Reserving numbers in advance

[Raman]

Originally Posted by R.D. Silverman

I don't know how he will handle the matrices either......

Haven't you read out my previous posts? I have access to 8 core compute cluster (with 14 nodes), with 8 GB of RAM for each node, more than 50% of the cluster will be sitting idle each day, if I were not to use it. This is for sure. Not disturbed by anyone, and will be accessible for 1 year, can be renewed as well. Perfect for Linear Algebra.

Yesterday, I tried my best to automate all the tasks. So, I no longer need to pay much attention to the setting up of tasks. Just simply I will only need to adjust the range of the task files. That's all. What do you think is the power of this shell script, especially when run at low priority?

This script is being linked up from the crontab file, for every period of certain interval only.

x=`pgrep gnfs | wc -l`
if test $x -eq 0
then
cd ~/2_935M
nohup ~/64bit/gnfs-lasieve4I15e -r 2_935M.poly -f 97000000 -c 1000000 -o 2_935M_97 -R
fi

Originally Posted by R.D. Silverman

NO! it is best done by GNFS!!!!

While preparing up the tables at the Mersenne Wiki, I encountered another dual case:
Is doing 2,1144+ better as a quintic by dividing by 11, or as a sextic by dividing by 13? Is quintic sub-optimal for any number of this size?
Because of the fact that 980 is a multiple of 35 and then 1144 is a multiple of 143.

Originally Posted by Batalov

Did I read this right?
It's a dangerous position.

Not exactly is the case over here. The administration is quite indifferent to the monitoring of CPU resources, i.e. there is no proper administration. Only the students like me are in charge of installing Linux and maintaining computers at the lab that I am using. So, students form the majority of administration.

I better think that I wouldn't have posted that message from that unknown student. It is not a mail actually, but a message sent personally through a single computer. You have command 'mail' in Linux terminal, right? Mails to me are sent through another e-mail address, and that mail sent is not to my mail address at all. Majority of such messages to me are from cron only. That message is already more than 3 months old, and then after that, nobody had warned me of again.

ps -f does not list out my processes at all. With ps -ef, a large number of processes are being listed out, making it difficult to find out mine actually. The only way to find out that my process is running on or not is by using the command top.

There are people in the lab, who do worse things than me, removing and fixing wires, to attach their laptops, charging their mobile phones, shifting system peripherals, etc. The administrators only warn of these people, not me. My binaries will run in the background quietly.

Labs are meant for academics, though the rules of the lab is not to do obscene things, watch videos, films, play games, like that only. Our tasks are not anything obscene at all.

The staff who directly administrate are quite not knowledgable of what is done or executed on the processor at all. Once, I said to one of those staff that I needed to copy the files (containing the relations) to the DVD, and that they are related to mathematics. They only partially understand about that, I can say that everything is related to academics. I said that long ago, he will not keep in mind about that every moment, he will have his own work, just simply he will forget about that soon. The funny thing is that he attends classes along with me. No need to worry about executing my binaries at the background at all. With current technology, all the machines can be accessed from within single computer itself.

Originally Posted by bdodson

I'm seeing six numbers on Sam's reservation page marked for Raman,
but two of them are finishing this week? -Bruce

Surely 10,351+ should finish off on Friday morning, when I see the factors, I
will inform, to be exactly at 3:30 am GMT or 9:00 am according to my time.

Regarding the other factors, I am right now sieving for 2,935- and then 6,355-.
A SNFS quartic of difficulty 220 will take about 9 days to sieve, after that I can
schedule that Linear Algebra within the compute cluster. Not quite exactly in
the way that you think of. While the linear algebra is in progress, I can pipeline
the execution of tasks, starting up with the sieving of the next number concurrently.

Anyone, who has got access to the Mersenne Wiki can post their progress regarding
the status of their current number that they are actually doing.

[Batalov]

Originally Posted by Raman

While preparing up the tables at the Mersenne Wiki, I encountered another dual case:
Is doing 2,1144+ better as a quintic by dividing by 11, or as a sextic by dividing by 13? Is quintic sub-optimal for any number of this size?

Quintic will be very slow. Sextic will be better. Want to try?
Furthermore, a bit higher, e.g. for 2,1193- a septic will be better than a sextic. This is easily tested. You don't have to ask, just build the polynomials and run them.

As for the communism anarchy in one separate country lab - you don't have to tell me, I've seen it, I've lived it. In a country, in a lab. It usually ends very bad. But it feels good while it lasts. Then you wake up. (c) Cormac McCarthy, almost.

[Raman]

Originally Posted by Batalov

2,1144+
Quintic will be very slow. Sextic will be better. Want to try?

This number is much bigger, out of reach with the current resources. SNFS difficulty 313.07 with quintic, 317.89 with sextic. Let me first of all finish off those numbers that are accessible or reserved for my resources. If I want to try, I would like to try out some test sieving only.

Though, it is true that numbers like 2,1133+ have to be done up only as a quintic!

Originally Posted by Batalov

As for the communism anarchy in one separate country lab - you don't have to tell me, I've seen it, I've lived it. In a country, in a lab. It usually ends very bad. But it feels good while it lasts. Then you wake up. (c) Cormac McCarthy, almost.

Most of the things that you write up, I don't understand at all!

[jasonp]

Originally Posted by Raman

Most of the things that you write up, I don't understand at all!

He means that everything will work fine and you will get lots of computing done, and then the next student in charge of the lab computers will be very smart and will immediately realize what you are doing. Or not. Or a professor will need something done and will complain when it goes too slow. Or not.

In the US college students have been kicked out of school or worse because somebody mistakenly thought they were doing something illegal ('you are breaking codes? Like using our computers to guess passwords or something?')

[Raman]

Are these really the factors of 10,351+

Tue Mar 24 15:39:40 2009 prp64 factor: 6862390300547244074038319769783944997739006024946890580945655121
Tue Mar 24 15:39:40 2009 prp133 factor: 8000274558764048855772521798953431026754861120047615036248955653510671403655103704934457289394961420440781989755335177962505013085247
Tue Mar 24 15:39:40 2009 elapsed time 02:49:17

I strongly doubt so.
msieve-1.43 crashed at the square root phase. I copied the files to my department machines and then ran up again with msieve-1.41. Even then, only one dependency out of seven dependencies gave away with the factors.

2,935- is now 50% over, it should be, even more than that, right now.
6,355- sieving in execution, concurrently only.

Originally Posted by Batalov

Raman, your (albeit unauthorized) resources are fairly small. It is easy to see that you don't have a good estimate for the time necessary for quartics of SNFS difficulty 230, so it would be a good idea to reserve in small portions. There's a lot of people who do not read this forum, so any reservations can be done only with Sam, ok?

You don't have anything to fear from NFS @ Home (or B+D). Their numbers need 10-100 times more time or resources than you have.

I have about 100 cores to do the sieving, more than 50% are being idle if I were not to use it up at all. You mean to say that you need to have around 1000 cores to be able to crack up all those harder numbers?

Alas! that unknown student mail turned out to be written up by hardly only an undergraduate student! It seems that he doesn't know about the significance of the resources at all, that the Computer CPU cycles are precious...

[Mini-Geek]

Originally Posted by Raman

Are these really the factors of 10,351+
I strongly doubt so.

http://factordb.com/search.php?id=97872
The FactorDB seems happy with them. And PARI/gp confirms that both of those factors are prime and divide 10^351+1.
So...yes, they are really the factors, regardless of the difficulties in obtaining them.

[bdodson]

Originally Posted by bdodson

During Nov+Dec NFS@Home factored 15 numbers. There are
currently 16 numbers reserved by NFS@Home (three not yet
started, three late in linear algebra). That might suggest that
the NFS@Home reservation is proportional to Bob's two month
supply.
... -Bruce

On second thought, in view of the most recent timing estimates
for linear algebra, two months may not be the correct time frame
for viewing NFS@Home reservations. The more wanted 7, 314+
C215 is a case in point, with more than two months estimated
for the linear algebra alone (at least Jan 22 to March 28). The easier
c180 gnfs matrix looks like six weeks, or so, to March 12. These
timings seem to be consistent with Greg's report that the present
round of NFS@Home numbers typically have larger difficulty than
the early ones. With a 3-months timeframe we should expect the
number of open NFS@Home reservations to head up into the 20's.

Meanwhile, three of the Batalov+Dodson numbers are in linear algebra,
with a fourth sieving (fairly quickly). Just 2p913, 2m913 and 3p568 C268
waiting to run. -Bruce

[Raman]

I thought that I would share with you all, some of my recent, and then fairly old conversations with Prof. Sam Wagstaff. I assume that Mr. Jason is receiving up everything, right?

December 4, 2008

1) Are you (yourself) working on any numbers for the Cunningham Project
(some ECM candidates or Number Field Sieve), or working on it some
years before, and stopped it now, i.e. working on some other
distributed computing projects, such as GIMPS, Seventeen or bust and
Riesel Sieve, Factoring some Fermat numbers, Eleven Smooth and Odd
Perfect number search, Aliquot sequence and home prime search, etc.?

Right now I have a few computers running ECM on some Cunningham Project
numbers. Some other computers run ECM on Bernoulli and Euler numbers.
See http://homes.cerias.purdue.edu/~ssw/bernoulli/index.html

About 20 to 25 years ago I was a leading contributer of factors to the
Cunningham Project. I hope to find more factors some day, but now I
mostly record factors others find.

I did work on one big distributed project, the record MPQS factorization
of 2,1606L c135 done with Leyland, Dodson, Lenstra and Muffett in 2002.

2) As soon as someone sends you some factor of a Cunningham number,
do you check if it divides, or do you directly make the entry of the
new factor on the web page?

After I create the new entry line, I let a checking program make sure
it divides, has correct syntax, and is prime. After it passes this
test I put on the web page.

December 2, 2009

Thus, what are you going to do so, with the factors?
Are you making any profit out of it or it is just simply your stamp
collecting hobby? What is the benefit of factoring up these numbers
finally? Do you give any cash awards for record breaking factors?
By the way, I am factoring numbers mainly due to strong interest
within these topics only.

Will let you know up my next reservation number to you up at anytime,
right.

If you collect stamps, you can enjoy them now and maybe sell
them for a profit later.

I make no profit at all from collecting factors. I have no
cash to give away to people who send me new factors.

Factoring has a long history. Some of the best mathematicians
have studied the problem. Factoring is basic piece of many
algorithms for integers. The invention of the RSA cipher thirty
years ago added an intriguing practical application of factoring.
But I have been factoring integers for > 40 years.

Many people look at the factors on my web page every day. Some
want to see how large numbers one can factor, so that they know
how large to choose parameters for RSA. Others solve mathematical
problems using the factors. For a recent example see the paper of
Ke-Jian Wu and Zhi-Wei Sun in Math. Comp. 78 (2009) 1853-1866.

December 5, 2009

Where do people come from to visit up your website? Have you published
up any article or journal to make up the people aware of your website?
How to make up people aware of one's website?

I was interested up in factoring Mersenne, Repunit primes and all. So, I
searched out that there must be some project going on within the Internet
to factor out these numbers. I found out the Mersenne Forum, next. Thus,
what about all those other people?

By the way, if I have any ideas about mathematics within the future, what
is the procedure to make up my ideas aware to the public? What is the
procedure to publish and then present our ideas? Where to do so, publishing
papers, and then, on the long run, books? I am worried that I do not know up
about these things at all, first of all, at once.

I don't know where people come from to my website. Probably they
come from all over the world. Many published papers refer to the
Cunningham tables. The Cunningham book refers to the website.

To make your ideas known, you publish them in journals.

Are you a student? If so, then ask some of your math teachers
about how to publish papers with your ideas.

[Raman]

December 22, 2009

In the DB, someone has entered the (previously unknown) factor of 7,391-:

p57 = 478566296656273815311438559010751123205277732759848440243

with a p187 cofactor

Paul Zimmermann factored 7,391- c244.

Keep the factors coming!

Still, why haven't you entered up the factors of 7,391- as well as
10,269- within the web into the page number 114, as yet?

Because I am right now reading 850 emails to pick out all the new
factors and put them in the tables.

Are you going to make
up an update of the latest version of the Cunningham tables? By the way,
when is the update likely to be up, ready?

I have needed to do an update to the tables for several months,
but I have no time to do it. I will get to it someday.

December 25, 2009

Yesterday, you told that you received upto 850 mails with factors. What project
do they come up from? There are only a few for Cunningham project, and then
may be another few for Euler, Bernoulli numbers. Where do the others come up
from? What other projects do you exactly maintain up?

I meant all my email for that day, not just for factoring projects.
The only factoring projects I maintain are Cunningham, Bernoulli,
Euler and Bell numbers.

8 January, 2010

Today, just glancing up at the Third Edition of the Cunningham book,
I am curious to know about what the table limits for
1925 Cunningham & Woodall tables
first edition / second edition of the cunningham book were.
(What would it be likely for fourth edition, if any sooner? Current table
limits or expanded?)

I have a copy of the 1925 Cunningham & Woodall tables in my
office somewhere, but I could not find it easily today.
I think the table limits in it were 500 for base 2 and about
100 or 110 for the higher bases. The cover letter for Page 51,
http://homes.cerias.purdue.edu/~ssw/cun/oldp/dir60/cunn51
says that in April, 1988, only the two numbers 10,109+ c93
and 11,107- c96 from the 1925 Cunningham & Woodall tables were
not yet finished.

There is a partial description of the Cunningham-Woodall
tables in my paper at
http://homes.cerias.purdue.edu/~ssw/cun1.pdf

The table limits for first and second editions were
(1200, 330, 210, 195, 180, 150, 135, 135) (first) and
(1200, 350, 260, 210, 210, 210, 150, 150) (second)
for bases (2, 3, 5, 6, 7, 10, 11, 12).

The table limits for third edition were
(1200, 540, 375, 330, 300, 330, 240, 240) for the bases
(2, 3, 5, 6, 7, 10, 11, 12) The present table limits are
higher though (1200, 600, 450, 400, 400, 400, 300, 300)
Twice that for the LM Aurifeuillian extension tables.
But I can simply see that the base 3 tables are lagging behind.
For base 2, 2^1200 = 4^600 = 8^400. For base 3, only 3^600 = 9^300.
Base 3 & Base 4 both are equivalent to 600 only. Base 3 is prime,
a smaller base, shouldn't it be higher enough?
Not only due to that reason, but that base 9 is only upto 300?
All the adjacent bases 6, 7, 8, 10 are upto 400.

Just curious, when will you likely be extending up the tables?
How much at a time? Hundreds or a few tens?
I understand that extending up the tables will make people concentrate
upon the extended tables equally as well, than merely finishing up
the old tables itself. Only the current list of Cunningham composites
have had more ECM work than the other extended list of the Cunningham
candidates.

I realize that some of the Cunningham tables are nearly
finished. The 3- table has only five holes, for example.

The five coauthors of the printed Cunningham table book
often discussed the proper length of the tables. We never
thought of it as a matter of keeping a certain minimum
number of holes in each table. Rather we considered the
needs of our "customers," the people who use the
factorizations in other mathematical works. The factors
of 2^n +- 1 are most often used; the 10- and 10+ tables
next most often used; and the other tables are seldom
used and then usually only for small exponents n.

I have not decided whether to extend the tables on my web
page, but I won't extend them in the near future unless
more "customers" appear who actually need the factors of
the numbers that would be added.

Just curious again, when will likely be the fourth edition of the
Cunningham book be printed up?
In my opinion, please don't do so until all the remaining accessible
candidates have been finished up.
(SNFS 270-280) (GNFS 170-180) levels,
(SNFS 240-250 for all those quartics only).

The fourth edition, if there is one, will be an electronic
book like the third edition. I agree with you that a good
time to publish it would be after known factoring methods
have done all they can reasonably do and when new factors
are appearing slowly.

In your cover for page 113, you have written up that (11^229)-1 is
the last candidate for SNFS difficulty < 240. It is not so being the
case at all. There are candidates with exponents being divisible up,
right directly by 3, 5, 7, 11, 13. For each of these cases, the SNFS
difficulty reduces down by 2/3 (sextic), 4/5 (quartic), 6/7 (sextic),
10/11 (quintic), 12/13 (sextic) respectively.

What I meant was that 11^229 - 1 < 10^240. The size of the full
number b^n is the most basic SNFS difficulty. I know how to
calculate actual SNFS difficulty.

For the actual SNFS difficulty of the remaining Cunningham candidates,
please have a look up at
http://mersennewiki.org/index.php/Re..._by_difficulty
There are 536 Cunningham composites, being remaining up right at this
moment, as I count that only, with 38 of them being reserved up, as of now,
right now - 1 January 2010 - at this instance of the new year only
2010 = 2*3*5*67

Just, for your information purposes only, simply for your sake, I report up
my status of numbers that 2,1778L is in Linear Algebra stage, matrix has
6.1 rows, taking upto 90% of memory of system with 2 GB RAM,
takes upto 5 days to finish off plus one they for the square root step,
if in any case, it goes upto more number of dependencies.
7,320+ was in the filtering phase yesterday. It should be within the Linear
Algebra right now, if msieve was able to fit in the memory for the filtering
and then the matrix construction only. Have to check out tomorrow.
10,339+ is almost sieved. Waiting up for a few computers to finish up their
old jobs only.
10,351+ is sieving on. More than half sieved, right now, at this moment - as
of now, by now itself.

I have reserved 2,935- c181 for you.

Keep the factors coming!

[bdodson]

Originally Posted by Raman

.... (from Wagstaff emails...)

What I meant was that 11^229 - 1 < 10^240. The size of the full
number b^n is the most basic SNFS difficulty. I know how to
calculate actual SNFS difficulty.
...
Keep the factors coming!

So Sam intended a distinction "basic difficulty" and "actual difficulty".

Also, sounds like Bob wins the "extending tables" question; empty
first-five-holes entries don't matter, entirely empty 3- table wouldn't
matter either. We're waiting for client requests; mostly likely from
base-2 or base-10! -Bruce

[bdodson]

Originally Posted by Raman

What I meant was that 11^229 - 1 < 10^240. The size of the full
number b^n is the most basic SNFS difficulty. I know how to
calculate actual SNFS difficulty.
...

Just to fill-in/connect-the-dots here, for "basic difficulty" (and as
distinct from "actual ..."), the report from

Originally Posted by R. Gerbicz

By hand I found no numbers in 240-249 digits range. In 250-259 digits there are only 4 numbers, all of them reserved:
6,323+
6,331+
6,332+
11,241-

seems to support that either 11^229-1 was also the last number
< 10^250, or else something factored soon after was; and that
(in view of the order of these four entries on page 114) 6^332+1
was the last one < 10^260. Wonder whether Sam will continue
reporting these, with credit to NFS@Home.

Next question, how feasible is clearing the b^n's < 10^270? Not
actual difficulty, which definitely isn't in reach any time soon (as on
Raman's wiki table); literally b^n < 10^270. -Bruce