fond of a factor? Urn yourself to become remains

[flashjh]

Originally Posted by alpertron

New P-1 factorization record:

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M164503 has a factor: 21054105612284665760256195805146033137688353 (44 digits, 143 bits)
k = 2⁴ × 7 × 97 × 757 × 1289 × 42737 × 23542721 × 36366457 × 164980549

Another nice find and working on factoring the lower numbers!

[TheJudger]

YACS2F (yet another composite stage #2 factor):

P-1 found a factor in stage #2, B1=565000, B2=11017500.
TheJudger/Pminus1, M63323077 has a factor: 68205072662349548620633421760422165673044571137810937540436645541918441353903 (255.23 bits / 77 digits)

Splits into 3 factors:
f₁ = 35159552370479510750561 (74.90 bits / 23 digits)
f₂ = 507279605993833393198631 (78.75 bits / 24 digits)
f₃ = 3824070900985809209362680950233 (101.59 bits / 31 digits)

k₁ = 2⁴ * 5 * 7 * 94153 * 5265373
k₂ = 5 * 181 * 257 * 2633 * 6540679
k₃ = 2² * 3 * 7 * 19 * 229 * 593 * 743 * 138829 * 1350647

Oliver

[firejuggler]

three factor? *whistle* really nice, and rare.

[Uncwilly]

Originally Posted by TheJudger

P-1 found a factor in stage #2, B1=565000, B2=11017500.
TheJudger/Pminus1, M63323077 has a factor: 68205072662349548620633421760422165673044571137810937540436645541918441353903 (255.23 bits / 77 digits)

[markr]

Originally Posted by YuL

My first factor above 100 bits

ECM found a factor in curve #6, stage #2
Sigma=2606317706517304, B1=1000000, B2=100000000.
M400069 has a factor: 17384946805580300647271050027369
k=22 × 3 × 251 × 7213624012067538472153

103.778 bits

Originally Posted by alpertron

New P-1 factorization record:

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M164503 has a factor: 21054105612284665760256195805146033137688353 (44 digits, 143 bits)
k = 2⁴ × 7 × 97 × 757 × 1289 × 42737 × 23542721 × 36366457 × 164980549

Originally Posted by TheJudger

YACS2F (yet another composite stage #2 factor):

P-1 found a factor in stage #2, B1=565000, B2=11017500.
TheJudger/Pminus1, M63323077 has a factor: 68205072662349548620633421760422165673044571137810937540436645541918441353903 (255.23 bits / 77 digits)

Splits into 3 factors:
f₁ = 35159552370479510750561 (74.90 bits / 23 digits)
f₂ = 507279605993833393198631 (78.75 bits / 24 digits)
f₃ = 3824070900985809209362680950233 (101.59 bits / 31 digits)

Very nice, all of them!
(Some emphasis added)

[Jwb52z]

P-1 found a factor in stage #1, B1=580000.
UID: Jwb52z/Clay, M61839119 has a factor: 21738927757882013620583

74.203 bits.

It was barely missed by trial factoring, I think.

[TheJudger]

Originally Posted by firejuggler

three factor? *whistle* really nice, and rare.

And I still haven't figured out when/why stage #2 finds composite factors. But I guess 3 factors in stage #2 don't happen every day.

Oliver

[flashjh]

Originally Posted by TheJudger

And I still haven't figured out when/why stage #2 finds composite factors. But I guess 3 factors in stage #2 don't happen every day.

Oliver

All 3 prime factors' min B2 value is lower than the actual B2 value that was used:

M63,323,077

P-1 found a factor in stage #2, B1=565000, B2=11,017,500
24 × 5 × 7 × 94153 × 5,265,373
5 × 181 × 257 × 2633 × 6,540,679
22 × 3 × 7 × 19 × 229 × 593 × 743 × 138829 × 1,350,647

[TheJudger]

Yes, I'm unsure about the

There is an enhancement to Pollard's algorithm called stage 2 that uses a second bound, B2. Stage 2 will find the factor q if k has just one factor between B1 and B2 and all remaining factors are below B1.

(taken from http://mersenne.org/various/math.php) part. And then there is Brent-Suyama extension aswell.

Oliver

[ryanp]

Found two today with some manual testing:

GMP-ECM 6.4.3 [configured with GMP 5.1.0, --enable-asm-redc] [ECM]
Input number is 2^201403-1 (60629 digits)
Using B1=1000000, B2=974637522, polynomial Dickson(3), sigma=3213589569
Step 1 took 14148836ms
Step 2 took 2368143ms
********** Factor found in step 2: 2508992110550760564547884607969
Found probable prime factor of 31 digits: 2508992110550760564547884607969
Composite cofactor (2^201403-1)/2508992110550760564547884607969 has 60598 digits

and:

GMP-ECM 6.4.3 [configured with GMP 5.1.0, --enable-asm-redc] [ECM]
Input number is 2^207481-1 (62459 digits)
Using B1=250000, B2=183032866, polynomial Dickson(3), sigma=2211227441
Step 1 took 3350126ms
Step 2 took 1023982ms
********** Factor found in step 2: 2051067332098179933221407
Found probable prime factor of 25 digits: 2051067332098179933221407
Composite cofactor (2^207481-1)/2051067332098179933221407 has 62434 digits

They're both on factordb.com now, not sure if there's a good way to also upload them to mersenne.org's database...

[Batalov]

You can mimic the recognizeable formats and paste into http://mersenne.org/manual_result/

M207481 has a factor: 2051067332098179933221407

M201403 has a factor: 2508992110550760564547884607969