3,607- factors

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Message boards : NFS Discussion : 3,607- factors

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Greg
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Message 613 - Posted: 2 Nov 2010, 20:32:45 UTC
Last modified: 2 Nov 2010, 20:47:33 UTC

The composite cofactor of 3,607- was the product of 85-digit, 96-digit, and 110-digit prime numbers:

85-digit prime factor:
2086414114912368934845698889752452759455632789377648284275990116236503745140234728069

96-digit prime factor:
120463408255967053578135908158245347326036064518355187873832329408825869652943374488400197042063

110-digit prime factor:
81529721835493524725988100443970680738653595633187211135428836315200448881013673156176891838179958882238447519

This is a new Cunningham project second-place SNFS record for size of the number factored. The factors will be reported to the Cunningham project and will be recorded on Page 119.

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Message 621 - Posted: 5 Nov 2010, 13:52:34 UTC

Is this number be factored use degree 6, I notice the poly of 6,379+ is
n: 190869828061621461659863636707439059948042541397156797021935219218350398154483149591895053229379732129532332295828579589760877766171097533506965397824066533846000077988917965921258973321630437676677267014005259227990906727916564002361612266675089370791738705252309553229
type: snfs
skew: 1
c6: 6
c5: 0
c4: 0
c3: 0
c2: 0
c1: 0
c0: 1
Y1: 1
Y0: -10556714443828879617693714491135314434982743638016
alim: 250000000
rlim: 200000000
lpbr: 33
lpba: 33
mfba: 66
mfbr: 96
alambda: 2.6
rlambda: 3.6

that is a degree 6,

but I read a article which suggest using degree 7 for SNFS 280 to 350.
So what's the matter here?

Greg
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Message 628 - Posted: 8 Nov 2010, 19:32:39 UTC - in response to Message 621.

Simulations of the entire sieving range yield more relations for a degree 6 polynomial than for a degree 7, even for an upcoming 310 digit number.

bdodson*
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Message 631 - Posted: 9 Nov 2010, 13:07:57 UTC - in response to Message 621.

Is this number be factored use degree 6, ...

but I read a article which suggest using degree 7 for SNFS 280 to 350.
So what's the matter here?


I'm somewhat curious as to which article you were reading; you're
most likely careful about sources, but the phrase "I read it on the
internet" (which you didn't use, I know) is often followed by info
that's not very reliable.

Another possible issue is that the 16e siever we're currently using
has some improvements (and/or corrections) in the assembly code due
to our friend Batalov. The initial source code of Franke/Kleinjung
is not very portable, and notoriously intricate, so that even a usually
reliable author may not have had the best code to work with. Establishing
a well docummented public source of data is one of the points of this
boinc project. There are very few public SNFS factorizations above
difficulty 280; and the author is quite likely making use of relatively
limited simulations, rather than examining the "entire sieving range yield".

-bdodson

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Message 1149 - Posted: 18 May 2013, 2:24:50 UTC

OK, Here is a somewhat more detail information.
I fogot this article's title,
but it is indeed a journal article.
The author only discuss monic polynomial,
I can not understand the theory discussed in this article.
In fact I want to study polynomial selection or some other technique of factoring in my master degree,
but my tutor does not think I have the ability to do it, so I select another area in mathematics.

This article is published in a Chinese jornal, I'll find its title and journal later. After Greg deny the result, I almost forgot this thread.

I also curious about the slow progress in the study of nfs.
I find some articles in the past 3 years, but most of them are introduction,
a paper discussed multiple polynomial, and another paper discuss gnfs polynomial degree, but stopped at 6, but it does not discuss degree 7, I dont know why the max degree discussed is 6.

And Comparing with so many numbers have been factored in the past 5 years, the progress in factoring theory is slow, it is a little strange. RSA768 is degree 6, M1061 is degree 6, so if we want to factor RSA1024 ,or F12, is it possible to try to use degree 7.

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Message 1150 - Posted: 19 May 2013, 2:42:06 UTC
Last modified: 19 May 2013, 2:43:48 UTC

Here is the article title and the journal name.

Zhang Peng, and Li Chao, "POLYNOMIAL SELECTIONS IN FACTORING r^e+-s WITH NFS",
Computer Applications and Software, no. 4, Vol. 26, pp. 28-30, Apr. 2009.

Zhang Peng is a postgraduate student in
Department of Mathematics and System Science, National University of Defense Technology, Changsha 410073, China.

This article's main conclusion is,
when N is less than 40 digits, degree should be 3;
when N's digit is between 40 to 100, should degree 4;
100 to 160, be degree 5;
170 to 270, be degree 6;
280 to 350, be degree 7.

Message boards : NFS Discussion : 3,607- factors


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