3,607- factors

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3,607- factors

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Send message Joined: 26 Jun 08 Posts: 631 Credit: 368,956,914 RAC: 303,658 |
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. |

Send message Joined: 5 Sep 09 Posts: 18 Credit: 57,074 RAC: 16 |
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? |

Send message Joined: 26 Jun 08 Posts: 631 Credit: 368,956,914 RAC: 303,658 |
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. |

Send message Joined: 2 Oct 09 Posts: 50 Credit: 111,128,218 RAC: 0 |
Is this number be factored use degree 6, ... 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 |

Send message Joined: 5 Sep 09 Posts: 18 Credit: 57,074 RAC: 16 |
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. |

Send message Joined: 5 Sep 09 Posts: 18 Credit: 57,074 RAC: 16 |
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. |