.edu/~ssw/cun/[/url]

the link to "Page 112 (the latest page)" brings up

[url]http://homes.cerias.purdue.edu/~ssw/cun/page112[/url]

for which the current last entry
[code]
5737 6, 304+ c216 693346929436160407667161921820423929978381970938958936441952882745560041213921. p138 Batalov+Dodson snfs
[/code]
shows the p78. Sam's label "5737" indicates that this is the
5737th factor in the Updates he maintains for the Cunningham tables.
Under "old pages" one finds the first factor, from the first page, which
appears to date from "August 1, 1981". -Bruce

kar_bon 2009-08-12 14:30

[QUOTE=bdodson;185122]We already have a link, displayed with the main "Factoring Projects" entry for Cunningham Tables
(...)
[/QUOTE]

what i meant was a quick view of all composites of this table, with the ability to download/see the factors as text/short text/html on [b]one[/b] click!

and the table in post #1 has not to be updated with C's and remaining composites (except the difficulties). the ECM-efforts could also be stored at the numbers in the Factoring-Database!

bdodson 2009-08-13 15:42

[QUOTE=kar_bon;185128]what i meant was a quick view of all composites of this table, with the ability to download/see the factors as text/short text/html on [b]one[/b] click!

and the table in post #1 has not to be updated with C's and remaining composites (except the difficulties). the ECM-efforts could also be stored at the numbers in the Factoring-Database![/QUOTE]

I was looking over post #1 in this subthread before the most recent
factorization (already updated by Serge). There seem to be a lot
(compared to the other 17 Cunningham lists?) of small numbers, six numbers
under c180. Some snfs's; worst case gnfs's also in our current range.
By contrast, the last 5-7 are above current msieve range. Might hope
to drop one or two by ecm?

On storing ECM-efforts, you're aware that each of the post #1s were
prepared by Garo (following earlier attempts from Bob and Rogue) at trying
to record the Lehigh curve counts, c. summer 2005? It may be somewhat
easier now, as the most recent cunningham.in from the ECMNET
quick_start page is down to just 600 numbers. I've included a recent
update among replies posted here, with counts corresponding to
7*t50, 4*t50, 3*t50, 2*t50 and 1.5*t50, depending upon size/digits
(for all but the c190-c233's, which were subdivided at snfs difficulty
250 (with 4*t50 below, 3*t50 above)). Almost all of these are either
with B1 = 110e6 or B1 = 260e6, but translated into t50 = "tested to
finding a given p50 to 62% probabilty", which might mean something
like 3133 p55-optimal curves, B1 = 110e6 and 1579 p60-optimal curves,
B1 = 260e6. (So these "t50" are the analog of pentium-90 years, for
ECMNET rather than GIMPS.)

You'd need to have a very good reason for adding a fourth version
of the Cunningham status (Sam's pages; PaulZ's ECMNET pages and
these Garo/Rogue tables, as maintained by Alex and Serge). -bd

ps - In particular, Cunninghams have been removed from the Database
ecm server, as having already been tested past the current target
range there

Andi_HB 2009-08-13 16:30

[quote=kar_bon;185128]what i meant was a quick view of all composites of this table, with the ability to download/see the factors as text/short text/html on [B]one[/B] click!
[/quote]

I think that`s a very good reason.
The Database is much more comfortable than the tables from Paul.
Sure it`s a lot of work to update all Numbers in the Database - but if all the Numbers are in the Database it will save a lot of time and no factor will be overlooked/lost. IMHO its a logic consequence to use the Database.

Regards Andi_HB

bdodson 2009-08-14 03:50

[QUOTE=Andi_HB;185323] ...
The Database is much more comfortable than the tables from Paul.
Sure it`s a lot of work to update all Numbers in the Database - but if all the Numbers are in the Database it will save a lot of time and no factor will be overlooked/lost. IMHO its a logic consequence to use the Database.

Regards Andi_HB[/QUOTE]

That would be my friend and co-author Xilman? Those are
"homogeneous" Cunninghams; they're different (and not in
this thread). As noted in my reply that you skipped over in
your follow-up to kar_bon's post, there's reason to be careful
here, since my friend and (on a different project) co-author
PaulZ _does_ have a repository for Cunningham info.

I'm also somewhat puzzled about your concern on having
(Cunningham?) factors "overlooked/lost", as my first reply to
kar_bon (the earlier post) carefully recorded that the current
standard for "factoring databases" has been maintained since
1981. Can we agree to resume this discussion five years from
now, to see which database has been more reliably maintained
over time?

I have no dispute with your logic in starting the mersenneforum
factoring database. But when I click on the link in kar_bon's
post, I find that the first entry has composite cofactor ... uhm,
well, I see first digits; and then another click to get a formula
for the cofactor. The main focus of the entry appears to be the
known prime factors. But what I want to know about 6, 314+
is specific info on that remaining composite factor; the one we're
giving our attention to in attempting to complete the factorization.
I want to know whether it is a candidate for gnfs; or -instead-
whether it's better by snfs. That would be the purpose of including
snfs difficulty, recorded in the new format Batalov has been introducing
in posts here in the "Cunningham Tables" forum. More specifically,
I'm interested to know how the runtime for snfs compares with the
runtime for gnfs; which is the purpose of the Serge ratio, which is
now being included in some of the tables. Depending upon how that
analysis turns out, I'm supposed to consider additional ecm efforts
before starting sieving; or else declare that the cofactor is ready
for sieving, and reserve further attention to the other composites
in the tables.

So again, you're more than welcome to include our factors in your
database; not that you need an invitation. But I hope you'll observe
that we have somewhat more specific data requirements than what
you'd include in a general purpose database. I'm doing my best not
to interpret your posts as suggesting that we'd be better off focussing
on your interests, rather than the ones related specifically to factoring
Cunningham numbers. I do know that there's a sub-thread on the
forum factoring database. I'm even happy to have a pointer to how
one accesses Cunningham numbers there. Perhaps with some further
experience I might move consulting the database up from it's current
standing as fourth among the four places one might consult for info on
Cunningham numbers. At the moment, if I'm in need of the known
prime factors of a Cunningham, I'm most likely to scroll down Sam's
appendix A (the "main tables"). Takes more than one click, and some
experience with the scrolling. Can't say for certain that I'd recommend
anyone else to start there; but your reply doesn't make the correct
comparison.

Regards, Bruce

PS -- you did say "tables" in the reference to Paul(?). There's
a "file" on Paul_Z's link "candidates"; namely c120-355, but
that seems unlikely to be what you meant. I can find prime
factors there, but only because I have a copy of the (very)
old appendix C used in ordering the entries. The ECMNET
database I'm referring to applies only to ecm factors of
Cunninghams, and is found on the quick_start page. It's
also not the most likely place to look for prime factors, as it
features the performance of gmp-ecm over time. Again,
different specific info than what's in the forum database.

PPS -- perhaps I'm neglecting my main reason for prefering
Sam's pages, Paul_Z's list(s) and the format here in the
"Cunningham Tables" threads --- the prime factors are
attributed to the person that found/reported them, with
a date and method used. Yet another special interest

Andi_HB 2009-08-14 05:15

First sorry that i have mixed homogeneous Cunningham & Cunningham Numbers. :unsure:
Hmm maybe i was to fast with my answer and decision for the Database.
I understand that for the Cunningham Numbers some more specific Informations are necessary like the ecm effort and the difference snfs/gnfs.
The last month i have updatet a lot of numbers with different kinds and noticed that the Database is a good place to bring all the great projects sites under one hat. But i don`t mean the project sites are needless.

Regards Andi_HB
[SIZE=2][/SIZE]

Batalov 2009-08-14 06:22

Well, just having a link to Markus' FactorDB will not hurt anyone, but let's not forget a simple fact that FactorDB was seeded with the Cunnigham tables (not any other way around). Both FactorDB and this thread messages are secondary and may at any time be terribly out of date to the real database of Prof.Wagstaff (and [URL="http://homes.cerias.purdue.edu/~ssw/cun/"]his pages[/URL]).

I'll try to make a simple one-liner to every header which will state the obvious and provide a link or two... 2+ and 2- pages have overlap with the GIMPS project's pages, and 10+ and 10-, to the rep-units (with many maintainers, for a list please see [URL="http://homepage2.nifty.com/m_kamada/math/10001.htm"]10001[/URL] and [URL="http://homepage2.nifty.com/m_kamada/math/11111.htm"]11111[/URL]).


[COLOR=green]P.S. I put out [/COLOR][URL="http://mersenneforum.org/showthread.php?t=12278"][COLOR=green]a test for discussions[/COLOR][/URL][COLOR=green].[/COLOR]

frmky 2009-10-02 05:48

1 Attachment(s)
6,317+ has been completed by NFS@Home:

[CODE]
68-digit prime factor:
11945361088850933777390788537647098376873971990473200125789018538899

158-digit prime factor:
13346683767756739751221171391453612510290695982921903538908296073270577730965354291094433347373531609778283156038003000968646967209671655512834647619164750607
[/CODE]

This one required 6 sqrt runs to find the factors.

frmky 2009-10-05 20:31

1 Attachment(s)
And 6,316+ has been completed by NFS@Home as well...

[CODE]
101-digit prime factor:
20718198856970031943042431298278006707891007274509577088151415807574320198826712628040225780951132201

110-digit prime factor:
12982820825896490041085564332226827434385115418527415362505503451547310539809374170981407741870653553618632449
[/CODE]

bdodson 2009-10-07 13:00

[QUOTE=frmky;191961]And 6,316+ has been completed by NFS@Home as well...
... [/QUOTE]

To complete the sequence of three Wanted from the 6+ list, we have
6, 314+ C209 factored as
[code]
prp69 factor:
127990570696623010387437346082972860280218929783270356827690059243181
prp141 factor:
188319680286819627530088258891375898122332689005870859461836523838286397646922041895253964126997311634948826781446996032824188043732759470097 [/code]
Batalov+Dodson, snfs. -Bruce

frmky 2009-12-06 21:18

1 Attachment(s)
NFS@Home has completed 6,334+. The postprocessing was completed with msieve. I ran the filtering, generated the matrix, and then transferred the matrix to Jeff Gilchrist. Jeff then completed the long linear algebra and transferred the dependencies back to me. I then ran the square roots. The log is attached.

80-digit prime factor:
51502221799707178125025528282930027721442937798693063043926320591434734001630893

101-digit prime factor:
41422280661767885986788301046332645192976796405559179732383361255631887230356707467626379138546914777

R.D. Silverman 2009-12-22 21:23

Toss Up!
 
[QUOTE=frmky;198041]NFS@Home has completed 6,334+. The postprocessing was completed with msieve. I ran the filtering, generated the matrix, and then transferred the matrix to Jeff Gilchrist. Jeff then completed the long linear algebra and transferred the dependencies back to me. I then ran the square roots. The log is attached.

80-digit prime factor:
51502221799707178125025528282930027721442937798693063043926320591434734001630893

101-digit prime factor:
41422280661767885986788301046332645192976796405559179732383361255631887230356707467626379138546914777[/QUOTE]

Bruce just found:

5799 6, 338+ c222 950762354554992360834931338167078172382237056559450288273. c165 Dodson ECMNET

Whether to do this by SNFS (exponent divisible by 13) or GNFS is a
toss-up. Since the former requires no polynomial search, I would go with
that.

smh 2009-12-23 07:33

[QUOTE=R.D. Silverman;199627]Bruce just found:

5799 6, 338+ c222 950762354554992360834931338167078172382237056559450288273. c165 Dodson [B]ECMNET[/B]

Whether to do this by SNFS (exponent divisible by 13) or GNFS is a
toss-up. Since the former requires no polynomial search, I would go with
that.[/QUOTE]Well, if it's done by ECMNET, the factor was probably found by ECM. At 57 digits not at all that unreasonable.

Andi47 2009-12-23 07:51

[QUOTE=smh;199684]Well, if it's done by ECMNET, the factor was probably found by ECM. At 57 digits not at all that unreasonable.[/QUOTE]

Silverman means that the [B]c165[/B] cofactor can either be done by SNFS or by GNFS (with almost equal difficulty).

bdodson 2009-12-23 07:52

[QUOTE=smh;199684]Well, if it's done by ECMNET, the factor was probably found by ECM. At 57 digits not at all that unreasonable.[/QUOTE]

Hi; sorry for not providing the info here. As the ECMNET report
lists B1 and sigma, the remaining question is the c165 cofactor,
rather than the p57. This was found during pre-testing for the
next round of NFS@Home reservations. Sounds like Greg still plans
snfs. -Bruce

smh 2009-12-23 09:21

[QUOTE=Andi47;199685]Silverman means that the [B]c165[/B] cofactor can either be done by SNFS or by GNFS (with almost equal difficulty).[/QUOTE]My bad. Should learn how to read more properly.

Raman 2010-01-01 08:28

6,323+ has been completed up
 
[quote=frmky]
One last result for 2009! The composite cofactor of 6,323+ was the product of 106-digit and 115-digit prime numbers:

106-digit prime factor:
8726220783196433420577926540172780111230892319895685342094694918556189538442501432986166567593663232876099

115-digit prime factor:
1262399687013820450821465131661532266367566719536571507703805450077992967534028821105944824066406612254496684743187

The factors will be reported to the Cunningham project and will be recorded on Page 114. Let's have a productive new year!
[/quote]
at this following website
[URL]http://escatter11.fullerton.edu/nfs/numbers.html[/URL]

frmky 2010-01-01 09:19

1 Attachment(s)
As Raman reports, 6,323+ finished a bit early and squeaked into 2009. It was originally due mid-December, but the linear algebra failed. A few relations were trimmed, and a new matrix was constructed and successfully solved. The log is attached.

In total, NFS@Home factored 22 Cunningham composites in its nearly four month existence, and has six more currently in linear algebra. I'm looking forward to what 2010 will bring!

frmky 2010-01-07 22:05

1 Attachment(s)
6,331+ is factored. As a test, it was completed with 32-bit large primes. The size of the matrix generated was about the same size as would have been generated with 31-bit LPs, demonstrating that the matrix size does not strongly depend of the large prime bound. The log is attached.

68-digit prime factor:
10001312033685801300032151531732232582514112692078389782701922973061

160-digit prime factor:
65895276032273530263048875365535917359061535246511133624566186538715266554188340585/
77770302531875655837482720443630406486478245944869941397820842114167390421773

mdettweiler 2010-01-07 22:31

[quote=frmky;201207]6,331+ is factored. As a test, it was completed with 32-bit large primes. The size of the matrix generated was about the same size as would have been generated with 31-bit LPs, demonstrating that the matrix size does not strongly depend of the large prime bound. The log is attached.

68-digit prime factor:
10001312033685801300032151531732232582514112692078389782701922973061

160-digit prime factor:
65895276032273530263048875365535917359061535246511133624566186538715266554188340585/
77770302531875655837482720443630406486478245944869941397820842114167390421773[/quote]
I've reported this factor to the FactorDB since it wasn't there already. Hope you don't mind...I didn't exactly count on it slapping my name on there like that. :ermm:

frmky 2010-01-08 19:09

1 Attachment(s)
Not a problem. I usually add them, but yesterday was a crazy day and I didn't get to it. :smile:

6,332+ is now also factored by SNFS. This one was routine. The log it attached.

69-digit prime factor:
650106680542055228216904187084969212101711180529566573956155238949369

108-digit prime factor:
437044495846780459786775320213708755010180640454196959129029284718895597993040438934936850297533075756275529

frmky 2010-02-04 22:36

1 Attachment(s)
NFS@Home has completed 6,338+. Another routine SNFS following Bruce's ECM find, but a nice split. The cofactor was definitely out of reach of ECM.

prp82 factor: 7374816340411679132081492812954747890931208487192188857067501570272900803526414417
prp83 factor: 19672458683457789288278992418450933122786990415625278087649712338543546066768023737

bdodson 2010-02-10 07:54

[quote=frmky;204595]NFS@Home has completed 6,338+. Another routine SNFS following Bruce's ECM find, but a nice split. [/quote]

Here's a non-routine p62, to finish 6,344+ C190
[code]
44098070546316336069732891124299479167253575131341897248372433 [/code]
a first hole, #5 on the most wanted list. Nearly the last number from
c190-c209 to finish t55 ("second smallest 100 Cunninghams", now at
either 7t50 or 6t50). I've started on c210-c233. -Bruce
____

[COLOR=green]ECM is not dead!! Long live ECM! :-) Congratulations on a nice factor! --SB. [/COLOR]

frmky 2010-02-10 08:07

[QUOTE=bdodson;205160]Here's a non-routine p62, to finish 6,344+ C190
[/QUOTE]
Excellent! Finds like this make up for the long stretchs of factorless ECM runs.

Raman 2010-03-29 17:19

6,355+
 
1 Attachment(s)
<snip>
that snip means what actually?

R. Gerbicz 2010-03-29 17:44

[QUOTE=Raman;209932]<snip>
that snip means what actually?[/QUOTE]

c211=p60*p61*p91
double ecm miss?

Raman 2010-03-29 17:55

[quote=R. Gerbicz;209937]c211=p60*p61*p91
double ecm miss?[/quote]

These days can we consider up the factors within the "low sixties" digit range as ECM misses?
6,355+ is easier by SNFS rather
If one has to find out a p60 factor by using ECM, then it should be a champion within the top 50 ECM factors table?
So, people have to run up with ECM upon all numbers till they find out the factors?
One cannot guarantee before itself that all the factors of the number are within the ECM range only

This is in my perspective. I always favour SNFS rather than ECM.
SNFS does guarantee the factors. That is why I don't actually prefer running up all those ECM curves.

R.D. Silverman 2010-03-29 19:04

[QUOTE=Raman;209939]These days can we consider up the factors within the "low sixties" digit range as ECM misses?

[/QUOTE]


No way, Jose.

xilman 2010-03-29 21:53

[quote=R.D. Silverman;209951]No way, Jose.[/quote]I'd allow exceptions for irony or for out-right teasing.

Paul

FactorEyes 2010-03-29 22:53

[QUOTE=xilman;209987]I'd allow exceptions for irony or for out-right teasing.

Paul[/QUOTE]

I employ a conversion formula:

Tragedy is me pulling a P63 factor on an SNFS-150 job.

Comedy is you pulling a P53 on the same job.

Since the first one happened to me, it's an ECM miss.

jasonp 2010-03-29 23:53

[url="http://mersenneforum.org/showpost.php?p=106715&postcount=11"]Bruce explained it all[/url]

Batalov 2010-03-30 00:20

Post-factum it is fairly easy to run a single "ecm -v -v 11e7" curve on one's own hardware and estimate if the factor had a 50/50 chance to have been found in 1/10th of the total time spent on NFS factoring. If it had not, sleep well and give an understanding chuckle to those who would invariably call your factor an ECM miss.
Because they will, no matter what... :jokedrum:

Raman 2010-04-01 07:24

[quote=R. Gerbicz;209937]c211=p60*p61*p91
double ecm miss?[/quote]

6,355+ c211 = p60*p61*p91
In any case, if you assume that this is an ECM miss

Think of 6,365+ c182. Remember that one?
That case 6,365+ c182 split up into as p60*p61*p62
That p60 was an ECM hit! Mr. Paul Zimmermann did the remaining c122 of 6,365+ by using GNFS.
And then why is there such a similarity between 6,355+ with 6,365+ :rolleyes:

Which state are you people from? Is this information right then?
Mr. Batalov, frmky -> California
Dr. Silverman -> Massachusetts (?)
jasonp -> Maryland
bdodson, Xyzzy -> Pennsylvania, where this mersenneforum server is being hosted up
Prof. Wagstaff -> Indiana
Prime95 (aka George Woltman) -> Florida
philmoore -> Oregon
jbristow -> Washington

Batalov 2010-04-01 07:53

1 Attachment(s)
Non sequitur?

[URL="http://en.wikipedia.org/wiki/Phil_Moore"]Phil_Moore[/URL] is from Maryland.
32.893,-117.2535 is definitely in California. You betcha.

P.S. Gotta love the new smilies.
:tantrum: [ATTACH]4946[/ATTACH]
Happy April's whatever!

bdodson 2010-04-01 22:21

[QUOTE=Raman;210274]6,355+ c211 = p60*p61*p91
In any case, if you assume that this is an ECM miss
...[/QUOTE]

This number was perhaps somewhat under-tested by ecm. Only
4t50, fewer curves than needed to find a p55 factor. A full ecm
pretest, relative to the sieving difficulty, still would not have been
sufficient to find a p60, or even two. -bd

FactorEyes 2010-05-21 03:49

6,368+
 
I have brought shame upon my family through the 11th generation: the C171 was a P61.P111.

[code]P61= 3892757110616175619125134299275807031820501573185619194311329[/code]

Thanks to jrk for the polynomial.

(I shall now absent myself from the presence of more worthy people.)d

FactorEyes 2010-08-20 16:10

6,353+
 
This C178 GNFS ran a little faster thanks to jrk's suggestion that we try triple large primes on the algebraic side:

n: [CODE]3495720155744160390308702080911694892393254003819177989194364433392602119210358965833430295064663146579080152295928278131537398607330890608815038143831212204077824454760817944697
# norm 1.828473e-17 alpha -7.945069 e 9.914e-14
skew: 5242872.26
c0: 1415684462271305089012313057623015234842880
c1: 56489085491552175398550702459917716
c2: -355405802142076475701272154680
c3: -30573939026244353965597
c4: 18914955682611026
c5: 637985160
Y0: -5594293033634964367018772799829077
Y1: 10914669743009582011
rlim: 60000000
alim: 60000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 90
rlambda: 2.6
alambda: 3.6[/CODE]

This seems to buy around an 8% improvement in speed for GNFS jobs of this magnitude. The individual Q values require more time, but we generate more relations per Q.

The C178 split as P68.P110:

[CODE]P68: 76772819749620922859599019064869997729081875556728878881833848945739
P110: 45533304197302470775235834478317413598842411794792485571017691246712640554863455599919842904873592456844389323[/CODE]

Batalov 2010-08-21 02:34

That's a very neat trick. Congratulations!

frmky 2010-11-02 21:04

1 Attachment(s)
NFS@Home has finished 6,346+. A standard, run-of-the-mill SNFS. The log is attached.

[CODE]prp95 factor: 56164757259658694865317697513568456493084555649771650505190443472644658585771052699471490056581
prp147 factor: 11960561240826642457187862060325535944398686262517008326251321014
2881955861855697561030442897124917553684448866765015014996075103318345732384959573
[/CODE]

frmky 2010-12-01 21:26

1 Attachment(s)
NFS@Home has finished 6,379+ by SNFS. This is a second-place Cunningham project champion for SNFS difficulty. Perhaps a little more ECM was in order. :smile: 690M unique relations produced a 36.3M matrix. The complete log is attached.

[CODE]prp62 factor: 39594233382490829759605818014230525162442624379592766682403039
prp208 factor: 4820647143682973621292002958588937598451150284915247942312749863705514560478233011200820934852999072676798890436532716898257110294756505772592641375094560163124805206507825142957485484934879455289116453808211
[/CODE]

R.D. Silverman 2010-12-02 14:01

[QUOTE=frmky;239530]NFS@Home has finished 6,379+ by SNFS. Perhaps a little more ECM was in order.[/QUOTE]

I concur. Perhaps we can cajole EPFL to running pre-sieving ECM
trials on NFS@Home candidates?????? Just an idea......:smile:

I'd like to cajole them into running ECM trials on the 2+ tables as well
as the 2-. They are doing such a terrific job with the latter. :bow:
I'm sure they could save a lot of NFS time by picking off some of these
numbers.

10metreh 2010-12-02 14:15

[QUOTE=frmky;239530]This is a second-place Cunningham project champion for SNFS difficulty.[/QUOTE]

Isn't it third (2,1039- is 1st, 2,1183- is 2nd)?

frmky 2010-12-02 18:12

[QUOTE=10metreh;239668]Isn't it third (2,1039- is 1st, 2,1183- is 2nd)?[/QUOTE]

Yes, it is. So many records are falling lately I can't keep track! :smile:

bdodson 2010-12-02 19:04

... when to quit ...
 
[QUOTE=frmky;239530]NFS@Home has finished 6,379+ by SNFS. This is a second-place Cunningham project champion for SNFS difficulty. Perhaps a little more ECM was in order. :smile:

[CODE]prp62 factor * prp208 factor
[/CODE][/QUOTE]

Despite much reduced resources, the Lehigh pretest on this number
was 23827 new curves (B1 = 260M, B2 = gmp-ecm default) upon it's
selection as a NFS@Home candidate; following an initial test of 1.5t50,
so c. 2400 additional curves. Past 3t55, but short of c. 5t55 = c. t60.

The current test of a new windows7 image is showing 100 cores by day,
600 cores overnight (core 2 duos). That's still below the c. 1200 cores
with the old xp image, but these may be faster, with more memory. But
a lot better than none during the c. six months (I forget how long it's been)
while the windows people had excluded condor/ecm. On purpose. The
daytime test is very good to see, if it passes; the first year-or-so was
24/7, which was dropped to 12/7 on wide-spread belief that there was
serious interference --- especially condor being slow to exit, while people
were trying to get in-class presentations to open. Very not good.

Even if/when enhanced resources are up and stable (they're being very
thorough about testing; which is good), I don't see tests past 2t55 as
good use of the University's resources. Near-term large distributed 16e
projects are a worthwhile exception, but 60% of t60 (= c. 3t55) is about
as far as I'd like to go (that's perhaps t57.5? no promises here about
p59-and-up).

I also find it hard to believe that a boinc project for testing past 2t55
(that is, after 2t55 has failed, running towards t60) would be attractive.
Just too few factors in [2t55, t60], unless one has a very large pool of
very patient users. Besides, GPU projects get far better credit/price than
any CPU app.

-Bruce (Looks like GPUgrid runs on our linux/tessla 20's (c2050), so perhaps
I'll see for myself.)

frmky 2011-01-21 22:47

1 Attachment(s)
Catching up here, NFS@Home finish 6,347+ a week or so ago.

[CODE]prp95 factor: 70511507899987042021399421608627600087695968291036987926849957371379710825930676085846246065057
prp101 factor: 36547331438884099727114410025437724191882639263092614191503321841305380338823023355542833953649420929
[/CODE]

frmky 2011-05-24 07:13

1 Attachment(s)
And 6,374+ is now done.

[CODE]Mon May 23 15:13:40 2011 prp104 factor: 16662090550947267817532833084936567469376561931117199336634319011364776739722634584799904405393505087889
Mon May 23 15:13:40 2011 prp111 factor: 551199432504034094014614942720208216988359859314312573575833568466762683056295417002390729187861797699416750129
[/CODE]

Batalov 2011-12-19 22:05

A large (p65!) ECM factor was uneventfully posted in the [URL="http://homes.cerias.purdue.edu/~ssw/cun/xtend/up6p"]extensions[/URL]:
[CODE]6, 822L c172 57670113141808252240352311142780968492223118520622897175521034757. p107 Wagstaff ECMNET[/CODE]

bdodson 2011-12-20 08:31

[QUOTE=Batalov;282829]A large (p65!) ECM factor was uneventfully posted in the [URL="http://homes.cerias.purdue.edu/~ssw/cun/xtend/up6p"]extensions[/URL]:
[CODE]6, 822L c172 57670113141808252240352311142780968492223118520622897175521034757. p107 Wagstaff ECMNET[/CODE][/QUOTE]
Sam bumped his p63 off of the top10, leaving the 10th a p64, one digit
better than the 10th of 2010. Not much time for another top10 factor
this year! -Bruce

Batalov 2013-09-12 04:51

6+,6LM tables were officially extended. (from 451 to 500, LM to 1000)

There may be some projects accessible to home-style enthusiasts, e.g. 6,456+.

frmky 2015-12-06 02:41

Here's the 6,490+ log.

[PASTEBIN]EnR8dw6p[/PASTEBIN]

frmky 2016-02-08 05:49

6,376+ is done.
[PASTEBIN]DUiuCNaF[/PASTEBIN]

frmky 2016-11-05 23:11

A nice split for 6,460+!

[PASTEBIN]jHfbAmf3[/PASTEBIN]

xilman 2016-11-06 08:27

[QUOTE=frmky;446481]A nice split for 6,460+![/QUOTE]
Brilliant!

frmky 2016-11-07 03:47

[QUOTE=xilman;446586]Brilliant![/QUOTE]
Pun intended I'm sure!

xilman 2016-11-07 07:26

[QUOTE=frmky;446637]Pun intended I'm sure![/QUOTE]Sometimes I'm too obvious.

pinhodecarlos 2017-02-13 22:09

6, 389+ c242 17773009901252360471924269249318148260447935679384645157188770608035885899698538249694861593754194361. p142 NFS@Home snfs

[url]http://pastebin.com/6N2HjzTB[/url]

pinhodecarlos 2018-01-30 18:06

6,394+ done by NFS@Home

pinhodecarlos 2020-01-01 15:26

6, 404+ c266 17779141835970240570705720301077355646755619077045499858214084160627856057. p193 NFS@Home snfs

pinhodecarlos 2021-01-04 22:33

6,442+ Done by NFS@Home


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