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 2009-12-27, 04:50 #1 Raman Noodles     "Mr. Tuch" Dec 2007 Chennai, India 3·419 Posts Cunningham Tables at Mersenne Wiki After the long time awaited December 2009 updates from Prof. Sam Wagstaff, Just have a look up at here No need to explain anything at all, as everything is self-explanatory... Remaining holes to be sorted up by order of difficulty levels, which I should do up by tonight. More information to be added up into the Mersenne Wiki, as I have planned up already. What is your opinion about the tables? Is it nice? By using the program of Mr. Tim Morrow actually, my credits goes up to him as well. Last fiddled with by Raman on 2009-12-27 at 05:47
2009-12-27, 10:41   #2
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

3·419 Posts
Changes to Mersenne Wiki: Reserved numbers

10metreh added up word "reserved" for those reserved numbers.
But in some cases, this word goes out of the aligned box, and then
in some cases (such as 10,530L) in which that word is in the center,
it spoils the alignment of the next factor as well.

I am going to use up magenta colour for those reserved numbers,
and then make a note above. Note for blue numbers, which are
derived factors, I will also include them up as well, in addition
to Mr. Tim Morrow's points as well.

Here is the modified cunningham.cpp file being attached up for
generating the tables.
Changes include up the following:
Removal of some HTML tags
<a> tag not being allowed up at all
Number of characters per line changed up as accommodated by the web browser
Some spelling, grammar errors being corrected up within the HTML header file

Not included up within the attachment file, as of now: (is Mr. Tim Morrow's bug within the code)
Most important thing is that, some Aurifeuillian extension tables have both the L, M parts being incompletely factored up. Both parts have been marked as red
Use of the colour magenta for those already reserved numbers
Note within the header for the use of the colours blue, magenta
Attached Files
 cunningham.zip (9.6 KB, 221 views)

Last fiddled with by Raman on 2009-12-27 at 10:44 Reason: Sorry that I forgot up about the attachment file itself, only

2009-12-28, 02:33   #3
bdodson

Jun 2005
lehigh.edu

20008 Posts

Quote:
 Originally Posted by Raman 10metreh added up word "reserved" for those reserved numbers. But in some cases, this word goes out of the aligned box, ... I am going to use up magenta colour for those reserved numbers, and then make a note above. Note for blue numbers, which are derived factors, I will also include them up as well, in addition ...
I hope you will excuse my presumption (as I was among those getting
unwanted emails when you were unhappy). You have three uses of the
word "up" that I've retained above; which makes following your sometimes
complex posts too difficult for me to manage.

1. For "added up word" we're expecting to see something like

2. For "going to use up magenta", just "going to use magenta".

3. And, for "include them up as well"; again, just "include them
as well".

For someone able to master "magenta" and the use of ggnfs/msieve,
I'm sure that you could reduce the number of these distractions, if you're
inclined to do so.

In any case, this was one of your posts I followed through (at least,
in part). I was noticing on reading Sam's recent cover letter for the
factors on page 113, the fourth paragraph, that
Quote:
 The factorization of 11,229- in # 5771 was the last of the numbers b^n +/- 1 < 10^240, that is, the last of the numbers with SNFS difficulty below 10^240.
Well. That's not the way we're using SNFS difficulty (cf the 2LM's).
In any case, while you're clarifying the difficulties (presumably to
make chosing numbers to factor more accessible), I was wondering
whether you might flag these decimal versions --- as we've recently
been doing for clearing base-2's to 800-bits (and next, perhaps,
900-bits). Are there more numbers with difficulty below 240?
Which numbers satisfy Sam's condition for 250 or 260? And other
numbers we might include as having difficulty below 250- resp 260-
digits? Keeping things simple, clearing all numbers of difficulty
below 270 seems to be above our current range of interest. -Bruce

2009-12-28, 08:41   #4
frmky

Jul 2003
So Cal

40078 Posts

Quote:
 Originally Posted by bdodson Are there more numbers with difficulty below 240?
Yes, lots. 51 unreserved by my count. Although admittedly most of them require decidedly suboptimal quartics or octics. However, there are eight, ranging from difficulty of 221.4 to 239, that can be done with a sextic. There are another 11, not counting those requiring quartics, with difficulties from 240 to 250 and 17 from 250 to 260. Lots to keep NFS@Home busy.

2009-12-28, 13:53   #5
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by frmky Yes, lots. 51 unreserved by my count. Although admittedly most of them require decidedly suboptimal quartics or octics. However, there are eight, ranging from difficulty of 221.4 to 239, that can be done with a sextic. There are another 11, not counting those requiring quartics, with difficulties from 240 to 250 and 17 from 250 to 260. Lots to keep NFS@Home busy.
Thanks for confirming Sam's non-standard use of the SNFS difficulty.
But on the question of b^n's < 10^250 and b^n's < 10^260; the mark
that Edwards (a forum user) cleared for 240? A smaller subset of the
ones you mention, but perhaps including otherwise unattractive quartics
(or optics? you too!). How many (and which) to clear Sam's version
of b^n < 250? -Bruce (@NFS: whizbang's back and doubling my daily totals!)

2009-12-28, 18:01   #6
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

1,429 Posts

Quote:
 Originally Posted by bdodson Thanks for confirming Sam's non-standard use of the SNFS difficulty. But on the question of b^n's < 10^250 and b^n's < 10^260; the mark that Edwards (a forum user) cleared for 240? A smaller subset of the ones you mention, but perhaps including otherwise unattractive quartics (or optics? you too!). How many (and which) to clear Sam's version of b^n < 250? -Bruce (@NFS: whizbang's back and doubling my daily totals!)
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-

2009-12-28, 18:25   #7
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

3×419 Posts

The list is now completely ready at the Mersenne Wiki
There are 537 composites remaining within the Cunningham Tables
as of 28 December 2009, 6:30 pm GMT
39 of them being reserved

For the software of Mr. Tim Morrow
To produce the tables
By using the following command lines:
awk -f pmain.awk pmainMMYY.txt > pmain.in
awk -f appa.awk appaMMYY.txt > appa.in
awk -f appc.awk appcMMYY.txt > appc.in
Modify the header files to suit for you
Compile, link and then run that C++ program, cunningham.cpp
It will produce 16 HTML files and then 16 text files, for the Cunningham Tables. Enjoy them up!
Attached Files
 cunningham_source.zip (13.1 KB, 199 views)

 2009-12-28, 19:00 #8 Raman Noodles     "Mr. Tuch" Dec 2007 Chennai, India 3×419 Posts 1) In this page, the SNFS quartics table, and then the GNFS candidates tables, have been pushed down, below. I don't know how to bring them up, to the top. What HTML table tag helps to do this? 2) If I can find any site with regular updates for the Fibonacci & Lucas numbers factors, Homogeneous Cunninghams, Factors of Factorials, Primorials ± 1, etc., I can add them up into the Mersenne Wiki, along with the Cunningham tables. Any idea from anyone, where I can find them out with regular updates, including extension to the Cunningham tables will be certainly nice, by the way.
2009-12-28, 19:01   #9
R.D. Silverman

Nov 2003

164448 Posts

Quote:
 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-
Perhaps you might look a little harder? e.g.

5,377+ , 5,785L/M, 5,805L, 5,815L, 10,366+, 2,1179+, 2,1191+/-1

(I intend to do these last 4) 2,1862L/M , 11,265-, ............

etc. etc. There are plenty of numbers with SNFS difficulty under 250.

2009-12-28, 20:01   #10
Raman
Noodles

"Mr. Tuch"
Dec 2007
Chennai, India

23518 Posts

Quote:
 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-
Dear Gerbicz,
in case you don't know about it:

If the exponent is a multiple of three, then you know the formula right?
$(x^3-1) = (x-1)(x^2+x+1)$
$(x^3+1) = (x+1)(x^2-x+1)$

We know the complete factorization of first part already, only we need to care about the second part. Using that part, we can create a sextic SNFS polynomial.
The difficulty reduces to (2/3)*exponent*log10(base)

Similarly, if exponent is a multiple of five, we can create a quartic,
with difficulty (4/5)*exponent*log10(base)
by using the polynomial
$(x^4 \pm x^3 + x^2 \pm x + 1)$
but since it is a quartic, it is slightly harder than a similar difficulty of quintic or sextic polynomial.

If the exponent is a multiple of seven, we can create a sextic out of it, actually, with difficulty (6/7)*exponent*log10(base)

For exponent being multiples of 11 or 13, you will get 10th and 12th degree polynomials for these respectively, and then you need to divide them up by using x5 and x6 respectively, then you substitute y=(x+(1/x)), actually y=(kx+(1/x)) for the Aurifeuillian parts of the table extensions for the base k, and then you can write them up as 5th and 6th degree polynomials in y respectively.

Thus, for exponents being multiples of 11, you will get up with quintics,
for those exponents being multiples of 13, sextics.

with that actual difficulty only being
(10/11)*exponent*log10(base) and then
(12/13)*exponent*log10(base) respectively.

Note that for those Aurifeuillian parts (such as those 2LM tables), you cannot use up with those multiples of 11 and 13 at all, as they lead you upto higher degree polynomials, more than 6, and then for multiples of 7, you will get sextics, for multiples of 3 and 5, both quartics only, within that case only, right then.

Last fiddled with by Raman on 2009-12-28 at 20:02

2009-12-29, 02:53   #11
bdodson

Jun 2005
lehigh.edu

100000000002 Posts

Quote:
 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-
My apologies for neither Bob nor Raman having read the post
you replied to. I expect that we'll see Sam's page reporting that
the numbers with "b^n < 10^260" have been completed (not
sure why we wouldn't have already gotten that for 10^250).

My question to Raman was silly to start with (as you likely noticed).
We just check the first hole on each of the 18 lists (or maybe 2LM
is excluded?). Looks like only 6+ and 11- met Sam's condition
(or one of them; for 260); and after that, check 2nd holes on those
two lists (yes for 6+, no for 11-); then finaly yes for the 3rd hole
on 6+, no for the fourth. Thanks; your list clarified my question.

Perhaps we might mail a copy of Raman's email to Sam; many exponents
n have b^n's with snfs difficulty well below log[10](b^n); divisibility by
3 etc. But that's not what Sam's saying on that cover letter (for
page 113); we hear that Sam was rather busy with other things on
the previous week. He must have been distracted. -Bruce

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