20100831, 19:58  #210 
"William"
May 2003
New Haven
2^{3}×5×59 Posts 
The low base Brent composite 43^1491 had 2 previously known factors of 9 and 11 digits. The remaining C224 was factored as P59 * P165.
ECM to t50 by yoyo@home SNFS sieving by RSALS Post Processing by Carlos Pinho Code:
49^1491 P59: 86959139755992334146951905688612930845160757695048012660011 P165: 210379001213136221541664472540640112042495029485679467795377614362692978042544981962987197932691344997299555981733468380709579937416527275299320760668948931886000961 
20100903, 14:23  #211 
Dec 2009
89 Posts 
5^1024+1024^5
The loveliest factorization I ever found was that of 5^1024+1024^5. It required a lot of luck and very little factoring effort.
5^1024+1024^5 = 113 * 809 * 160313 * 42387041 * 7329030409 * 425520498209 * 3024735158536046561 * P324 * P335 
20100903, 15:04  #212  
Nov 2003
7460_{10} Posts 
Quote:
This is far beyond current capabilities otherwise. 

20100903, 17:57  #213 
Dec 2009
59_{16} Posts 

20100903, 21:20  #214 
Nov 2003
2^{2}·5·373 Posts 

20100905, 02:41  #215 
Feb 2003
2·3·29 Posts 
643945470136695841369  M52272617
Found with P1 where k = 2^2 * 3 * 17 * 31 * 499 * 709 * 2753 Man, that is smooth. 
20100908, 07:51  #216 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10501_{10} Posts 
Nothing too unusual about a p49 these days but this one was found by gmpecm using a B1 value of 1M, which is optimal for factors 14 digits smaller.
Code:
[20100907 11:15:27 GMT] GC_5_691_C421: probable factor returned by pcl@maat (maat4)! Factor=2341673831256161998097409059802772958624071425517 Method=ECM B1=1000000 Sigma=1067295280 Paul 
20100915, 12:16  #217 
Nov 2003
2^{2}×5×373 Posts 
Top 10?
Why hasn't Blair Kelly's P64 factor of L1956 shown up on the
ECM Top 10 page? 
20100930, 17:31  #218 
(loop (#_fork))
Feb 2006
Cambridge, England
7×911 Posts 
5748 index 1368:
Code:
Thu Sep 30 17:37:00 2010 prp69 factor: 674788222835164103353823038231553835542017738166824174868830262813749 Thu Sep 30 17:37:00 2010 prp86 factor: 28250192298752567946214115957812098958537842561773991296565797999910836802368478096257 
20101011, 21:40  #219 
"William"
May 2003
New Haven
2^{3}×5×59 Posts 
The Brent composite 541^891 had 3 previously known factors of 3, 6, and 11 digits. The remaining C223 has been factored as P89 * P135.
ECM to t50 by yoyo@home SNFS sieving by RSALS Post Processing by ZetaFlux Code:
541^891 P89: 22258230882835545380142293457243394259854811189356144633053908389611484579705336039818299 P135: 156308318050822004478554684741294957177596514375932813652522859001742185442920716992906314508709642460414410563253635690990135902349719 
20101015, 09:02  #220 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9259_{10} Posts 
a factor of 220 digits...
> echo "(10^92701)/3^4/7"  ecm 5e4
Input number is (10^92701)/3^4/7 (9268 digits) Using B1=50000, B2=15446350, polynomial x^2, sigma=3682263502 Step 1 took 99069ms ********** Factor found in step 1: 9573726981993820200551709701677247363792903115583020462044881149461982541836124423370428786937847788404630054782651343281856841362377745746844353951111544591359795066465415084994921961147188454685295861838434800628490443 Found composite factor of 220 digits: 9573726981993820200551709701677247363792903115583020462044881149461982541836124423370428786937847788404630054782651343281856841362377745746844353951111544591359795066465415084994921961147188454685295861838434800628490443 Composite cofactor ((10^92701)/3^4/7)/9573726981993820200551709701677247363792903115583020462044881149461982541836124423370428786937847788404630054782651343281856841362377745746844353951111544591359795066465415084994921961147188454685295861838434800628490443 has 9048 digits 
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