### July 24, 20102010 年 7 月 24 日 (Maksym Voznyy)

# all remaining 117 unidentified factors are composite

n=91739: x91057(1296627918......) is composite

n=91741: x84649(1394790267......) is composite

n=91891: x89684(2499653375......) is composite

n=91993: x83608(8353948971......) is composite

n=91997: x91977(4780149661......) is composite

n=91999: x91324(3265952212......) is composite

n=92003: x91982(9943427815......) is composite

n=92021: x86556(6685532111......) is composite

n=92027: x84924(3986506234......) is composite

n=92147: x83743(1458626822......) is composite

n=92333: x92292(1575679979......) is composite

n=92341: x91354(1623033352......) is composite

n=92441: x91381(1281717934......) is composite

n=92887: x89619(3651106591......) is composite

n=92923: x90708(2802071466......) is composite

n=92933: x92256(2432708320......) is composite

n=93061: x89812(9169079842......) is composite

n=93091: x92220(8469567954......) is composite

n=93101: x92320(4179279394......) is composite

n=93193: x90862(4342678516......) is composite

n=93221: x91860(2174594556......) is composite

n=93311: x89220(7249542255......) is composite

n=93721: x85237(1110695691......) is composite

n=93811: x93780(1658262478......) is composite

n=93823: x88261(1024442941......) is composite

n=94063: x94041(1828853556......) is composite

n=94189: x93328(9901323002......) is composite

n=94211: x86933(5511081765......) is composite

n=94217: x92799(2107340631......) is composite

n=94279: x90988(6399743816......) is composite

n=94361: x93480(4299020126......) is composite

n=94373: x89376(7594223944......) is composite

n=94387: x91783(2418618758......) is composite

n=94399: x94376(1224936869......) is composite

n=94411: x89394(1769592648......) is composite

n=94679: x87364(2487015318......) is composite

n=94907: x94878(1427218595......) is composite

n=94957: x94317(9933586774......) is composite

n=95021: x94998(1145946146......) is composite

n=95027: x95006(5008369847......) is composite

n=95243: x87981(2946998163......) is composite

n=95309: x94600(5783685773......) is composite

n=95323: x86669(8551755306......) is composite

n=95357: x94600(6142746626......) is composite

n=95579: x86868(5526288178......) is composite

n=95699: x94452(3251770240......) is composite

n=95827: x94514(1057191177......) is composite

n=95863: x90196(2148490371......) is composite

n=95873: x95855(8579928228......) is composite

n=95941: x93300(5433564375......) is composite

n=96007: x87469(1596969308......) is composite

n=96139: x95236(3821982643......) is composite

n=96191: x93900(2791706636......) is composite

n=96223: x96204(9045267257......) is composite

n=96247: x95244(9037161523......) is composite

n=96319: x94639(7567856207......) is composite

n=96431: x96397(4699466318......) is composite

n=96511: x95446(2625336687......) is composite

n=96611: x90900(6526638069......) is composite

n=96721: x96384(2041461621......) is composite

n=96847: x96826(7653513427......) is composite

n=96869: x96078(2430176170......) is composite

n=96937: x90459(8451525145......) is composite

n=97141: x88279(5356872116......) is composite

n=97157: x97134(1122148196......) is composite

n=97159: x97119(3965467476......) is composite

n=97283: x97260(8097850689......) is composite

n=97327: x97306(2380847547......) is composite

n=97399: x96652(3509375945......) is composite

n=97411: x94012(2028870632......) is composite

n=97457: x95022(6906377350......) is composite

n=97543: x93268(8467183498......) is composite

n=97597: x91828(9259005009......) is composite

n=97657: x83632(2036778728......) is composite

n=97679: x89814(3563410118......) is composite

n=97831: x92328(2849487803......) is composite

n=97859: x97836(1096164942......) is composite

n=98017: x97993(2407042654......) is composite

n=98083: x95694(5762569956......) is composite

n=98099: x97452(4191499976......) is composite

n=98177: x94959(7576966897......) is composite

n=98179: x98147(1709429621......) is composite

n=98327: x98308(3993877854......) is composite

n=98357: x84276(1567296765......) is composite

n=98359: x95900(6615041614......) is composite

n=98471: x96732(6143687715......) is composite

n=98479: x98450(1232071201......) is composite

n=98497: x84396(1367450440......) is composite

n=98641: x98588(3770583681......) is composite

n=98713: x98692(3346683222......) is composite

n=98953: x98923(3684873603......) is composite

n=99041: x99023(5462091623......) is composite

n=99157: x98451(7410422783......) is composite

n=99263: x93397(1380626040......) is composite

n=99283: x98179(3091006519......) is composite

n=99323: x85079(5111646390......) is composite

n=99359: x91675(5997899927......) is composite

n=99437: x91763(2012939337......) is composite

n=99439: x99418(3925705449......) is composite

n=99451: x90381(1006770211......) is composite

n=99499: x92715(3800054434......) is composite

n=99571: x99552(1792943569......) is composite

n=99599: x98716(5853090506......) is composite

n=99607: x99586(7516441829......) is composite

n=99613: x92379(7141118133......) is composite

n=99629: x98064(9344893671......) is composite

n=99701: x85407(3581302703......) is composite

n=99703: x98951(7928740432......) is composite

n=99751: x95371(3480907070......) is composite

n=99781: x88299(8440821321......) is composite

n=99797: x95421(5927712446......) is composite

n=99839: x99811(2973062372......) is composite

n=99847: x87329(3049235270......) is composite

n=99919: x99120(5183080454......) is composite

n=99937: x95890(7690827302......) is composite

n=99959: x94668(9592230488......) is composite

n=99983: x92268(3981458342......) is composite

### July 22, 20102010 年 7 月 22 日 (Kurt Beschorner)

n=7051: c6374(4777501349......) = 10233250707709193086806049 * c6349(4668605788......)

n=7357: c6300(9000000900......) = 13799611926418431967883 * c6278(6521923187......)

n=7855: c6273(6944111495......) = 55671079438234808680639711 * c6248(1247346300......)

n=8965: c6453(1612124491......) = 143971108461336502171600391 * c6427(1119755559......)

n=9205: c6273(2056104020......) = 3116748019245495652711 * c6251(6596953001......)

n=9411: c6256(9790162716......) = 644418622759574580283 * c6236(1519224052......)

### July 22, 20102010 年 7 月 22 日 (Juno Fukos)

n=10647: c5617(1000000000......) = 1228881852249604948284662683 * c5589(8137478783......)

# ECM B1=50000, sigma=3023631877

```Results:
Using B1=50000, B2=15446350, polynomial x^2, sigma=3023631877
Step 1 took 246185ms
Step 2 took 51621ms
********** Factor found in step 2: 1228881852249604948284662683
Found probable prime factor of 28 digits: 1228881852249604948284662683
Composite cofactor 8137478783411023168970316729798212637345493467746555986244239
08197377252633590245324250049600933245837967189980813750397054882431894661917525
(snip)
91462671360126873511322325915577796655807809506852177615832818056735235852233601
98003347 has 5589 digits
```

### July 20, 20102010 年 7 月 20 日 (Kurt Beschorner)

n=12580L: c2248(1029202153......) = 28023250907119295576858038564333784221 * c2210(3672672226......)

# 28023250907119295576858038564333784221 is the largest known factor that appears after n=8460M.

```Largest known factors that appear after the previous one
1  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
2  n=1060L: 1866584856050670751142049533200645741569755944852998334484263922627299824538001 (Edwards and King / Feb 16, 2010)
3  n=1220M: 27186363592392725942593454290345801336551729326489701011779461 (Shaopu Lin / Sep 7, 2007)
4  n=1780L: 1770802747819705674494038777570386129969127178558041 (Yousuke Koide / Sep 12, 2009)
5  n=5100L: 185898550709887865845976723509058449254706894935901 (Frank Boerner / Jun 28, 2010)
6  n=7140L: 154171650837800469380227217503464603601 (Yousuke Koide / Jun 1, 2007)
7  n=8460M: 32392612190601505925687792712748935421 (Yousuke Koide / Jan 14, 2008)
8  n=12580L: 28023250907119295576858038564333784221 (Kurt Beschorner / Jul 20, 2010)
9  n=30180M: 3152213324193437059705520007587221 (Alfred Reich / May 12, 2010)
10  n=40610: 1028282517874156981827943844801 (Alfred Reich / Apr 8, 2010)
11  n=70140M: 461904211182554850127110960541 (Alfred Reich / Apr 26, 2010)
12  n=99380M: 6592290434322258947071767721 (Alfred Reich / Apr 26, 2010)
13  n=99874: 20466106492496275108462693 (Alfred Reich / Mar 29, 2010)
14  n=99940M: 17594820928226575015141 (Alfred Reich / Dec 2008)
15  n=99992: 371044131599480009569 (Alfred Reich / Jun 17, 2010)
16  n=99999: 821893328984521 (Alfred Reich / Jul 28, 2008)
17  n=100000: 66489400001 (Kurt Beschorner / Mar 13, 2008)
```

### July 19, 20102010 年 7 月 19 日 (Kurt Beschorner)

n=6569: c6548(2326042502......) = 178184708606143049573489359 * c6522(1305410840......)

n=6859: c6488(1590947752......) = 6236185604775603125041 * c6466(2551155230......)

n=7835: c6243(1309456521......) = 6704063410365652102507121 * c6218(1953228126......)

n=8515: c6230(2916148381......) = 162158620480063489648991 * c6207(1798330777......)

n=12129: c7425(2032396888......) = 1292289739102618571563 * c7404(1572709917......)

### July 16, 20102010 年 7 月 16 日 (Kurt Beschorner)

n=6551: c6537(1060315095......) = 28567447395474592730557 * c6514(3711620015......)

n=8635: c6229(1037890874......) = 7065967983966382587905161 * c6204(1468858727......)

n=12126: c3864(9100000000......) = 1649009847556920673302907837 * c3837(5518463102......)

n=12460M: c2112(3537460769......) = 11325306711919864144476865825321801 * c2078(3123501075......)

# 11325306711919864144476865825321801 is the largest known factor that appears after n=12300M.

```Largest known factors that appear after the previous one
1  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
2  n=1060L: 1866584856050670751142049533200645741569755944852998334484263922627299824538001 (Edwards and King / Feb 16, 2010)
3  n=1220M: 27186363592392725942593454290345801336551729326489701011779461 (Shaopu Lin / Sep 7, 2007)
4  n=1780L: 1770802747819705674494038777570386129969127178558041 (Yousuke Koide / Sep 12, 2009)
5  n=5100L: 185898550709887865845976723509058449254706894935901 (Frank Boerner / Jun 28, 2010)
6  n=7140L: 154171650837800469380227217503464603601 (Yousuke Koide / Jun 1, 2007)
7  n=8460M: 32392612190601505925687792712748935421 (Yousuke Koide / Jan 14, 2008)
8  n=12300M: 1753201085295414260272950235862143501 (Kurt Beschorner / Apr 28, 2010)
9  n=12460M: 11325306711919864144476865825321801 (Kurt Beschorner / Jul 16, 2010)
10  n=30180M: 3152213324193437059705520007587221 (Alfred Reich / May 12, 2010)
11  n=40610: 1028282517874156981827943844801 (Alfred Reich / Apr 8, 2010)
12  n=70140M: 461904211182554850127110960541 (Alfred Reich / Apr 26, 2010)
13  n=99380M: 6592290434322258947071767721 (Alfred Reich / Apr 26, 2010)
14  n=99874: 20466106492496275108462693 (Alfred Reich / Mar 29, 2010)
15  n=99940M: 17594820928226575015141 (Alfred Reich / Dec 2008)
16  n=99992: 371044131599480009569 (Alfred Reich / Jun 17, 2010)
17  n=99999: 821893328984521 (Alfred Reich / Jul 28, 2008)
18  n=100000: 66489400001 (Kurt Beschorner / Mar 13, 2008)
```

n=12500L: c2462(6442605342......) = 7355683307782160268476171662501 * c2431(8758676893......)

### July 13, 20102010 年 7 月 13 日 (Kurt Beschorner)

n=6533: c6310(5304339139......) = 84394462738704528845563 * c6287(6285174366......)

n=7147: c6104(1404052847......) = 460722331941333286020325403 * c6077(3047503344......)

n=7273: c6228(9000000900......) = 9415368381475938239 * c6209(9558840966......)

n=10089: c6230(2391495526......) = 10897449031180249265057293 * c6205(2194546191......)

n=10689: c6055(7658704788......) = 1419385583876756360747401 * c6031(5395788766......)

### July 7, 20102010 年 7 月 7 日 (Kurt Beschorner)

n=6809: c6169(6881753959......) = 881498826999535152871 * c6148(7806878181......)

n=7091: c6072(9000000900......) = 142217186259619914689 * c6052(6328349714......)

n=9171: c6084(7534045356......) = 20275047808279783053319 * c6062(3715919897......)

n=10689: c6097(1109999889......) = 28378933424769565681 * x6077(3911351679......)

n=10689: x6077(3911351679......) = 5107066778195380729123 * c6055(7658704788......)

n=12117: c6896(7165165802......) = 99790884232574019787 * c6876(7180180692......)

### July 5, 20102010 年 7 月 5 日 (Kurt Beschorner)

n=6467: c6206(2891497921......) = 40913935672229021968256323 * c6180(7067269071......)

n=6473: c6438(2541307733......) = 12001332370057422792347 * c6416(2117521334......)

n=8305: c5987(4407772737......) = 317651320298238491057791 * c5964(1387613542......)

n=9003: c5996(2501599147......) = 5792204976596170286448187 * c5971(4318906456......)

n=9123: c6043(1264090410......) = 1668837133556452535587 * c6021(7574678107......)

n=9417: c6033(7308906000......) = 60872730592259578504147 * c6011(1200686404......)

n=12115: c9658(1717417956......) = 3453217502373635446231751 * c9633(4973384835......)

n=12340L: c2416(3139562781......) = 17840606029938490276754751093341 * c2385(1759784828......)

### July 2, 20102010 年 7 月 2 日 (Kurt Beschorner)

n=6427: c6422(1728790762......) = 10252910946319410979660877 * c6397(1686146277......)

n=6449: c6424(2176217592......) = 1641354500544414785449 * x6403(1325866893......)

n=6449: x6403(1325866893......) = 16739417885171475752499431 * c6377(7920627243......)

n=7163: c6019(3804476560......) = 61358725457968491906128414927003 * c5987(6200383942......)

n=7495: c5969(9474183138......) = 2674763213597667128727281 * c5945(3542064243......)

n=9213: c5905(1109999999......) = 40370837122694693285553962231209 * c5873(2749509495......)

n=12115: c9683(4643027017......) = 27034927642921838306154001 * c9658(1717417956......)

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