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2013-07-21, 10:41   #353
prgamma10

Jan 2013

1558 Posts

Quote:
 Originally Posted by swishzzz How do I find the group order for this factorization? factordb's group order calculator clearly fails for this one...
sigma 1:<something> is not a Brent-Suyama curve, and Factordb up to now only supports Brent-Suyama curves (sigma 0:<something>).

Tried some Magma code, based on the GMP-ECM manual: (won't work, and I have no idea why)
Code:
FindGroupOrder := function (p, s)
K := GF(p);
A := K ! (4*s^2-2);
x := 2;
b := x^3 + A*x^2 + x;
E := EllipticCurve([0,b*A,0,b^2,0]);
return FactoredOrder(E);
end function;

p := 26759964491830480636236398774973830719679139755537527;
s := 3576746370;
FindGroupOrder(p,s);

Last fiddled with by prgamma10 on 2013-07-21 at 10:43

 2013-10-09, 17:48 #354 maxal     Feb 2005 22·32·7 Posts I've just got factorization of 102^103 + 1 = 103^2 * prp74 * prp130 with SNFS: Code: prp74 factor: 16577923085747542727498881886756397313868752518022676502052070512564532587 prp130 factor: 4371325251720559422253332573045929417056159075217221344318685656228760863793509418168865967108430523971884258595890393501349300723
 2013-10-27, 16:43 #355 YuL     Feb 2012 Paris, France 2418 Posts A P58 I've found by ECM last week (which broke my previous personal record): Code: GMP-ECM 6.4.4 [configured with MPIR 2.6.0] [ECM] Input number is (3*10^204+7)/(2111*12379*80141*360193*36529453*83762087274812203759) (160 digits) Using B1=260000000, B2=3178559884516, polynomial Dickson(30), sigma=2078429522 Step 1 took 1093707ms Step 2 took 363420ms ********** Factor found in step 2: 4269986142493572515510539041322472993083083125849142037361 Found probable prime factor of 58 digits: 4269986142493572515510539041322472993083083125849142037361 Probable prime cofactor ((3*10^204+7)/(2111*12379*80141*360193*36529453*83762087274812203759))/4269986142493572515510539041322472993083083125849142037361 has 102 digits Details here. A P53 found by ECM in step 1 (details here): Code: GMP-ECM 6.4.4 [configured with MPIR 2.6.0] [ECM] Input number is (26*10^238-17)/(9*3*31*17914895525348997871953180891109) (206 digits) Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=4255384633 Step 1 took 648620ms ********** Factor found in step 1: 77799771931273889262077139536983524215512156277756839 Found probable prime factor of 53 digits: 77799771931273889262077139536983524215512156277756839 Probable prime cofactor ((26*10^238-17)/(9*3*31*17914895525348997871953180891109))/77799771931273889262077139536983524215512156277756839 has 153 digits
 2013-11-11, 17:21 #356 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 47·197 Posts Code: Msieve v. 1.52 (SVN 886M) Mon Nov 11 01:03:57 2013 random seeds: 187198dc e395e0be factoring 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 (253 digits) ...initial square root is modulo 4585129 sqrtTime: 7150 p117 factor: 211857628677636264166676902114066256198845941934180788645905936104472665184004014226679863567582409810768749673482061 p137 factor: 47201510100993602326827859852217555163129145401663287219390072454758015933440888931227171966024510895342063068118093723212737563878094459
 2013-11-11, 19:03 #357 YuL     Feb 2012 Paris, France 101000012 Posts Code: GMP-ECM 6.4.4 [configured with MPIR 2.6.0] [ECM] Input number is (10^248+3)/(19*223*126165718229274337) (228 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3741404180 Step 1 took 20467ms Step 2 took 9969ms ********** Factor found in step 2: 16031381961952347637116191005607843989279 Found probable prime factor of 41 digits: 16031381961952347637116191005607843989279 Composite cofactor ((10^248+3)/(19*223*126165718229274337))/16031381961952347637116191005607843989279 has 188 digits Group order: 2^3 · 3^2 · 5 · 7 · 19^3 · 163 · 1307 · 1487 · 120163 · 134639 · 2337983 · 77402051 Code: GMP-ECM 6.4.4 [configured with MPIR 2.6.0] [ECM] Input number is (10^248+3)/(19*223*126165718229274337*16031381961952347637116191005607843989279) (188 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1601899263 Step 1 took 14883ms Step 2 took 8283ms ********** Factor found in step 2: 12824921391934305400334065366552991673187 Found probable prime factor of 41 digits: 12824921391934305400334065366552991673187 Probable prime cofactor ((10^248+3)/(19*223*126165718229274337*16031381961952347637116191005607843989279))/12824921391934305400334065366552991673187 has 147 digits Group order: 2^10 · 3^2 · 7 · 13 · 521 · 757 · 5209 · 9883 · 74699 · 2923747 · 3448573771
2013-11-11, 19:08   #358
YuL

Feb 2012
Paris, France

A116 Posts

Quote:
 Originally Posted by Batalov Code: Msieve v. 1.52 (SVN 886M) Mon Nov 11 01:03:57 2013 random seeds: 187198dc e395e0be factoring 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 (253 digits) ...initial square root is modulo 4585129 sqrtTime: 7150 p117 factor: 211857628677636264166676902114066256198845941934180788645905936104472665184004014226679863567582409810768749673482061 p137 factor: 47201510100993602326827859852217555163129145401663287219390072454758015933440888931227171966024510895342063068118093723212737563878094459
Impressive. How long did it take? How much processing power?

 2013-11-11, 23:29 #359 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 242B16 Posts It was about 25 thousand hours for sieving, two hrs for filtering, 24 hours LA (on an 4x8 MPI grid), and two hours per sqrt.
 2014-01-02, 09:07 #360 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 11000111010012 Posts Further exploration of pointless places I ran 480 curves at 1e7 on {60..79}^512+1 over Christmas No complete factorisations; a couple of new factors of interest: Code: e62:Found probable prime factor of 30 digits: 415279119367083281900859703297 e77:Found probable prime factor of 33 digits: 341126180420063151380968669975553 e65:Found probable prime factor of 37 digits: 1869269849997935174077690896845848577 e75:Found probable prime factor of 38 digits: 13734192372070026415774074593138282497 e65:Found probable prime factor of 43 digits: 4769997756860644904012186212092431977208833 This was clearly untouched ground, I found a ten-digit factor of 79^512+1 that wasn't in factordb.
 2014-01-17, 09:50 #361 kar_bon     Mar 2006 Germany 1011001100102 Posts Reverse Smarandache numbers Hi, the last days I've factored 2 Reverse Smarandache type numbers for n=103 and n=104. RSm(103).C160 = P53 * P108 Running yafu over night: prp53 = 22633393225636817509048253413614523936779379142819839 (curve 50 stg2 B1=260000000 sigma=4172026601 thread=1) Finished 400 curves using Lenstra ECM method on C160 input, B1=260M, B2=gmp-ecm Default RSm(104).C149 = P52 * P97 Running msieve: total time: 85.26 hours. Intel64 Family 6 Model 58 Stepping 9, GenuineIntel processors: 8, speed: 3.39GHz Windows-7-6.1.7601-SP1 Running Python 2.7 Both reported to World of numbers. Also shown on my page.
 2014-02-04, 09:29 #362 kar_bon     Mar 2006 Germany 2·1,433 Posts Reverse Smarandache for n=105, C156 factored in: r1=505609049620430043564818948424594740095377638674786008583783558052966689 (pp72) r2=1460218912197798897796479876892816487811802580775089126778648005904642208642833062339 (pp85)
 2014-02-15, 18:27 #363 sean     Aug 2004 New Zealand 13·17 Posts rSm(106) C167 is factored Code: GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 18177692096553830368675737725463580456289708131712261558393850692666532966863437168425047460718124572874681287411912149791448198810931545176347119222043777538034560927 (167 digits) Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=2318285213 Step 1 took 434355ms Step 2 took 41233ms ********** Factor found in step 2: 414338872062791501547344020582712133249557 Found probable prime factor of 42 digits: 414338872062791501547344020582712133249557 Probable prime cofactor 43871558577296772025736976053227175068325706197701002055248304277569975777948248915189631633909304741312836729962564905149411 has 125 digits

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