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.
80digit prime factor: 51502221799707178125025528282930027721442937798693063043926320591434734001630893 101digit 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 tossup. Since the former requires no polynomial search, I would go with that. 
[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 tossup. 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. 
[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). 
[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 pretesting for the next round of NFS@Home reservations. Sounds like Greg still plans snfs. Bruce 
[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.

6,323+ has been completed up
[quote=frmky]
One last result for 2009! The composite cofactor of 6,323+ was the product of 106digit and 115digit prime numbers: 106digit prime factor: 8726220783196433420577926540172780111230892319895685342094694918556189538442501432986166567593663232876099 115digit 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] 
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As Raman reports, 6,323+ finished a bit early and squeaked into 2009. It was originally due midDecember, 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! 
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6,331+ is factored. As a test, it was completed with 32bit large primes. The size of the matrix generated was about the same size as would have been generated with 31bit LPs, demonstrating that the matrix size does not strongly depend of the large prime bound. The log is attached.
68digit prime factor: 10001312033685801300032151531732232582514112692078389782701922973061 160digit prime factor: 65895276032273530263048875365535917359061535246511133624566186538715266554188340585/ 77770302531875655837482720443630406486478245944869941397820842114167390421773 
[quote=frmky;201207]6,331+ is factored. As a test, it was completed with 32bit large primes. The size of the matrix generated was about the same size as would have been generated with 31bit LPs, demonstrating that the matrix size does not strongly depend of the large prime bound. The log is attached.
68digit prime factor: 10001312033685801300032151531732232582514112692078389782701922973061 160digit 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: 
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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. 69digit prime factor: 650106680542055228216904187084969212101711180529566573956155238949369 108digit prime factor: 437044495846780459786775320213708755010180640454196959129029284718895597993040438934936850297533075756275529 
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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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