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

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


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