### October 31, 20212021 年 10 月 31 日 (Kurt Beschorner)

n=274301: x274301(1111111111......) = 3851879422687577443 * x274282(2884594737......)

n=274583: x274573(7925068671......) = 120900352917058357 * x274556(6555041801......)

n=274679: x274679(1111111111......) = 120483721806251569 * x274661(9222084896......)

n=274777: x274760(2046805292......) = 123789627686850883 * x274743(1653454599......)

n=274831: x274831(1111111111......) = 515049728169895147 * x274813(2157288996......)

n=274871: x274871(1111111111......) = 14771607848042739791 * x274851(7521937507......)

n=274951: x274927(3496002712......) = 14491370422833073921 * x274908(2412472119......)

n=274993: x274982(3459515805......) = 259693845059197951 * x274965(1332151635......)

n=275039: x275039(1111111111......) = 110455776013660199 * x275022(1005933008......)

n=275131: x275131(1111111111......) = 1566250580971879427 * x275112(7094082674......)

n=275251: x275238(2107171832......) = 12749574876292742561 * x275219(1652738897......)

# gr-mfaktc

# 206844 of 300000 Φn(10) factorizations were cracked. 300000 個中 206844 個の Φn(10) の素因数が見つかりました。

# 19869 of 25997 Rprime factorizations were cracked. 25997 個中 19869 個の Rprime の素因数が見つかりました。

### October 30, 20212021 年 10 月 30 日 (Makoto Kamada)

n=44856: c12628(1273666432......) = 45317048403817 * c12614(2810567937......)

### October 28, 20212021 年 10 月 28 日 (Kurt Beschorner)

n=5002: c2401(1099999999......) = 522346250245015592799109827193626997 * c2365(2105882830......)

# ECM B1=11e6, sigma=0:7715223337182973

n=273061: x273061(1111111111......) = 163178372176225213 * x273043(6809181243......)

n=273073: x273055(1603674373......) = 5399179797132721351 * x273036(2970218503......)

n=273157: x273157(1111111111......) = 403936707494102357 * x273139(2750705965......)

n=273181: x273144(1046009407......) = 2938631864980648523 * x273125(3559511553......)

n=273269: x273252(9482450357......) = 329485867200504277 * x273235(2877953594......)

n=273281: x273281(1111111111......) = 1983156493168103969 * x273262(5602740454......)

n=273313: x273306(6775567655......) = 3445094047802837249 * x273288(1966729372......)

n=273857: x273857(1111111111......) = 2056692014344053311 * x273838(5402418560......)

n=273899: x273883(2215572060......) = 3471448001176655329 * x273864(6382270626......)

n=273899: x273864(6382270626......) = 13222436172540061003 * x273845(4826849260......)

n=273941: x273926(1376064830......) = 262661501043042481 * x273908(5238928527......)

n=274069: x274053(6322715922......) = 399721169562503813 * x274036(1581781602......)

n=274081: x274081(1111111111......) = 1273619675192014079 * x274062(8724041664......)

n=274093: x274075(2519175121......) = 1518923273700025079 * x274057(1658526908......)

# gr-mfaktc

# 206838 of 300000 Φn(10) factorizations were cracked. 300000 個中 206838 個の Φn(10) の素因数が見つかりました。

# 19863 of 25997 Rprime factorizations were cracked. 25997 個中 19863 個の Rprime の素因数が見つかりました。

### October 26, 20212021 年 10 月 26 日 (Kurt Beschorner)

n=40019: c34247(1692252876......) = 61620387150019925819822231 * x34221(2746254859......)

# ECM B1=25e4, sigma=0:7925212246147850

n=40019: x34221(2746254859......) = 66459048737033637939135822043619279 * c34186(4132251231......)

# ECM B1=25e4, sigma=0:3980336408708090

### October 25, 20212021 年 10 月 25 日 (Alfred Eichhorn)

# via Kurt Beschorner

n=97927: c97927(1111111111......) = 4330628433327671445689 * c97905(2565704096......)

# ECM B1=5e4, sigma=2444771095148551

# 206832 of 300000 Φn(10) factorizations were cracked. 300000 個中 206832 個の Φn(10) の素因数が見つかりました。

# 19858 of 25997 Rprime factorizations were cracked. 25997 個中 19858 個の Rprime の素因数が見つかりました。

### October 25, 20212021 年 10 月 25 日 (Kurt Beschorner)

n=299942: c149958(3574050291......) = 83308428885922445773 * x149938(4290142473......)

# ECM B1=5e4, sigma=0:4620972490834684

n=269419: x269382(1567614389......) = 3837362385443044747 * x269363(4085135133......)

n=269623: x269609(9845244839......) = 681453187781247719 * x269592(1444742649......)

n=269701: x269692(1593112380......) = 5579295029130449839 * x269673(2855400856......)

n=269719: x269708(4888586038......) = 2886377680293296911 * x269690(1693675111......)

n=269741: x269741(1111111111......) = 11675297161904717573 * x269721(9516769429......)

n=269987: x269949(5746995605......) = 277121759041303769 * x269932(2073816081......)

n=270143: x270131(8724694746......) = 1894594335335258639 * x270113(4605046359......)

n=270209: x270209(1111111111......) = 1717400393284335049 * x270190(6469726660......)

n=270229: x270212(1005269231......) = 638669513432603843 * x270194(1574005350......)

n=270241: x270241(1111111111......) = 3388439674484420639 * x270222(3279123188......)

n=270337: x270330(1712539872......) = 182404284786229199 * x270312(9388704190......)

n=270443: x270443(1111111111......) = 137810051322210277 * x270425(8062627511......)

n=270539: x270539(1111111111......) = 185842886908151849 * x270521(5978765879......)

n=270563: x270563(1111111111......) = 3593513077600618253 * x270544(3091991282......)

n=270679: x270661(2953152429......) = 14444676718953266363 * x270642(2044457267......)

n=270961: x270961(1111111111......) = 15361056971310340837 * x270941(7233298549......)

n=271097: x271045(3152204625......) = 3972766603758758867 * x271026(7934532632......)

n=271129: x271108(6123223867......) = 1089875032935185467 * x271090(5618280704......)

n=271181: x271173(6208036659......) = 148159834013863481 * x271156(4190094232......)

n=271853: x271847(2043584340......) = 1926532437419318507 * x271829(1060757815......)

n=271867: x271860(4086964223......) = 9328792920686308637 * x271841(4381021486......)

n=271919: x271891(5595165522......) = 10985887740839237267 * x271872(5093048148......)

n=272053: x272039(2311964044......) = 696341486872476043 * x272021(3320158411......)

n=272141: x272141(1111111111......) = 426183958859602157 * x272123(2607116218......)

n=272287: x272280(1133517001......) = 1619530646276307529 * x272261(6999046323......)

n=272477: x272464(2754198484......) = 9274305694214503643 * x272445(2969708542......)

n=272563: x272550(1378746289......) = 227112773475062281 * x272532(6070756253......)

n=272693: x272687(2037289321......) = 87399873105059639 * x272670(2330998031......)

n=272737: x272725(7426181247......) = 826631267715988919 * x272707(8983668459......)

n=272971: x272971(1111111111......) = 4611753488915525159 * x272952(2409302912......)

# gr-mfaktc

# 206831 of 300000 Φn(10) factorizations were cracked. 300000 個中 206831 個の Φn(10) の素因数が見つかりました。

# 19857 of 25997 Rprime factorizations were cracked. 25997 個中 19857 個の Rprime の素因数が見つかりました。

```Largest known factors that appear after the previous one
1  n=604: 188981422179250214477885038956646476812007525220846625175628245017547495717341304519447280552146559165713534073382085460954497219653965265520569 (NFS@Home / Mar 16, 2017)
2  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
3  n=816: 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881 (Yousuke Koide / Apr 5, 2020)
4  n=1540M: 647799461893729229242068652342456021003805852058736425973158141325454469108253161834095467738437014341 (NFS@Home / Sep 18, 2013)
5  n=1740M: 38500497070688096027556817882565728990416892548263819672284096593431517949011701136219584563960572421 (Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner / Jun 27, 2021)
6  n=2340L: 54416219768345058780693800256182138078138198676424989328564702046179663087831396313663972761 (Bo Chen, Wenjie Fang, Maksym Voznyy and Kurt Beschorner / Feb 15, 2016)
7  n=2700M: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201 (Bo Chen, Maksym Voznyy, Wenjie Fang, Alfred Eichhorn and Kurt Beschorner / May 7, 2017)
8  n=2820M: 832530561417330269513686172453574642103980456844602894975421 (Eric_ch / Aug 23, 2016)
9  n=5900M: 593243597135622945022444401922545308692618865123732027101 (pi / Sep 17, 2018)
10  n=13980M: 21166873440679239162423181074773929272724025103001 (Kurt Beschorner / Jul 14, 2011)
11  n=103748: 1941549624124837091592820526305327246593529 (Makoto Kamada / Jun 18, 2018)
12  n=112666: 356334694333381082120764457775238849699 (Makoto Kamada / Oct 17, 2018)
13  n=120833: 79670409416595961896605938971188364397 (Maksym Voznyy / Nov 27, 2015)
14  n=135070: 9855589830288396166509564150666175361 (Makoto Kamada / Dec 6, 2017)
15  n=199700M: 16745944922383579468094190800250901 (Serge Batalov / Jul 6, 2015)
16  n=199900L: 612937240365283738637341628923301 (Serge Batalov / Jul 6, 2015)
17  n=217319: 327136068049348903751880841 (Alfred Reich / Feb 18, 2019)
18  n=299011: 221045463366486747587120747 (Alfred Reich / Feb 18, 2019)
19  n=299807: 1096020580210100960507 (Alfred Reich / Feb 18, 2019)
20  n=299912: 107911061915460883817 (Kurt Beschorner / Oct 11, 2020)
21  n=299942: 83308428885922445773 (Kurt Beschorner / Oct 25, 2021)
22  n=299992: 8045689530757649 (Makoto Kamada / Oct 23, 2021)
23  n=299999: 246755644878443 (Makoto Kamada / Oct 23, 2021)
24  n=300000: 47847600001 (Makoto Kamada / Feb 15, 2019)
```

### October 25, 20212021 年 10 月 25 日 (Makoto Kamada)

n=23193: c15438(7699361484......) = 28676926450027 * c15425(2684862862......)

n=23263: c22675(1758544081......) = 25601477110403 * c22661(6868916485......)

### October 24, 20212021 年 10 月 24 日 (Kurt Beschorner)

n=13051: c12596(1149322538......) = 289792400507496591746951639 * x12569(3966020282......)

# ECM B1=25e4, sigma=0:916112482751869

n=13051: x12569(3966020282......) = 1336449884279254346334474191 * c12542(2967578754......)

# ECM B1=25e4, sigma=0:7320727441128006

n=40019: c34265(7554920600......) = 4464415870915646717 * c34247(1692252876......)

# ECM B1=25e4, sigma=0:4019875591801662

### October 24, 20212021 年 10 月 24 日 (Makoto Kamada)

n=23925: c11179(1109381809......) = 68681194274551 * c11165(1615262841......)

### October 23, 20212021 年 10 月 23 日 (Makoto Kamada)

n=48456: c16122(7643430891......) = 62750806229593 * c16109(1218060986......)

n=24237: c16131(2170162196......) = 92029029738643 * c16117(2358127867......)

n=48504: c15445(3294644493......) = 65666215380217 * c15431(5017259597......)

n=48586: c22828(6069879193......) = 78947487163007 * c22814(7688502080......)

n=49928: c24648(9999999999......) = 89065254930857 * c24635(1122772287......)

n=299923: x276830(2486468958......) = 2534005535068489 * x276814(9812405394......)

n=149960: c57024(9999000099......) = 3523451171697521 * c57009(2837842675......)

n=299926: c136321(1099999999......) = 1950527513172041 * x136305(5639500045......)

n=149963: c136320(9000000000......) = 3629653154156591 * x136305(2479575766......)

n=299928: c99943(4657792387......) = 794179035075889 * c99928(5864914814......)

n=299962: c135782(6779453554......) = 3450437016677197 * x135767(1964810115......)

n=299960: c119969(1000099999......) = 4802266301641441 * x119953(2082558394......)

n=299964: c85660(8346463820......) = 210020864571589 * c85646(3974111732......)

n=149986: c70996(3068742277......) = 2133869360269601 * c70981(1438111598......)

n=299974: c148668(2461436749......) = 336489058687289 * x148653(7315057312......)

n=299992: c116618(5119339382......) = 8045689530757649 * x116602(6362834860......)

n=299999: x241899(2519629081......) = 246755644878443 * x241885(1021102914......)

# 206822 of 300000 Φn(10) factorizations were cracked. 300000 個中 206822 個の Φn(10) の素因数が見つかりました。

```Largest known factors that appear after the previous one
1  n=604: 188981422179250214477885038956646476812007525220846625175628245017547495717341304519447280552146559165713534073382085460954497219653965265520569 (NFS@Home / Mar 16, 2017)
2  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
3  n=816: 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881 (Yousuke Koide / Apr 5, 2020)
4  n=1540M: 647799461893729229242068652342456021003805852058736425973158141325454469108253161834095467738437014341 (NFS@Home / Sep 18, 2013)
5  n=1740M: 38500497070688096027556817882565728990416892548263819672284096593431517949011701136219584563960572421 (Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner / Jun 27, 2021)
6  n=2340L: 54416219768345058780693800256182138078138198676424989328564702046179663087831396313663972761 (Bo Chen, Wenjie Fang, Maksym Voznyy and Kurt Beschorner / Feb 15, 2016)
7  n=2700M: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201 (Bo Chen, Maksym Voznyy, Wenjie Fang, Alfred Eichhorn and Kurt Beschorner / May 7, 2017)
8  n=2820M: 832530561417330269513686172453574642103980456844602894975421 (Eric_ch / Aug 23, 2016)
9  n=5900M: 593243597135622945022444401922545308692618865123732027101 (pi / Sep 17, 2018)
10  n=13980M: 21166873440679239162423181074773929272724025103001 (Kurt Beschorner / Jul 14, 2011)
11  n=103748: 1941549624124837091592820526305327246593529 (Makoto Kamada / Jun 18, 2018)
12  n=112666: 356334694333381082120764457775238849699 (Makoto Kamada / Oct 17, 2018)
13  n=120833: 79670409416595961896605938971188364397 (Maksym Voznyy / Nov 27, 2015)
14  n=135070: 9855589830288396166509564150666175361 (Makoto Kamada / Dec 6, 2017)
15  n=199700M: 16745944922383579468094190800250901 (Serge Batalov / Jul 6, 2015)
16  n=199900L: 612937240365283738637341628923301 (Serge Batalov / Jul 6, 2015)
17  n=217319: 327136068049348903751880841 (Alfred Reich / Feb 18, 2019)
18  n=299011: 221045463366486747587120747 (Alfred Reich / Feb 18, 2019)
19  n=299807: 1096020580210100960507 (Alfred Reich / Feb 18, 2019)
20  n=299912: 107911061915460883817 (Kurt Beschorner / Oct 11, 2020)
21  n=299941: 476143900733778479 (Alfred Reich / Feb 18, 2019)
22  n=299992: 8045689530757649 (Makoto Kamada / Oct 23, 2021)
23  n=299999: 246755644878443 (Makoto Kamada / Oct 23, 2021)
24  n=300000: 47847600001 (Makoto Kamada / Feb 15, 2019)
```

### October 22, 20212021 年 10 月 22 日 (Makoto Kamada)

n=25653: c16060(2163447482......) = 58126879094443 * c16046(3721939860......)

n=25715: c19868(2160370204......) = 67704433752191 * c19854(3190884385......)

n=26059: c22433(8199669899......) = 69288853557683 * c22420(1183403892......)

### October 18, 20212021 年 10 月 18 日 (Yousuke Koide)

n=846: c249(2433960276......) = 8147270298945964118744634040617462692098679807835492529 * p194(2987454923......)

# SNFS

# 1195 of 300000 Φn(10) factorizations were finished. 300000 個中 1195 個の Φn(10) の素因数分解が終わりました。

### October 18, 20212021 年 10 月 18 日 (Makoto Kamada)

n=29469: c16551(1801502621......) = 73039692772399 * c16537(2466470699......)

n=29477: c25260(9000000900......) = 70219350485159 * c25247(1281698112......)

# 206817 of 300000 Φn(10) factorizations were cracked. 300000 個中 206817 個の Φn(10) の素因数が見つかりました。

### October 17, 20212021 年 10 月 17 日 (Makoto Kamada)

n=30531: c20352(9009009009......) = 62095945931827 * c20339(1450820802......)

n=30605: c24461(1338636743......) = 94167239028791 * c24447(1421552502......)

n=30987: c18721(1001000999......) = 78155872424587 * c18707(1280775159......)

# 206816 of 300000 Φn(10) factorizations were cracked. 300000 個中 206816 個の Φn(10) の素因数が見つかりました。

### October 13, 20212021 年 10 月 13 日 (Kurt Beschorner)

n=267227: x267227(1111111111......) = 5802699966039622757 * x267208(1914817442......)

n=267497: x267480(4016066625......) = 75110974071743443 * x267463(5346844020......)

n=267647: x267619(6398420592......) = 6591528654040759453 * x267600(9707035997......)

n=267677: x267677(1111111111......) = 1272126774560122973 * x267658(8734279737......)

n=267763: x267740(2600961558......) = 5795140650529128809 * x267721(4488176759......)

n=267811: x267795(5998975916......) = 2051527349761559963 * x267777(2924151080......)

n=267893: x267884(9299535625......) = 176993151402036511 * x267867(5254178227......)

n=268013: x268013(1111111111......) = 11125077469663849283 * x267993(9987446057......)

n=268123: x268123(1111111111......) = 196858632027395321 * x268105(5644208230......)

n=268237: x268212(1596912410......) = 107502744926918951 * x268195(1485461986......)

n=268271: x268238(2626866423......) = 1627397530950607111 * x268220(1614151658......)

n=268487: x268487(1111111111......) = 14908781637327253009 * x268467(7452729123......)

n=268519: x268519(1111111111......) = 941578665312035329 * x268501(1180051282......)

n=268607: x268597(7626415857......) = 2292233533421438521 * x268579(3327067572......)

n=268613: x268588(1322165179......) = 5792304796588693853 * x268569(2282623629......)

n=268643: x268610(7797805424......) = 1087082814733148329 * x268592(7173147545......)

n=268729: x268684(3099542495......) = 1495003159231853881 * x268666(2073268191......)

n=268841: x268841(1111111111......) = 3779903927160364093 * x268822(2939522095......)

n=268937: x268923(2514337609......) = 100367602797034733 * x268906(2505128686......)

n=268979: x268970(6074775053......) = 900899209332127963 * x268952(6743012970......)

n=269117: x269100(5925596253......) = 178225823410173031 * x269083(3324768622......)

# gr-mfaktc

# 206814 of 300000 Φn(10) factorizations were cracked. 300000 個中 206814 個の Φn(10) の素因数が見つかりました。

# 19848 of 25997 Rprime factorizations were cracked. 25997 個中 19848 個の Rprime の素因数が見つかりました。

### October 11, 20212021 年 10 月 11 日 (Alfred Eichhorn)

# via Kurt Beschorner

n=42943: c42943(1111111111......) = 12040267178027196292637 * c42920(9228292816......)

# ECM B1=5e4, sigma=3097410500777759

n=61091: c61091(1111111111......) = 22591912851401440910039 * c61068(4918180759......)

# ECM B1=5e4, sigma=2067528895893704

n=97787: c97787(1111111111......) = 1755655860865731936416422009 * c97759(6328752324......)

# ECM B1=5e4, sigma=7614901593777729

# 206807 of 300000 Φn(10) factorizations were cracked. 300000 個中 206807 個の Φn(10) の素因数が見つかりました。

# 19841 of 25997 Rprime factorizations were cracked. 25997 個中 19841 個の Rprime の素因数が見つかりました。

### October 7, 20212021 年 10 月 7 日 (Kurt Beschorner)

n=264791: x264784(6993631529......) = 251458761234405001 * x264767(2781224044......)

n=264931: x264924(3494969009......) = 86117538170944363 * x264907(4058370784......)

n=264931: x264907(4058370784......) = 2087554989301673401 * x264889(1944078505......)

n=265021: x265006(3947092608......) = 9715832824398626587 * x264987(4062536562......)

n=265273: x265259(2450145305......) = 554723902290299681 * x265241(4416873502......)

n=265399: x265388(1958536941......) = 962467233355684267 * x265370(2034912851......)

n=265451: x265451(1111111111......) = 3085748498439365173 * x265432(3600783121......)

n=265459: x265446(3066236766......) = 9315853036831073479 * x265427(3291418138......)

n=265807: x265807(1111111111......) = 11956857517308323881 * x265787(9292668324......)

n=265873: x265849(2514632300......) = 124022916936114563 * x265832(2027554554......)

n=265873: x265832(2027554554......) = 5623725838371026801 * x265813(3605358106......)

n=266047: x266031(3255738872......) = 7088188830646864013 * x266012(4593188684......)

n=266293: x266266(1135722749......) = 195734817274382761 * x266248(5802354254......)

n=266411: x266376(1302544355......) = 8987281812303016921 * x266357(1449319585......)

n=266587: x266580(6946515374......) = 1153223175691599839 * x266562(6023565534......)

n=266603: x266581(5460265156......) = 3755034721566797957 * x266563(1454118420......)

n=266641: x266641(1111111111......) = 539030633745274523 * x266623(2061313479......)

n=266681: x266652(4483226888......) = 2527803409042646521 * x266634(1773566279......)

n=266719: x266719(1111111111......) = 3098749672732718843 * x266700(3585675606......)

n=266759: x266747(1584169224......) = 1451633476156381351 * x266729(1091301110......)

n=266897: x266880(5359386290......) = 1525828751668404839 * x266862(3512442851......)

n=267017: x267009(1168876361......) = 3943279215994780253 * x266990(2964224183......)

n=267049: x267035(1901280434......) = 626738994607284907 * x267017(3033608009......)

# gr-mfaktc

# 206804 of 300000 Φn(10) factorizations were cracked. 300000 個中 206804 個の Φn(10) の素因数が見つかりました。

# 19838 of 25997 Rprime factorizations were cracked. 25997 個中 19838 個の Rprime の素因数が見つかりました。

### October 1, 20212021 年 10 月 1 日 (Kurt Beschorner)

n=12017: c11735(4490661143......) = 4242772710733294354040968914239 * c11705(1058426045......)

# ECM B1=1e6, sigma=0:130400900789959

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