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 2010-08-31, 19:58 #210 wblipp     "William" May 2003 New Haven 23×5×59 Posts The low base Brent composite 43^149-1 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: 49^149-1 P59: 86959139755992334146951905688612930845160757695048012660011 P165: 210379001213136221541664472540640112042495029485679467795377614362692978042544981962987197932691344997299555981733468380709579937416527275299320760668948931886000961
 2010-09-03, 14:23 #211 warut   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
2010-09-03, 15:04   #212
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by warut 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
Please explain. Is there an algebraic factorization here that I am missing?
This is far beyond current capabilities otherwise.

2010-09-03, 17:57   #213
warut

Dec 2009

5916 Posts

Quote:
 Originally Posted by R.D. Silverman Please explain. Is there an algebraic factorization here that I am missing? This is far beyond current capabilities otherwise.
Yes, it admits an algebraic factorization because
5^1024 + 1024^5 = (5^256)^4 + 4*(2^12)^4.

2010-09-03, 21:20   #214
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by warut Yes, it admits an algebraic factorization because 5^1024 + 1024^5 = (5^256)^4 + 4*(2^12)^4.
Yes. Nice result.

 2010-09-05, 02:41 #215 apocalypse   Feb 2003 2·3·29 Posts 643945470136695841369 | M52272617 Found with P-1 where k = 2^2 * 3 * 17 * 31 * 499 * 709 * 2753 Man, that is smooth.
 2010-09-08, 07:51 #216 xilman Bamboozled!     "πΊππ·π·π­" May 2003 Down not across 1050110 Posts Nothing too unusual about a p49 these days but this one was found by gmp-ecm using a B1 value of 1M, which is optimal for factors 14 digits smaller. Code: [2010-09-07 11:15:27 GMT] GC_5_691_C421: probable factor returned by pcl@maat (maat4)! Factor=2341673831256161998097409059802772958624071425517 Method=ECM B1=1000000 Sigma=1067295280 GC_5_691 is 691*5^691+1 Paul
 2010-09-15, 12:16 #217 R.D. Silverman     Nov 2003 22×5×373 Posts Top 10? Why hasn't Blair Kelly's P64 factor of L1956 shown up on the ECM Top 10 page?
 2010-09-30, 17:31 #218 fivemack (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
 2010-10-11, 21:40 #219 wblipp     "William" May 2003 New Haven 23×5×59 Posts The Brent composite 541^89-1 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: 541^89-1 P89: 22258230882835545380142293457243394259854811189356144633053908389611484579705336039818299 P135: 156308318050822004478554684741294957177596514375932813652522859001742185442920716992906314508709642460414410563253635690990135902349719
 2010-10-15, 09:02 #220 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 925910 Posts a factor of 220 digits... > echo "(10^9270-1)/3^4/7" | ecm 5e4 Input number is (10^9270-1)/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 ((10^9270-1)/3^4/7)/9573726981993820200551709701677247363792903115583020462044881149461982541836124423370428786937847788404630054782651343281856841362377745746844353951111544591359795066465415084994921961147188454685295861838434800628490443 has 9048 digits

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