Gratuitous factors thread

[prgamma10]

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)

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);

[maxal]

I've just got factorization of 102^103 + 1 = 103^2 * prp74 * prp130 with SNFS:

prp74 factor: 16577923085747542727498881886756397313868752518022676502052070512564532587
prp130 factor: 4371325251720559422253332573045929417056159075217221344318685656228760863793509418168865967108430523971884258595890393501349300723

[YuL]

A P58 I've found by ECM last week (which broke my previous personal record):

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):

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

[Batalov]

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

[YuL]

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

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

[YuL]

Originally Posted by Batalov

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?

[Batalov]

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.

[fivemack]

I ran 480 curves at 1e7 on {60..79}^512+1 over Christmas

No complete factorisations; a couple of new factors of interest:

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.

[kar_bon]

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.

[kar_bon]

Reverse Smarandache for n=105, C156 factored in:

r1=505609049620430043564818948424594740095377638674786008583783558052966689 (pp72)
r2=1460218912197798897796479876892816487811802580775089126778648005904642208642833062339 (pp85)

[sean]

rSm(106) C167 is factored

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