Another Brent composite with no previously known factors.

ECM to t50 by yoyo@home
SNFS sieving by RSALS
Post Processing by Carlos Pinho

[code](971^73-1)/970 = P94 * P122

P94: 7301993584996352018423967893607251486202260927217901674208672075404136696633478270198913907277
P122: 16473679102988462780517793172944047865186542084189994639205055312545452886118612142573867571362310098581364983638042119829
[/code]

Another Brent composite with no previously known factors.

ECM to t50 by yoyo@home
SNFS sieving by RSALS
Post Processing by Carlos Pinho

[code](709^79-1)/708 = P103 * P120

P103: 3265048507457607509514118788891969721101060439064954454744472431751852451297744518806644922752209694749
P120: 687273635059837837112240728105079662820988138420249488404904366981254199386302230536972921796752546749492243666039395839
[/code]

A Curio
 

This dropped out after only 603 trials, by which time I would expect to have found almost all p28s:

[code]GMP-ECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM]
Input number is 8942391253220120724792369846184350004422970554909937973523793125892503966249969509033344875755986267902321369397956127681382245048167463409787699967879654325078733243833427701425823704664041045924437093283158114509154763672320817 (229 digits)
Using B1=239049, B2=128973400, polynomial Dickson(3), sigma=1568738653
Step 1 took 2125ms
Step 2 took 1656ms
********** Factor found in step 2: 312831586607365644204415768445243517253551786710765503285642403654087
Found composite factor of 69 digits: 312831586607365644204415768445243517253551786710765503285642403654087
Composite cofactor 28585320779783339891354158589177572297705993567124278948012276674473264463512433195630506634213128358105308127158208853033789681613785160413652088075041528574791 has 161 digits[/code]

msieve tidied up:
[code]prp33 factor: 155987366473971075756698545127569
prp37 factor: 2005493096516675099352436067045880023[/code]

Lucky to find a p33 after so little work. Extremely lucky to find a p37. Finding both on the same trial? I'd guess about one in 44,000,000 (as that's how many trials I've run on this project and this is the luckiest find so far). No, that is not a serious estimate :wink:.

I thought it was worth sharing. :sorry: if you disagree.

--Andy Steward

Another Brent composite with no previously known factors.

ECM to t50 by yoyo@home
SNFS sieving by RSALS
Post Processing by Carlos Pinho

[code]
(937^79-1)/936 aka sigma(936^78) = P92 * P141

P92: 27041233006608197184935428356203666605944675687190254488284107230694979211417083669797007121
P141: 231273216776252815636165441586020237984220549802989881457557779638672297405316269533037157418896850825375946121671871846218060682888723537287
[/code]

This Brent composite had one four digit factor previously known. It was factored by yoyo@home's ECM with B1=43M, saving a SNFS factorization by RSALS.
[code]
643^79-1 = P50 * P166

P50: 77257889852086726525775815698800676875152288293307
P166: 2572677405869610247296006851540894449249430402341296110792645273951547330727458769568704596642097469132620208925933945128276217347912438185833131568325318051988952029
[/code]

[QUOTE=wblipp;224662]This Brent composite had one four digit factor previously known. It was factored by yoyo@home's ECM with B1=43M, saving a SNFS factorization by RSALS.
[code]
643^79-1 = P50 * P166[/code][/QUOTE]Ugh, I ran a lot of curves at 43M and some at 110M on my [URL="http://www.mersenneforum.org/showpost.php?p=223227&postcount=197"]c146[/URL] that missed a c43!

This Brent composite had a single factor of six digits previously known,

ECM to t50 by yoyo@home
SNFS sieving by RSALS
Post Processing by Carlos Pinho

[code]
Composite from 23^167-1 aka sigma(12^166) = P80 * P142

P80: 10161473543764444434291215383032451031371411086076788308585620646466269527558451
P142: 1770387493170058114487905901395829213241269022867729236625766182071271122944885396939230048085533781242093668275727874173606781691576168942751[/code]

A Brent composite that had a few small factors previously known. A three way split with B1=11M (45 digits), saving the 50 digit ECM and the SNFS
[code]
103^113-1 C201 = P44 * P50 * P107

P44: 84129598291520950241390575083068719360021171
P50: 44524249152081676378516429019402317394611073486533
P107: 82315835207242691235211750813760600929204133699173549798646811508286030336608729162527059866348699396126153
[/code]

ECM B1=1e6 kill shot
 

Called ecm with the -v flag, just to get my bearings.

Well, it named that tune in 1:

[CODE]
C:\al\zahlen\ggnfs\projects\235416>ecm -v 1e6 < 2851c113
GMP-ECM 6.2.3 [powered by GMP 4.3.0] [ECM]
Input number is 92047662531663565390842482351084663150917243804901464964197093733017673896259378196247891860624551698300716957203 (113 digits)
Using MODMULN
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1355166397
dF=4096, k=6, d=39270, d2=13, i0=13
Expected number of curves to find a factor of n digits:
20 25 30 35 40 45 50 55 60 65
5 20 118 904 8613 97057 1270662 1.9e+007 3.2e+008 6.
1e+009
Step 1 took 10015ms
********** Factor found in step 1: 934755100218937800337186649945447
Found probable prime factor of 33 digits: 934755100218937800337186649945447
Composite cofactor 98472490291953705278096018200190093279508291454377707825490220624218931524024949 has 80 digits
[/CODE]

The Brent composite 491^83-1 had 5 previously known factors ranging from 3 to 10 digits. The remaining C195 was factored as P61 * P135

ECM to t50 by yoyo@home
SNFS Sieving by RSALS
Post Processing by Carlos Pinho

[code]
P61: 1667360023476578025263413764232230672807644148255835927567361
P135: 205525195924680389727849382931556003363755140788960585678710010582760763836207173324875835050154079859722456787347359906517258848929453[/code]

The Brent composite 599^83-1 had 3 previously known factors ranging from 3 to 9 digits. The remaining C213 was factored as P55 * P63 * P96

ECM to t50 by yoyo@home
SNFS Sieving by RSALS
Post Processing by Jeff Gilchrist
[code]
599^83-1

P55: 5163739412794483831625171731355488900616191583344901813
P63: 128707803852363372849465276089219316121940177238759012038589467
P96: 505056584916499255637800227107119527780741030449529468084665044722203901250285575250908384336319[/code]