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

 R.D. Silverman 2009-12-22 21:23

Toss Up!

[QUOTE=frmky;198041]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[/QUOTE]

Bruce just found:

5799 6, 338+ c222 950762354554992360834931338167078172382237056559450288273. c165 Dodson ECMNET

Whether to do this by SNFS (exponent divisible by 13) or GNFS is a
toss-up. Since the former requires no polynomial search, I would go with
that.

 smh 2009-12-23 07:33

[QUOTE=R.D. Silverman;199627]Bruce just found:

5799 6, 338+ c222 950762354554992360834931338167078172382237056559450288273. c165 Dodson [B]ECMNET[/B]

Whether to do this by SNFS (exponent divisible by 13) or GNFS is a
toss-up. Since the former requires no polynomial search, I would go with
that.[/QUOTE]Well, if it's done by ECMNET, the factor was probably found by ECM. At 57 digits not at all that unreasonable.

 Andi47 2009-12-23 07:51

[QUOTE=smh;199684]Well, if it's done by ECMNET, the factor was probably found by ECM. At 57 digits not at all that unreasonable.[/QUOTE]

Silverman means that the [B]c165[/B] cofactor can either be done by SNFS or by GNFS (with almost equal difficulty).

 bdodson 2009-12-23 07:52

[QUOTE=smh;199684]Well, if it's done by ECMNET, the factor was probably found by ECM. At 57 digits not at all that unreasonable.[/QUOTE]

Hi; sorry for not providing the info here. As the ECMNET report
lists B1 and sigma, the remaining question is the c165 cofactor,
rather than the p57. This was found during pre-testing for the
next round of NFS@Home reservations. Sounds like Greg still plans
snfs. -Bruce

 smh 2009-12-23 09:21

[QUOTE=Andi47;199685]Silverman means that the [B]c165[/B] cofactor can either be done by SNFS or by GNFS (with almost equal difficulty).[/QUOTE]My bad. Should learn how to read more properly.

 Raman 2010-01-01 08:28

6,323+ has been completed up

[quote=frmky]
One last result for 2009! The composite cofactor of 6,323+ was the product of 106-digit and 115-digit prime numbers:

106-digit prime factor:
8726220783196433420577926540172780111230892319895685342094694918556189538442501432986166567593663232876099

115-digit prime factor:
1262399687013820450821465131661532266367566719536571507703805450077992967534028821105944824066406612254496684743187

The factors will be reported to the Cunningham project and will be recorded on Page 114. Let's have a productive new year!
[/quote]
at this following website
[URL]http://escatter11.fullerton.edu/nfs/numbers.html[/URL]

 frmky 2010-01-01 09:19

1 Attachment(s)
As Raman reports, 6,323+ finished a bit early and squeaked into 2009. It was originally due mid-December, but the linear algebra failed. A few relations were trimmed, and a new matrix was constructed and successfully solved. The log is attached.

In total, NFS@Home factored 22 Cunningham composites in its nearly four month existence, and has six more currently in linear algebra. I'm looking forward to what 2010 will bring!

 frmky 2010-01-07 22:05

1 Attachment(s)
6,331+ is factored. As a test, it was completed with 32-bit large primes. The size of the matrix generated was about the same size as would have been generated with 31-bit LPs, demonstrating that the matrix size does not strongly depend of the large prime bound. The log is attached.

68-digit prime factor:
10001312033685801300032151531732232582514112692078389782701922973061

160-digit prime factor:
65895276032273530263048875365535917359061535246511133624566186538715266554188340585/
77770302531875655837482720443630406486478245944869941397820842114167390421773

 mdettweiler 2010-01-07 22:31

[quote=frmky;201207]6,331+ is factored. As a test, it was completed with 32-bit large primes. The size of the matrix generated was about the same size as would have been generated with 31-bit LPs, demonstrating that the matrix size does not strongly depend of the large prime bound. The log is attached.

68-digit prime factor:
10001312033685801300032151531732232582514112692078389782701922973061

160-digit prime factor:
65895276032273530263048875365535917359061535246511133624566186538715266554188340585/
77770302531875655837482720443630406486478245944869941397820842114167390421773[/quote]
I've reported this factor to the FactorDB since it wasn't there already. Hope you don't mind...I didn't exactly count on it slapping my name on there like that. :ermm:

 frmky 2010-01-08 19:09

1 Attachment(s)
Not a problem. I usually add them, but yesterday was a crazy day and I didn't get to it. :smile:

6,332+ is now also factored by SNFS. This one was routine. The log it attached.

69-digit prime factor:
650106680542055228216904187084969212101711180529566573956155238949369

108-digit prime factor:
437044495846780459786775320213708755010180640454196959129029284718895597993040438934936850297533075756275529

 frmky 2010-02-04 22:36

1 Attachment(s)
NFS@Home has completed 6,338+. Another routine SNFS following Bruce's ECM find, but a nice split. The cofactor was definitely out of reach of ECM.

prp82 factor: 7374816340411679132081492812954747890931208487192188857067501570272900803526414417
prp83 factor: 19672458683457789288278992418450933122786990415625278087649712338543546066768023737

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