I recently brought 9547^79-1 from a c311 to a c197 by finding p34, p34 & p47.

It is now a GNFS candidate. It has had about ~2t50.

I just found a fairly large P-1-factor with low bounds:
[CODE]Input number is (6079^71-1)/((6079-1)*21837976373*320471502941*1543332987289*16951665951059473446613*2517078791601109362779579593) (182 digits)
Using B1=30000000, B2=1017589462248, polynomial x^1, x0=4102967280
Step 1 took 19282ms
Step 2 took 22059ms
********** Factor found in step 2: 5176642807873431885196822871968034981569737462753773
Found probable prime factor of 52 digits: 5176642807873431885196822871968034981569737462753773
Composite cofactor ((6079^71-1)/((6079-1)*21837976373*320471502941*1543332987289*16951665951059473446613*2517078791601109362779579593))/5176642807873431885196822871968034981569737462753773 has 130 digits[/CODE]

3821^83-1 is factored
 

I just found found a p55 with ECM.

(3821^83-1)/3820 = 167*997*p11*p20*p31*p37*p39*p55*p100

[URL="http://factorization.ath.cx/index.php?query=%283821^83-1%29%2F3820"]Details.[/URL]

[QUOTE=lorgix;330786]I just found a fairly large P-1-factor with low bounds:
[CODE]Input number is (6079^71-1)/((6079-1)*21837976373*320471502941*1543332987289*16951665951059473446613*2517078791601109362779579593) (182 digits)
Using B1=30000000, B2=1017589462248, polynomial x^1, x0=4102967280
Step 1 took 19282ms
Step 2 took 22059ms
********** Factor found in step 2: 5176642807873431885196822871968034981569737462753773
Found probable prime factor of 52 digits: 5176642807873431885196822871968034981569737462753773
Composite cofactor ((6079^71-1)/((6079-1)*21837976373*320471502941*1543332987289*16951665951059473446613*2517078791601109362779579593))/5176642807873431885196822871968034981569737462753773 has 130 digits[/CODE][/QUOTE]
Aaand the cofactor had a nice split; p65*p65.

Oooh, nice one! (and not an ECM miss!!)
 

From my aliquot sequences, this is 7044:i3416 (c168):[code]prp82 factor: 4675529087864363160522394641539211781338311038942140683451905613940416262041105757
prp86 factor: 28060693304291823849789377538088181707754591698257888761192358007908855150941587822313
elapsed time 106:17:23[/code]Elapsed time was for the LA and square root, sieving was 8 cores from 3/4 to 5/8.

Attached is the complete log for the morbidly curious....first bunch of runs were to monitor progress.....

This is the most egregious ECM miss I've seen in a long time. It's a C150 from the GCW tables which had had a t50 performed.

[code]sqrtTime: 7371
prp46 factor: 3972487550630460351502859391676731582688869649
prp52 factor: 1841613936712040612911088491714918945539357832738333
prp54 factor: 114414018049271559291394436584415577000795151599116413
elapsed time 02:02:52
-> Computing time scale for this machine...
sumName = g150-c5_375.txt
-> Factorization summary written to g150-c5_375.txt.
[/code]

The p54 showed up first. Any of the three factors could reasonably have been found by the ECM effort applied beforehand.

GNFS avoided
 

13^229-1 is factored by ECM.

c157 = p51*p107

[URL="http://factorization.ath.cx/index.php?id=1100000000042138697"]Details.[/URL]

I don't think the primitive of 2^50937+1 was factored until just now.

I used Prime95 to find a p18. (p-1)

(2^50937+1)/(2^16979+1)/3 = p18*prp10205

This is a small step towards proving 2^458465+2^32+1 prime. It is the current #153 on [URL]http://www.primenumbers.net/prptop/prptop.php[/URL]

nice split
 

92[SUP]109[/SUP]-1 c213 = p106.p107

[CODE]p106=1437534230748894007787001205378681381374213557341803151116399682866608700925266942689271366255264439244963
p107=86340307962454646680166401866065974573545581482953022650654130193806384927796031771317801153096333537538287 [/CODE](Although, one really shouldn't get any credit for just pressing the Start button:coffee:).

Factorization of C158 related to the 10th Fermat number
 

Brent's "Factorization of the Tenth Fermat Number" published the 40-digit prime cofactor 4659775785220018543264560743076778192897 of F10 discovered by the Elliptic Curve Method, leaving the largest prime cofactor P252. His initial attempt to prove the primality of P252 by factoring P252-1 found small prime cofactors 2 3 13 23 29 6329 760347109 211898520832851652018708913943317 9409853205696664168149671432955079744397 (this 40-digit cofactor also notably discovered by ECM as published in the paper), but there remained a C158 composite cofactor. The primality of P252 was later proven by other means (the Cube Root Theorem).

Here is the factorization of that C158 (525 bits) as computed with Yafu using the general number field sieve: C158 = P58 * P101, where P58 = 3035625952640765962086368602839492329385321995258480540549 and P101 = 21014737139156086365509400019795978246705779843330697799891230652189207470396514322958290676782759071 .

Logs and more information at
[url]http://kenta.blogspot.com/2013/06/bgvtnpai-factorization-of-brents-c158.html[/url]

The P252-1 is listed [url=http://factordb.com/index.php?id=1100000000213169281]here[/url] and dated on March 17, 2011 (see 'more information').

The C158 is dated the same day, but the P58 and P101 are from November 14, 2011, so they seem to be known long before yours.