December 31, 20102010 年 12 月 31 日 (Kurt Beschorner)

n=8353: c8321(6553452235......) = 61243575241198328324911 * c8299(1070063628......)

n=8357: c8160(9000000000......) = 10301783319460670666801 * c8138(8736351484......)

n=8363: c8348(4333235597......) = 146396966168913117523 * c8328(2959921719......)

n=8767: c7941(1476079334......) = 3636198065623702718701013 * c7916(4059403001......)

n=8833: c7890(9122532678......) = 23553954540637952953669093 * c7865(3873036547......)

December 31, 20102010 年 12 月 31 日 (Serge Batalov)

n=2358: c771(4172295560......) = 292987356406918272425934690293373859 * c736(1424053109......)

# The ratio of factored part of 10^35371-11 was raised from 3.89% to 3.99%.

# The ratio of factored part of (31*10^4717-301)/9 was raised from 25.02% to 25.77%.

# The ratio of factored part of (28*10^4716-19)/9 was raised from 25.01% to 25.76%.

December 31, 20102010 年 12 月 31 日 (Makoto Kamada)

n=64402: c29693(7333779534......) = 7940845428049 * c29680(9235514783......)

n=64425: c34321(1000010000......) = 8953385389951 * c34308(1116907132......)

n=64426: c32212(9090909090......) = 9872022201383 * c32199(9208760784......)

n=64457: c62916(9000000000......) = 7747194473191 * c62904(1161710865......)

n=64468: c31631(2055725934......) = 5252714742949 * c31618(3913644724......)

n=32239: c31824(9000000000......) = 5743114392893 * c31812(1567093981......)

n=64541: c64027(6972258159......) = 9479897995637 * c64014(7354781836......)

n=64548: c19440(9999990000......) = 5074263835741 * c19428(1970727247......)

n=64551: c43026(2406278757......) = 7660142973877 * c43013(3141297447......)

n=64649: c59658(2245375088......) = 5023130455799 * c59645(4470071220......)

n=64671: c43112(9009009009......) = 6049276836751 * c43100(1489270412......)

n=64775: c51800(9999900000......) = 7474817356001 * c51788(1337811952......)

n=64787: c58732(1288879925......) = 8754500677837 * c58719(1472248359......)

December 30, 20102010 年 12 月 30 日 (Paul Bourdelais)

n=27011: c27011(1111111111......) = 11363611605025609 * c26994(9777799081......)

n=28057: c28057(1111111111......) = 51511588127323067 * c28040(2157011949......)

n=29803: c29803(1111111111......) = 32698097993089363 * c29786(3398090957......)

n=30713: c30713(1111111111......) = 867130155995963 * c30698(1281366013......)

n=32621: c32621(1111111111......) = 6358730359818121 * c32605(1747378876......)

n=33629: c33629(1111111111......) = 405643362120904679 * c33611(2739132979......)

n=35267: c35267(1111111111......) = 23464280579455969176827 * c35244(4735329972......)

n=36109: c36109(1111111111......) = 241729792334338601 * c36091(4596500499......)

n=54787: c54787(1111111111......) = 1223178488474717 * c54771(9083801927......)

n=55843: c55843(1111111111......) = 722463983867477 * c55828(1537946715......)

n=56999: c56999(1111111111......) = 614498038047529 * c56984(1808160551......)

n=58613: c58613(1111111111......) = 1958687018690107 * c58597(5672734339......)

n=59627: c59627(1111111111......) = 121971964668365479 * c59609(9109561481......)

n=75377: c75377(1111111111......) = 6894764854720387 * c75361(1611528651......)

n=80153: c80153(1111111111......) = 345812539713239 * c80138(3213044593......)

n=80239: c80239(1111111111......) = 5031542566434599 * c80223(2208291187......)

n=90149: c90149(1111111111......) = 1221465905607209 * c90133(9096538069......)

n=91969: c91969(1111111111......) = 69503145608240212877 * c91949(1598648667......)

# The number of blank factorizations of the form Phi_n(10) (n<=100000) became less than 30000.

# The number of blank factorizations of the form R_n (n<=100000) is 2531.

December 30, 20102010 年 12 月 30 日 (Makoto Kamada)

n=63729: c41454(2250085192......) = 9978777442639 * c41441(2254870604......)

n=63815: c51030(5127162283......) = 6790805836361 * c51017(7550152967......)

n=31945: c25518(9706128215......) = 9397920250361 * c25506(1032795337......)

n=63897: c39647(2722224124......) = 6315000828769 * c39634(4310726471......)

n=63911: c63024(9000000000......) = 9750165015281 * c63011(9230613005......)

n=63912: c21297(1000099999......) = 8065283445841 * c21284(1240006016......)

n=63937: c60160(9000000000......) = 6209432159387 * c60148(1449407895......)

n=63949: c63935(8086310453......) = 9834948844871 * c63922(8222015773......)

n=63957: c42616(2875789215......) = 5188525951369 * c42603(5542593875......)

n=63995: c51192(9000090000......) = 5293270654921 * c51180(1700289024......)

n=64001: c53270(1109714397......) = 7569157626241 * c53257(1466100261......)

n=64044: c21291(2245907732......) = 8968686023449 * c21278(2504165857......)

n=64080: c16879(1326010905......) = 5020645443841 * c16866(2641116406......)

n=64083: c41588(2731128030......) = 6392641318951 * c41575(4272299812......)

n=64112: c32038(2932538647......) = 7494313321073 * c32025(3913018474......)

n=64145: c51312(9000090000......) = 6967947036991 * c51300(1291641562......)

n=64190: c21840(9999999000......) = 7306901691811 * c21828(1368568980......)

n=64287: c42835(1555522023......) = 7545159085879 * c42822(2061615939......)

n=64293: c41290(1327182119......) = 7088725397839 * c41277(1872243661......)

n=64302: c18350(1692941096......) = 9106458242281 * c18337(1859055465......)

n=64313: c63338(1531719100......) = 9693764333083 * c63325(1580107631......)

December 29, 20102010 年 12 月 29 日 (Makoto Kamada)

n=62637: c41737(2962218841......) = 8684018734801 * c41724(3411115213......)

n=62694: c20391(6865564864......) = 5213100141001 * c20379(1316983115......)

n=20907: c13157(1367272660......) = 5391220309507 * c13144(2536109789......)

n=62723: c62713(3616252026......) = 9487593881401 * c62700(3811558622......)

n=62741: c53772(9000000900......) = 7877032164401 * c53760(1142562415......)

n=62793: c41837(1001550378......) = 5750947516159 * c41824(1741539764......)

n=62911: c61672(9000000000......) = 8886440837227 * c61660(1012778925......)

n=62931: c38110(5769866282......) = 6043904693443 * c38097(9546587140......)

n=63027: c40849(1001000999......) = 7515814955689 * c40836(1331859560......)

n=63037: c58032(9999999999......) = 9869848327249 * c58020(1013186795......)

n=63083: c62568(9000000000......) = 7830629301613 * c62556(1149332914......)

n=63175: c41026(2791425019......) = 6276050629801 * c41013(4447741396......)

n=63354: c21110(1788186296......) = 6119419498477 * c21097(2922150209......)

n=63411: c40380(1554353967......) = 5571085008361 * c40367(2790038144......)

n=63430: c25369(1099989000......) = 9811126525771 * c25356(1121164829......)

n=63486: c21152(1576700740......) = 9422901169849 * c21139(1673264647......)

n=63503: c54994(2822093822......) = 8596054129609 * c54981(3283010762......)

December 28, 20102010 年 12 月 28 日 (Makoto Kamada)

n=61577: c60979(2977358325......) = 8938778160173 * c60966(3330833669......)

n=61615: c49288(9000090000......) = 7386490489321 * c49276(1218452797......)

n=61673: c61663(3411765273......) = 5776019475227 * c61650(5906775917......)

n=61685: c44921(3129613147......) = 8789116657361 * c44908(3560782351......)

n=61697: c60988(1002847459......) = 6777078460987 * c60975(1479763684......)

n=61738: c30857(1220974985......) = 5285620277527 * c30844(2309993758......)

n=61755: c31323(1823552923......) = 5472843334831 * c31310(3332002785......)

n=61776: c17280(9999999999......) = 5670151549921 * c17268(1763621291......)

n=61885: c49478(9034870654......) = 6047040172751 * c49466(1494098004......)

n=61925: c49520(9999900000......) = 5451551522201 * c49508(1834321836......)

n=61926: c20623(5377584482......) = 9990898152007 * c20610(5382483537......)

n=61937: c61425(6602714212......) = 7604904195871 * c61412(8682179344......)

n=61949: c61936(8486257626......) = 9509959491281 * c61923(8923547607......)

n=61957: c51782(6576063572......) = 8858428467281 * c51769(7423510385......)

n=61970: c24779(3550057931......) = 7601760252241 * c24766(4670047217......)

n=62051: c56400(9000000000......) = 8501689913729 * c56388(1058613062......)

n=62088: c18999(7326916022......) = 8676943906801 * c18986(8444120534......)

n=31067: c30360(9000000000......) = 6040590433841 * c30348(1489920579......)

n=62142: c20701(1772920656......) = 6724612949011 * c20688(2636464982......)

n=62172: c18715(1787151795......) = 6476180574601 * c18702(2759576844......)

n=31111: c30447(1602851790......) = 9572647189631 * c30434(1674408090......)

n=62230: c21162(1487908879......) = 6696253362611 * c21149(2222002063......)

n=62253: c41488(3187806787......) = 7704703450117 * c41475(4137481484......)

n=62276: c31129(5823649699......) = 5885344057409 * c31116(9895172894......)

n=62333: c61500(9000000000......) = 8046509748307 * c61488(1118497371......)

n=62440: c21312(9999000099......) = 5110630954801 * c21300(1956509908......)

n=62453: c58814(2136522682......) = 7188322188631 * c58801(2972213301......)

n=62482: c26759(4691344083......) = 6802879331333 * c26746(6896115387......)

n=62541: c41688(9990000009......) = 5613214604797 * c41676(1779728856......)

n=62584: c31288(9999000099......) = 9563289685009 * c31276(1045560725......)

December 27, 20102010 年 12 月 27 日 (Kurt Beschorner)

n=8311: c8304(6366264299......) = 8957474616212633094529483 * c8279(7107208864......)

n=11637: c7727(5231399450......) = 23121545609825167890547 * c7705(2262564769......)

n=11709: c7790(2178772433......) = 4540317443753219479693 * c7768(4798722689......)

n=12175: c9713(6376917470......) = 17707660494510553601 * x9694(3601219637......)

n=12175: x9694(3601219637......) = 259370447596066366601 * x9674(1388446398......)

n=12175: x9674(1388446398......) = 687240594278593687201 * x9653(2020320699......)

n=12175: x9653(2020320699......) = 764319180237746158678001 * c9629(2643294518......)

December 27, 20102010 年 12 月 27 日 (Makoto Kamada)

n=60880: c24321(1000000009......) = 7521796325441 * c24308(1329469672......)

n=60931: c54408(2349523870......) = 9998056408133 * c54395(2349980611......)

n=60977: c50401(1111110999......) = 6735242218559 * c50388(1649697165......)

n=60989: c60060(9000000000......) = 6136278206453 * c60048(1466687085......)

n=61133: c60475(7360939583......) = 8972510094827 * c60462(8203879968......)

n=61152: c16124(1635242751......) = 7308822463489 * c16111(2237354594......)

n=61208: c26209(1000099999......) = 8435733506537 * c26196(1185551913......)

n=61214: c30241(1099999999......) = 6724102453979 * c30228(1635906067......)

n=61254: c19680(9990010000......) = 8291308056571 * c19668(1204877436......)

n=61266: c20421(1098901098......) = 9219560892379 * c20408(1191923467......)

n=61309: c59616(9000000000......) = 6417357228769 * c59604(1402446471......)

n=61310: c24521(1099989000......) = 5064447990571 * c24508(2171982024......)

n=61411: c50761(1111110999......) = 5178370929803 * c50748(2145676729......)

n=61419: c40111(5755653500......) = 9335894490679 * c40098(6165079849......)

n=61426: c30712(9090909090......) = 6983082559823 * c30700(1301847574......)

n=61467: c35113(1109999889......) = 7193170511773 * c35100(1543130233......)

December 26, 20102010 年 12 月 26 日 (Makoto Kamada)

n=60032: c25328(7045021864......) = 6384123691009 * c25316(1103522144......)

n=60145: c45915(9922469557......) = 8765775766961 * c45903(1131955667......)

n=60160: c23547(1385193116......) = 9971803594241 * c23534(1389109907......)

n=60219: c40140(9990000009......) = 8388359765641 * c40128(1190936045......)

n=60243: c39145(1109999999......) = 5679369185107 * c39132(1954442410......)

n=60286: c29392(5467892997......) = 7475143278481 * c29379(7314766812......)

n=60330: c16054(7271902699......) = 7921523745241 * c16041(9179929181......)

n=60482: c30240(9090909090......) = 5868082063757 * c30228(1549213012......)

n=60507: c39852(9999999999......) = 7037181683173 * c39840(1421023422......)

n=60554: c26104(1381766779......) = 8896189179281 * c26091(1553212000......)

n=60560: c24183(1276519813......) = 5092378485121 * c24170(2506726114......)

n=60564: c17115(6961210699......) = 7033701403009 * c17102(9896938042......)

n=60650: c24241(1000009999......) = 7233807984001 * c24228(1382411590......)

n=60659: c60635(6474648525......) = 7107161960653 * c60622(9110033740......)

n=60712: c30333(5086613748......) = 6540967842529 * c30320(7776546026......)

n=60726: c19488(9100000000......) = 5930904502093 * c19476(1534335951......)

n=60769: c59796(9000000000......) = 7645594490603 * c59784(1177148488......)

n=60781: c49249(1111110999......) = 7051699661399 * c49236(1575664099......)

n=60854: c30416(1175148322......) = 7491489724717 * c30403(1568644375......)

December 25, 20102010 年 12 月 25 日 (nenym)

n=1044: c269(1791140799......) = 60567370378102931159842571650342558304322238516849 * p219(2957270207......)

# Phi_1044(10) is the 1012th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

December 25, 20102010 年 12 月 25 日 (Kurt Beschorner)

n=8297: c8280(1933020564......) = 273988155723828497204117 * c8256(7055124553......)

n=10615: c7650(9417257688......) = 614816080936168759231 * c7630(1531719481......)

n=11691: c7748(2720701979......) = 7811277347637107051329 * c7726(3483043627......)

December 25, 20102010 年 12 月 25 日 (Makoto Kamada)

n=78686: c39342(9090909090......) = 8255220670933 * c39330(1101231505......)

n=78702: c24192(9100000000......) = 6618633653503 * c24180(1374906132......)

n=78704: c39344(9999999900......) = 7798857198257 * c39332(1282239133......)

n=78743: c67452(9999999000......) = 7054739706281 * c67440(1417486599......)

n=78995: c51834(1726248338......) = 6498715948831 * c51821(2656291415......)

n=79056: c25911(1838288225......) = 5051191256929 * c25898(3639316217......)

n=79072: c33769(3857046446......) = 7868719927489 * c33756(4901745749......)

n=79104: c26100(3116489850......) = 5031501126913 * c26087(6193956380......)

n=26373: c17164(2104385083......) = 6302132008723 * c17151(3339163763......)

n=79148: c38623(1191919571......) = 5114950264129 * c38610(2330266199......)

n=79173: c49889(8209877054......) = 5837021191009 * c49877(1406518288......)

n=26425: c17980(1185938668......) = 8117921086801 * c17967(1460889624......)

n=79320: c21104(2242166015......) = 5586656087041 * c21091(4013431255......)

n=39665: c31703(2889223641......) = 8651425410791 * c31690(3339592614......)

n=79407: c49520(1787056624......) = 5002266198961 * c49507(3572494051......)

n=39719: c39711(3614250168......) = 5437370635241 * c39698(6647055003......)

n=79482: c24432(9100000000......) = 5476903451059 * c24420(1661522807......)

n=39759: c25522(2798661151......) = 5726433504991 * c25509(4887267352......)

n=79563: c48194(9965139965......) = 7573841454631 * c48182(1315731260......)

n=79608: c25429(7546091398......) = 6410003202289 * c25417(1177236759......)

n=79704: c25909(5821430067......) = 6897336997897 * c25896(8440112567......)

n=79715: c62747(6969159071......) = 7891915094881 * c62734(8830757792......)

n=79736: c39864(9999000099......) = 9597633983569 * c39852(1041819277......)

n=26587: c24154(1226490059......) = 5002453269397 * c24141(2451777144......)

n=79779: c43675(2823105603......) = 6736627474249 * c43662(4190680892......)

n=79786: c33120(9090910000......) = 5311255484291 * c33108(1711631087......)

n=79839: c53193(1040944428......) = 6100318511929 * c53180(1706377177......)

December 24, 20102010 年 12 月 24 日 (Kurt Beschorner)

n=9013: c8989(1867975751......) = 48698318398497200595711517 * c8963(3835811611......)

n=9575: c7600(1433077660......) = 3041590641237064252151 * c7578(4711605964......)

n=9865: c7873(3730592669......) = 82716644835165934729673321 * c7847(4510087029......)

n=12172: c5697(1009999999......) = 1865052270445253610151129 * c5672(5415397820......)

December 24, 20102010 年 12 月 24 日 (Makoto Kamada)

n=78134: c33470(3313229680......) = 7580135240371 * c33457(4370937423......)

n=78143: c72120(9000000000......) = 9980576026279 * c72107(9017515598......)

n=78201: c52122(3548546715......) = 6823719788329 * c52109(5200311304......)

n=78293: c76897(1268452588......) = 6966170722037 * c76884(1820874967......)

n=78331: c71192(9574753188......) = 6182554443319 * c71180(1548672684......)

n=78395: c62703(1759292448......) = 7566437671801 * c62690(2325126466......)

n=78411: c51273(1109999999......) = 8814668383243 * c51260(1259264616......)

n=78442: c30948(3749568490......) = 9746685908779 * c30935(3847018899......)

n=78490: c30544(9091000000......) = 6693798308201 * c30532(1358122784......)

n=39280: c15672(2321561979......) = 9110163185441 * c15659(2548320960......)

n=78614: c37553(8475337275......) = 7090195795247 * c37541(1195360117......)

December 23, 20102010 年 12 月 23 日 (Serge Batalov)

n=30097: c30097(1111111111......) = 22215398451255312323717 * c30074(5001535820......)

# 2549 of 9592 R_prime factorizations are still blank.

December 23, 20102010 年 12 月 23 日 (Makoto Kamada)

n=78082: c39040(9090909090......) = 5358474305927 * c39028(1696548041......)

n=78093: c52046(3839336781......) = 8417706944401 * c52033(4561024524......)

December 20, 20102010 年 12 月 20 日 (Serge Batalov)

n=36375: c19190(1731772839......) = 29812840293001 * c19176(5808815338......)

n=38505: c19186(1550419798......) = 205279712249041 * c19171(7552718098......)

n=33537: c19142(9994072389......) = 14050306027801 * c19129(7113063850......)

n=38264: c19128(9999000099......) = 410086512095211995206055441 * c19102(2438266025......)

n=35925: c19121(1000010000......) = 298932443469601 * c19106(3345270886......)

n=34647: c23078(6921037041......) = 88273559599562107 * c23061(7840441772......)

n=40509: c23081(6292912282......) = 12055272350161321 * c23065(5220049866......)

n=35313: c23082(3655020104......) = 214370636138813923 * c23065(1705000353......)

n=34653: c23089(1722714121......) = 330402682104403 * c23074(5213983464......)

n=34677: c23105(5276322158......) = 360188567824588093 * c23088(1464877741......)

n=36651: c23113(1109999999......) = 2016746605678933 * c23097(5503914060......)

n=34737: c23135(3540853015......) = 210248098315147 * c23121(1684130816......)

n=40551: c23138(6036222402......) = 19150192313071 * c23125(3152042707......)

n=34803: c23166(2404224275......) = 204441669589425481 * c23149(1175995226......)

n=34767: c23167(2873406182......) = 4519584182607643 * c23151(6357678199......)

n=37355: c28801(1111099999......) = 25173207867881 * x28787(4413819668......)

n=37355: x28787(4413819668......) = 977896746679661201 * c28769(4513584571......)

n=33719: c28882(1734176671......) = 11346956874809711 * c28866(1528318729......)

n=35119: c28897(1111110999......) = 22873134008159 * c28883(4857712107......)

n=37349: c32436(3111422899......) = 122784793876369 * c32422(2534045789......)

n=32849: c32436(9000000000......) = 1534287023602520274721 * c32415(5865916781......)

n=32443: c32435(3280469260......) = 493634286330401 * c32420(6645545803......)

n=33239: c32424(9000000000......) = 18570324020659093 * c32408(4846442092......)

n=35929: c32401(1111111111......) = 249502957420185107 * c32383(4453298360......)

n=38159: c34680(9000000000......) = 3311409613105903453 * c34662(2717875784......)

n=35341: c34684(9000000000......) = 239971343898271 * c34670(3750447805......)

n=34729: c34712(1370675568......) = 2031832972945331797 * x34693(6746005141......)

n=34729: x34693(6746005141......) = 1227209385492218058071 * c34672(5497028641......)

n=41299: c41287(5416115876......) = 10054332238804493 * c41271(5386847925......)

n=41807: c41262(2003322490......) = 18838880989157039 * c41246(1063397816......)

December 19, 20102010 年 12 月 19 日 (Alfred Reich)

n=47380M: c8972(5901310652......) = 13055005269941 * c8959(4520343370......)

n=49620M: c6602(2683481372......) = 94211350366381 * c6588(2848363135......)

n=62300M: c10543(6714858455......) = 74420208074801 * c10529(9022896641......)

n=96020L: c19195(1960743622......) = 15834972089381 * c19182(1238236235......)

n=28540L: c5686(3433651098......) = 329464206767581 * c5672(1042192453......)

n=50580L: c6709(3102616692......) = 682752399708781 * c6694(4544277975......)

n=89460M: c10057(6740914891......) = 423850319596621 * c10043(1590399860......)

n=25060M: c4239(3985991803......) = 1304941222619161 * c4224(3054537426......)

n=38460M: c5092(7564017364......) = 6386199901785601 * c5077(1184431662......)

n=53420L: c10672(3762114835......) = 3533393677655761 * c10657(1064731297......)

n=65060M: c12977(5847072617......) = 5691262037332681 * c12962(1027377158......)

n=66140L: c13203(6880840986......) = 3259802171715581 * c13188(2110815510......)

n=66620M: c13310(1838854885......) = 1304661412412741 * c13295(1409449890......)

n=70140M: c7934(1218801102......) = 9186799271513641 * c7918(1326687420......)

n=70780M: c14153(2824060999......) = 1375203821623081 * c14138(2053558138......)

n=25900L: c4298(2207239319......) = 13704618377807701 * c4282(1610580651......)

n=35020L: c6501(4755300180......) = 34735132429846201 * c6485(1369017432......)

n=53900L: c8371(5192030720......) = 94859796036135901 * c8354(5473373270......)

n=65780L: c10544(2137641006......) = 16646138387361341 * c10528(1284166307......)

n=75540L: c10048(1083717341......) = 98276218336825381 * c10031(1102725929......)

n=76780L: c13873(1216107457......) = 18633578554263641 * c13856(6526429980......)

n=82300M: c16390(3769493491......) = 36180129507952901 * c16374(1041868435......)

n=83420M: c16106(3169953587......) = 40829912182583921 * c16089(7763802118......)

n=96540L: c12864(3913542626......) = 16304172726130501 * c12848(2400331922......)

n=34140M: c4510(1008255956......) = 704609659465764121 * c4492(1430942569......)

n=47340M: c6272(5326120328......) = 113163714435027961 * c6255(4706561953......)

n=47660M: c9510(2104543788......) = 159754725756938581 * c9493(1317359332......)

n=50420M: c10061(2199758757......) = 149485916587362181 * x10044(1471549165......)

n=55100M: c10047(1106905398......) = 675078533730687601 * c10029(1639669080......)

n=58220M: c11184(3808695766......) = 807749610900210761 * c11166(4715193563......)

n=76740M: c10225(2529932837......) = 374248578463840141 * c10207(6760033257......)

n=81620L: c12474(5247737515......) = 165892225183326181 * c12457(3163341446......)

n=96900L: c11521(1010050099......) = 170101606910205301 * c11503(5937922152......)

n=33500L: c6561(7286766254......) = 8438452815784435501 * c6542(8635192272......)

n=45340L: c9060(1557149001......) = 4363691029782646241 * c9041(3568421756......)

n=46780L: c9332(2489908460......) = 1522924039734213461 * c9314(1634952496......)

n=50540L: c8198(3574994553......) = 3764244590169412861 * c8179(9497242986......)

n=60700L: c12102(1328700262......) = 6374432607943917301 * c12083(2084421225......)

n=61980L: c8233(2357380752......) = 3804767165691055321 * c8214(6195860746......)

n=63100M: c12575(9396055875......) = 2264167294052821301 * c12557(4149894709......)

n=66300L: c7673(2765347947......) = 1054402420742704801 * c7655(2622668435......)

n=72220L: c13729(2796100000......) = 9020135104369957241 * c13710(3099842704......)

n=82620M: c10368(9999999999......) = 1784763975164554081 * c10350(5602981760......)

n=84940L: c16305(8998434764......) = 2978377392702548381 * c16287(3021254051......)

n=87060M: c11600(3913542626......) = 6686537838202932781 * c11581(5852868437......)

n=92940L: c12385(2529932837......) = 8579511591223852861 * c12366(2948807528......)

n=95380L: c18000(3540999996......) = 1303206075879300401 * c17982(2717145094......)

n=37220M: c7424(3261152401......) = 35292813744923405401 * c7404(9240273175......)

n=46020M: c5553(1944492799......) = 24182504416909957561 * c5533(8040907448......)

n=47140L: c9414(2390002857......) = 79115520710173344161 * c9394(3020902644......)

n=50420M: x10044(1471549165......) = 14764244014807000981 * x10024(9966979439......)

n=51860M: c10353(1194691186......) = 83539504647377758961 * c10333(1430091298......)

n=55300M: c9360(9900498006......) = 10299571977767073401 * c9341(9612533441......)

n=55900M: c10081(1010050200......) = 41524300973994521801 * c10061(2432431556......)

n=57860L: c10472(5396722576......) = 83605392613344430181 * c10452(6454993401......)

n=60700M: c12109(1659808128......) = 10155715445707909001 * c12090(1634358640......)

n=60780M: c8089(2548954640......) = 11420120134223014561 * c8070(2231985837......)

n=73820L: c14742(8225091150......) = 10397782857535521641 * c14723(7910427889......)

n=76100L: c15195(4424204014......) = 20534853418363588001 * c15176(2154485315......)

n=85140M: c10051(1115700145......) = 94359332468502246421 * c10031(1182395122......)

n=25700M: c5093(3968514554......) = 125171379263069055701 * c5073(3170464827......)

n=34020M: c3878(2284208476......) = 441527209812818555581 * c3857(5173426294......)

n=40700M: c7182(2519459682......) = 417611173194342975101 * c7161(6033027477......)

n=41900L: c8335(1724897378......) = 631159667782425895601 * c8314(2732901779......)

n=49740M: c6610(4209658502......) = 426892581836355937201 * c6589(9861165739......)

n=66060L: c8772(3091994807......) = 832454043670527204061 * c8751(3714312917......)

n=70780L: c14133(3415330246......) = 387793369327658428441 * c14112(8807087785......)

n=87460M: c17477(1320466762......) = 310622262335569454041 * c17456(4251037103......)

n=95340M: c10829(1693966761......) = 398029959411773084761 * c10808(4255877532......)

n=96980M: c17846(4689314754......) = 101267813344629677201 * c17826(4630607296......)

n=99740L: c19932(2810695561......) = 456531863767106326181 * c19911(6156625166......)

n=44140M: c8810(3162811720......) = 8980406800328625305201 * c8788(3521902504......)

n=49500L: c6001(1000000000......) = 2940127486878232084501 * c5979(3401213057......)

n=96380L: c18706(3514759582......) = 1082493988508258450461 * c18685(3246909100......)

n=38100L: c5024(2414397412......) = 50381952288958440708601 * c5001(4792187089......)

n=45260L: c8627(6734564314......) = 11743072637467785826441 * c8605(5734925195......)

n=47820M: c6362(4232425619......) = 98114893375565447114821 * c6339(4313744298......)

n=71060M: c11521(2824089271......) = 21549295254455511361061 * c11499(1310525118......)

n=82460M: c12942(4902213852......) = 29918578086001502002561 * c12920(1638518327......)

n=35420M: c5281(2826914742......) = 193821575772659280082561 * c5258(1458513961......)

n=47060M: c8567(5491657989......) = 450545439664397979873401 * c8544(1218891038......)

n=50420M: x10024(9966979439......) = 112392146316700149121441 * c10001(8868039063......)

n=63100L: c12581(2129079819......) = 823120996920652066620701 * c12557(2586593984......)

n=74020L: c14800(3576409999......) = 100214315714092674846901 * c14777(3568761582......)

n=84540L: c11264(3913542626......) = 838488617833083291536881 * c11240(4667377163......)

n=87220L: c14770(5226908799......) = 167978201494503938156501 * c14747(3111658985......)

n=91020L: c11515(2807324546......) = 141609462075024248534461 * c11492(1982441360......)

n=33700L: c6720(9900498007......) = 5377348809663968671750901 * c6696(1841148558......)

n=38020M: c7579(2909016162......) = 2996357917115559088428841 * c7554(9708506936......)

n=47020M: c9389(1633967814......) = 2233815069879680610750221 * c9364(7314695994......)

n=48980L: c9355(2409810740......) = 8012599465594530238516801 * c9330(3007526771......)

n=49860L: c6616(3930004819......) = 2028384706347983239158421 * c6592(1937504659......)

n=62060L: c11849(1419436463......) = 1050439010735195506303181 * c11825(1351279273......)

n=63460L: c11928(2535738779......) = 7891755910260035637222901 * c11903(3213149023......)

n=65340M: c7907(8452788811......) = 1270390880786166425680021 * c7883(6653691347......)

n=71540M: c12097(1001000500......) = 1657544388036128561893981 * c12072(6039056977......)

n=86780L: c17352(3576409999......) = 2366185604116388593431601 * c17328(1511466384......)

n=91900L: c18361(1010050200......) = 8243956737890053517838101 * c18336(1225200753......)

n=97580M: c15355(1830711741......) = 1096310621292742766480641 * c15331(1669884160......)

n=29460L: c3899(1244175842......) = 61231252869973723408615801 * c3873(2031929421......)

n=50220L: c6468(6652181337......) = 39014404102351617687874801 * c6443(1705057783......)

n=91380M: c12153(2148622803......) = 52251738682921546390614961 * c12127(4112059919......)

n=93060M: c10989(1540234628......) = 70072989603434840580200281 * c10963(2198043264......)

n=70340M: c14064(3576409999......) = 315496064767146102025399861 * c14038(1133583077......)

n=95540L: c17890(1195084153......) = 1514042552200872299475805301 * c17862(7893332665......)

n=73580L: c13536(3541003541......) = 37342417495061621511265951801 * c13507(9482523571......)

n=33460M: c5712(3537460769......) = 143073612933960977378098121701 * c5683(2472476019......)

n=48780L: c6454(3188102665......) = 129711324072293286777808231321 * c6425(2457844516......)

n=80540L: c16105(2824060999......) = 115292375845557608175544049341 * c16076(2449477668......)

n=99220L: c17536(4223385037......) = 30847430620382008736997413844941 * c17505(1369120523......)

# 30847430620382008736997413844941 is the largest known factor that appears after n=82700L.

```Largest known factors that appear after the previous one
1  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
2  n=1060M: 22534789481525070481066146802824209631029690388674663333618185041786620876200193924826168812981 (Raman / Sep 22, 2010)
3  n=1220M: 27186363592392725942593454290345801336551729326489701011779461 (Shaopu Lin / Sep 7, 2007)
4  n=1500L: 36605832263463437733314604426708004731796978480010361966001 (Polybius / Nov 3, 2010)
5  n=1860L: 1891014345342089253412148254805092014919223493735583702021 (Yousuke Koide / Aug 14, 2010)
6  n=5100L: 185898550709887865845976723509058449254706894935901 (Frank Boerner / Jun 28, 2010)
7  n=13020M: 38362725655723071852811291205867646748081 (Kurt Beschorner / Sep 2, 2010)
8  n=82700L: 7732652742988151960568776872507813340801 (Alfred Reich / Dec 12, 2010)
9  n=99220L: 30847430620382008736997413844941 (Alfred Reich / Dec 19, 2010)
10  n=99380M: 6592290434322258947071767721 (Alfred Reich / Apr 26, 2010)
11  n=99874: 20466106492496275108462693 (Alfred Reich / Mar 29, 2010)
12  n=99940M: 17594820928226575015141 (Alfred Reich / Dec 2008)
13  n=99980M: 1848253916056919784641 (Serge Batalov / Nov 21, 2010)
14  n=99992: 371044131599480009569 (Alfred Reich / Jun 17, 2010)
15  n=99999: 1756539274631599 (Alfred Reich / Nov 16, 2010)
16  n=100000: 66489400001 (Kurt Beschorner / Mar 13, 2008)
```

December 18, 20102010 年 12 月 18 日 (Kurt Beschorner)

n=8189: c7694(1448205065......) = 5284306795479217547747 * c7672(2740577186......)

n=10235: c7703(1527650754......) = 21528783149030233065751 * c7680(7095852766......)

n=10505: c7574(3308948501......) = 95694252626132894894236231 * c7548(3457834102......)

n=11493: c7638(5434006015......) = 45500429710138309313401 * x7616(1194275757......)

n=11493: x7616(1194275757......) = 1403062550822209848040441 * c7591(8511920987......)

n=11541: c7671(4236622344......) = 28032115475570320242889 * c7649(1511345923......)

n=11559: c7685(7233620113......) = 110617598471933731710919 * c7662(6539303161......)

December 17, 20102010 年 12 月 17 日 (Makoto Kamada)

n=77007: c41472(9009009909......) = 5631001804723 * c41460(1599894694......)

n=77021: c66000(1915562082......) = 7961348834951 * c65987(2406077314......)

n=77052: c25681(1009998990......) = 8506782358021 * c25668(1187286740......)

n=77056: c32247(1589785099......) = 7034018971393 * c32234(2260137634......)

n=38615: c30877(1572595601......) = 7082457469201 * c30864(2220409524......)

n=77276: c38623(2871020153......) = 6232715717209 * c38610(4606371097......)

n=77302: c38650(9090909090......) = 8644549159447 * c38638(1051634842......)

n=77318: c38005(1330095433......) = 6537788641249 * c37992(2034472979......)

n=77432: c38712(9999000099......) = 8585560505017 * c38700(1164629856......)

n=77434: c33181(1099999890......) = 5716922562779 * c33168(1924111928......)

n=77506: c32393(4101152683......) = 7699831322327 * c32380(5326288995......)

n=77513: c77502(1541073731......) = 7172343155947 * c77489(2148633574......)

n=77514: c25837(1098901098......) = 7122230101531 * c25824(1542917152......)

n=77559: c50975(1314166059......) = 6121294282123 * c50962(2146876133......)

n=38811: c24303(1545546922......) = 6250171876129 * c24290(2472807073......)

n=77623: c61336(6626943530......) = 7188450393307 * c61323(9218876347......)

n=77644: c32007(6223415062......) = 6406675631749 * c31994(9713953725......)

n=77646: c25876(1415252487......) = 7269162847819 * c25863(1946926375......)

n=77669: c76788(2619506003......) = 5162642119511 * c76775(5073963956......)

n=77723: c77708(9048222233......) = 7605761684333 * c77696(1189653661......)

n=77752: c38841(8210933020......) = 5431177333649 * c38829(1511814569......)

n=38883: c23905(1109999999......) = 8709410246707 * c23892(1274483539......)

n=77783: c77776(1400466016......) = 6341539093801 * c77763(2208400824......)

n=38902: c19004(6222652313......) = 8357199175961 * c18991(7445858573......)

n=77890: c31146(2353722695......) = 8341753628771 * c31133(2821616174......)

n=77916: c25200(9901000000......) = 5834775501361 * c25188(1696894764......)

n=77966: c33389(1028643619......) = 6376025330893 * c33376(1613299141......)

December 16, 20102010 年 12 月 16 日 (Makoto Kamada)

n=75894: c19862(2130996577......) = 6347294509921 * c19849(3357330551......)

n=75928: c37942(6877435076......) = 6733724716553 * c37930(1021341882......)

n=75981: c45354(1796503195......) = 8522373001969 * c45341(2107984706......)

n=75990: c18945(1098890109......) = 7359569796121 * c18932(1493144491......)

n=76044: c25345(1009998990......) = 7365109683661 * c25332(1371329190......)

n=38025: c18713(1092129881......) = 9687906908551 * c18700(1127312526......)

n=76208: c34561(1000000009......) = 8197371361873 * c34548(1219903266......)

n=76232: c35137(1000099999......) = 8266273407913 * c35124(1209855941......)

n=76254: c24920(9100000000......) = 8353489967881 * c24908(1089365048......)

n=76282: c37213(1099999999......) = 6796021583167 * c37200(1618594035......)

n=76325: c58781(5859093229......) = 8936118177401 * x58768(6556642508......)

n=76325: x58768(6556642508......) = 9937598499551 * c58755(6597813856......)

n=76359: c50892(3077031522......) = 6319986415969 * c50879(4868731227......)

n=76374: c25420(2199563894......) = 6602551317127 * c25407(3331384777......)

n=76386: c24513(9943587206......) = 9039128678383 * c24501(1100060366......)

n=76401: c46922(4037006996......) = 5712317268373 * c46909(7067196737......)

n=38211: c24831(4799145324......) = 8320030202119 * c24818(5768182576......)

n=76437: c47945(4918296525......) = 9948176029027 * c47932(4943917870......)

n=76584: c25514(6529427472......) = 6775118665753 * c25501(9637362523......)

n=76600: c30551(3041524226......) = 8111968035601 * c30538(3749428267......)

n=76651: c76645(1449569687......) = 8776286705003 * c76632(1651689076......)

n=76654: c38317(1751279818......) = 9230609907371 * c38304(1897252550......)

n=38345: c30664(2840192657......) = 7516288430041 * c30651(3778716961......)

n=76698: c25561(1000999998......) = 7730775063397 * c25548(1294824892......)

n=76751: c70817(6070799740......) = 5327736824363 * c70805(1139470649......)

n=76920: c20461(1018231328......) = 6599455703521 * c20448(1542901981......)

n=76927: c75073(2708779539......) = 5671655239667 * c75060(4775994705......)

n=76952: c38466(5414086425......) = 5902977993193 * c38453(9171788258......)

n=76988: c36411(1898772578......) = 6067866961001 * c36398(3129225790......)

n=76993: c61995(2143816131......) = 6027735928187 * c61982(3556586017......)

December 15, 20102010 年 12 月 15 日 (Makoto Kamada)

n=75223: c75216(1136222654......) = 5607939040889 * c75203(2026096657......)

n=75307: c75296(6219248204......) = 5225075584849 * c75284(1190269519......)

n=75337: c75324(4531651868......) = 9402334086791 * c75311(4819709474......)

n=75373: c71382(1421501601......) = 6335003720323 * c71369(2243884399......)

n=75433: c74880(9000000000......) = 5500669103849 * c74868(1636164588......)

n=75482: c33120(9090909091......) = 6901055525893 * c33108(1317321539......)

n=75486: c24016(9507267674......) = 5924236618819 * c24004(1604808903......)

n=37751: c32341(1298735643......) = 7616412460427 * c32328(1705180293......)

n=75529: c73870(3504690639......) = 7799732095277 * c73857(4493347458......)

n=75532: c36072(6896243335......) = 6776568646201 * c36060(1017660071......)

n=75636: c22800(9999990000......) = 6263774161921 * c22788(1596479972......)

n=37841: c37269(8866226833......) = 6047342813117 * c37257(1466135971......)

n=75693: c48202(2622226077......) = 9446144419027 * c48189(2775975002......)

n=75694: c37840(4448175178......) = 7345572690613 * c37827(6055586631......)

n=75702: c21582(2448732465......) = 5650242923623 * c21569(4333853426......)

n=75703: c75688(9066554147......) = 6031347793759 * x75676(1503238489......)

n=75703: x75676(1503238489......) = 7789121792591 * c75663(1929920380......)

n=37877: c32424(9999999000......) = 7137541046707 * c32412(1401042590......)

n=75770: c30299(1209788164......) = 5934315265091 * c30286(2038631434......)

n=75771: c50503(2197405787......) = 5903688827107 * c50490(3722089446......)

n=37896: c12625(1000099999......) = 8663604575089 * c12612(1154369398......)

n=37909: c37488(4378107702......) = 8365843187797 * c37475(5233313133......)

December 14, 20102010 年 12 月 14 日 (Kurt Beschorner)

n=8359: c7672(4872356892......) = 2414596578764011768697907616853 * c7642(2017876168......)

n=8591: c7660(9122784205......) = 36602350283047185935453 * x7638(2492403939......)

n=8591: x7638(2492403939......) = 478264488163237094744129 * c7614(5211350626......)

# The ratio of factored part of 6*10^85910-7+1 was raised from 1.53% to 1.58%.

n=11919: c7603(5561192559......) = 9251834079773358133 * c7584(6010908228......)

December 14, 20102010 年 12 月 14 日 (Makoto Kamada)

n=74439: c49572(9999999999......) = 6700412200681 * c49560(1492445494......)

n=74541: c49692(9009009009......) = 6322065959071 * c49680(1425010284......)

n=74575: c56161(1000010000......) = 6464721356551 * c56148(1546872548......)

n=74588: c35944(1308314218......) = 6797584167509 * c35931(1924675276......)

n=74593: c73728(9000000000......) = 5258594805067 * c73716(1711483834......)

n=74809: c64108(1879787375......) = 5115267508919 * c64095(3674856441......)

n=74855: c54384(9504082786......) = 5903220549271 * c54372(1609982670......)

n=74937: c49956(9009009009......) = 5145462178081 * c49944(1750864878......)

n=37493: c37466(5065234881......) = 6258057336199 * c37453(8093941313......)

n=75019: c64250(3852565903......) = 5872984846009 * c64237(6559809031......)

n=75080: c29989(3004645248......) = 5444650989521 * c29976(5518526815......)

n=75151: c74592(9000000000......) = 7830575631391 * c74580(1149340792......)

n=75175: c57593(1007759661......) = 6176563982951 * c57580(1631586209......)

December 13, 20102010 年 12 月 13 日 (Makoto Kamada)

n=73659: c47853(3825326836......) = 8126414443201 * c47840(4707275100......)

n=73683: c49104(9999999990......) = 8854210093483 * c49092(1129406224......)

n=73829: c61765(9745077361......) = 6232772790119 * c61753(1563521997......)

n=73891: c69976(1877906737......) = 7166452229929 * c69963(2620413389......)

n=73987: c73433(8219120285......) = 9387849817363 * c73420(8755061537......)

n=74019: c44822(4089166791......) = 6483223396123 * c44809(6307305088......)

n=37025: c29600(9999900000......) = 8848305810151 * c29588(1130148552......)

n=74119: c67872(2177167108......) = 5322345453329 * c67859(4090615926......)

n=74147: c72696(9000000000......) = 6986065832111 * c72684(1288278727......)

n=74195: c50390(1680690818......) = 5557273165841 * c50377(3024308448......)

n=37113: c24276(4816197278......) = 7985905641787 * c24263(6030871756......)

n=74237: c72943(1150994116......) = 6414080808799 * c72930(1794480223......)

n=74287: c74276(2209319713......) = 5081418003241 * c74263(4347840921......)

n=37165: c29713(3461297089......) = 6793483931471 * c29700(5095025063......)

n=37169: c32375(8702152524......) = 7248774873803 * c32363(1200499763......)

n=74345: c59466(5044098996......) = 9950778937031 * c59453(5069049396......)

n=74377: c74367(6027641756......) = 8304395396719 * c74354(7258375196......)

December 12, 20102010 年 12 月 12 日 (Serge Batalov)

n=30003: c19585(1109999999......) = 744253341263137081 * c19567(1491427634......)

n=30005: c22529(1111099999......) = 2990437555661509351 * c22510(3715509785......)

n=30043: c27708(1588058584......) = 133275709218686858071 * c27688(1191558907......)

n=30081: c19441(1109999999......) = 130805592594929947 * c19423(8485875702......)

n=30085: c21825(8700456354......) = 14812497899129921 * c21809(5873726641......)

n=30251: c27760(1588656209......) = 23973340864997317 * c27743(6626761860......)

n=30311: c28507(1649563140......) = 238764344521557521 * c28489(6908749897......)

n=30407: c28056(9000000000......) = 8165759530319 * c28044(1102163242......)

n=30609: c19225(1001000999......) = 577364358057031081 * c19207(1733742282......)

n=30679: c27880(9000000000......) = 3590331418373723 * c27865(2506732374......)

n=30823: c28430(1973103678......) = 43750095060517 * c28416(4509941466......)

n=30957: c19373(2302606401......) = 12334293662443 * x19360(1866832803......)

n=30957: x19360(1866832803......) = 127983310621963 * c19346(1458653315......)

n=30975: c13902(1598416047......) = 13612818164401 * c13889(1174199220......)

n=31263: c19573(2492273669......) = 21900322183123 * c19560(1138007764......)

n=31467: c19706(2383448816......) = 44170753839439 * c19692(5395988541......)

n=32095: c21841(1000000100......) = 34675352498921 * c21827(2883893105......)

n=32131: c27711(3544334875......) = 1297470761864311 * c27696(2731726201......)

n=32153: c28081(1111111111......) = 54469386473987 * c28067(2039881818......)

n=32165: c22021(6622614380......) = 15149309399351 * c22008(4371561901......)

n=32227: c28513(1111111111......) = 213872406987409 * c28498(5195205528......)

n=32439: c19621(2261744277......) = 29701363753438081 * c19604(7614950937......)

n=32467: c32467(1111111111......) = 1929546233282145557 * c32448(5758406261......)

# 2552 of 9592 R_prime factorizations are still blank.

n=32473: c27813(3418849817......) = 79782189422209 * c27799(4285229374......)

n=32479: c32471(1100712318......) = 28752652760413 * c32457(3828211357......)

n=32491: c32483(1102434040......) = 76300986884631569 * c32466(1444848992......)

n=32493: c21660(9009009009......) = 372818004428557 * c21646(2416462966......)

n=32501: c27848(1384551620......) = 20969476129799 * c27834(6602700096......)

n=32511: c21649(6752204197......) = 167549102554723 * c21635(4029985296......)

n=32517: c21665(7211828445......) = 1192885944695281 * c21650(6045698230......)

n=32537: c32530(1566474856......) = 6110121021843959 * c32514(2563737855......)

n=32543: c27885(1935900387......) = 31575799129729 * c27871(6130962447......)

n=32561: c32549(3119004463......) = 6244678948122533 * c32533(4994659436......)

n=32563: c32550(2987296046......) = 27785037066719 * c32537(1075145604......)

n=32579: c32570(3145069382......) = 863353458683563 * c32555(3642852589......)

n=32591: c28502(2393459096......) = 1157853927262787 * c28487(2067151166......)

n=32609: c32593(6328236217......) = 22631147004677 * c32580(2796250767......)

n=32633: c32628(1702408738......) = 265599987978991 * c32613(6409671743......)

n=32641: c27972(9000000900......) = 337766136838201 * c27958(2664565780......)

n=32647: c32641(5672320268......) = 5088020585321 * c32629(1114838309......)

n=32771: c32754(1783046987......) = 27048524768443 * c32740(6592030446......)

n=32795: c22438(4626313688......) = 8575637422981173791 * c22419(5394716987......)

n=32799: c19474(1634436131......) = 28237771642081 * c19460(5788120081......)

n=32803: c32774(6662609777......) = 107612435364641 * c32760(6191300990......)

n=32831: c32813(1035890576......) = 973518243096439 * c32798(1064068993......)

n=32857: c28554(5123720690......) = 14502612488756936904361 * c28532(3532963936......)

n=32881: c32470(4808499102......) = 20133784211227 * x32457(2388273884......)

n=32881: x32457(2388273884......) = 1510434655552409 * c32442(1581183188......)

n=32883: c21495(1973899150......) = 77680534613557 * c21481(2541047329......)

n=32911: c32905(3376098371......) = 175330534226018089 * c32888(1925562131......)

n=32939: c32930(2056852891......) = 14898556083721 * c32917(1380571969......)

n=32967: c19426(2164645453......) = 861521429840347 * c19411(2512584572......)

n=32969: c32961(9684393649......) = 89476280454853 * c32948(1082342001......)

n=32977: c28219(1684672844......) = 159529025500562831 * c28202(1056029045......)

n=33013: c32999(5732670125......) = 204026997137477 * c32985(2809760573......)

n=33029: c33005(8059891884......) = 60091992868561 * x32992(1341258876......)

n=33029: x32992(1341258876......) = 5847188471397054889 * c32973(2293852649......)

n=33043: c32663(1368474118......) = 198676646086649 * c32648(6887946549......)

n=33047: c28320(9000000900......) = 11406588933388929169 * c28301(7890177293......)

n=33093: c22048(2674787606......) = 9144540637143951187 * c22029(2925010356......)

n=33103: c28363(2265650203......) = 5730008979003163 * c28347(3954008121......)

n=33143: c28581(1640720726......) = 538555603544641 * c28566(3046520574......)

n=33173: c28377(1902275434......) = 16339514736712407997 * c28358(1164217827......)

n=33177: c22106(2515720118......) = 564491084237653 * c22091(4456616213......)

n=33183: c22104(9999999990......) = 39339057441721057723 * c22085(2542002945......)

n=33213: c22130(1342267686......) = 101547540406729 * c22116(1321812110......)

n=33221: c32838(6450304346......) = 21447487543975489 * c32822(3007487163......)

n=33249: c22146(2341354239......) = 232583699769301477 * c22129(1006671680......)

n=33271: c28224(9999999999......) = 1458530896265129 * c28209(6856214034......)

n=33291: c22032(9999999999......) = 18898831230319 * c22019(5291332505......)

n=33319: c27841(1111111111......) = 747012732276848467 * c27823(1487405854......)

n=33361: c32811(1000173498......) = 357992127049201 * c32796(2793842163......)

n=33401: c33000(2548786129......) = 370808312305693 * c32985(6873594912......)

n=33417: c21513(3129723267......) = 4395512038183759 * c21497(7120270039......)

n=33431: c32989(5971560654......) = 6422278502467 * c32976(9298196351......)

n=33433: c32863(6729827342......) = 417146093377993043 * c32846(1613302257......)

n=33443: c32752(4353196564......) = 6134512831043 * c32739(7096238420......)

n=33447: c22296(9009009009......) = 23970905666161 * c22283(3758309817......)

n=33467: c28636(2965480091......) = 41724007624027 * c28622(7107371175......)

n=33471: c22308(9990000009......) = 28987953168961 * c22295(3446259193......)

n=33477: c22316(9009009009......) = 7982042095879 * c22304(1128659671......)

n=33549: c21823(1128865925......) = 186450565477147 * c21808(6054505240......)

n=33571: c32936(3056881731......) = 437149606128062959 * c32918(6992758746......)

n=33621: c19201(1109999889......) = 64074336741807774649 * c19181(1732362667......)

n=33633: c21590(4051497872......) = 643706785823707 * c21575(6294011438......)

n=33723: c22458(1114787555......) = 580654641749564960173 * c22437(1919880554......)

n=33777: c22356(9999999999......) = 5274098383483 * x22344(1896058676......)

n=33777: x22344(1896058676......) = 87989928018380816671 * c22324(2154858765......)

n=33783: c22520(9009009009......) = 1769325449683711 * c22505(5091776083......)

n=33841: c32996(7139256007......) = 216591285699053 * c32982(3296188018......)

n=33843: c21729(1109999999......) = 80250120681751 * c21715(1383175490......)

n=33849: c22560(9990000009......) = 2239243428459511 * c22545(4461328269......)

n=33861: c22548(1001425650......) = 314965516810969 * c22533(3179477108......)

n=33901: c27866(2992866932......) = 1357417071891834689 * c27848(2204824880......)

n=33909: c22177(1109999999......) = 1075810513605049 * c22162(1031780212......)

n=33911: c33889(5663689533......) = 49599889275181559 * c33873(1141875438......)

n=33927: c21999(1260306504......) = 91543964186929 * c21985(1376722666......)

n=33945: c17241(1389477554......) = 281004643525481127361 * c17220(4944678269......)

n=34041: c19441(1109999889......) = 121893941518147 * c19426(9106276121......)

n=34053: c22700(9009009009......) = 893639137113988609 * c22683(1008126058......)

n=34061: c34054(1647535728......) = 700310337918768391 * c34036(2352579477......)

n=34063: c32550(4731243711......) = 6049992904187116235441 * c32528(7820246711......)

n=34069: c28075(8153327414......) = 42466662387237271 * c28059(1919936005......)

n=34101: c22670(4554281344......) = 10243312482805147 * c22654(4446102129......)

n=34109: c32596(1630980206......) = 47006528112689 * c32582(3469688726......)

n=34113: c22287(1029201123......) = 19448930859439 * c22273(5291813369......)

n=34131: c21950(8721634605......) = 5828322893226445455264397 * c21926(1496422687......)

n=34161: c22252(1579144400......) = 15933925638449558431 * c22232(9910579703......)

n=34173: c22776(9990000009......) = 508550118459373 * c22762(1964408157......)

n=34177: c28546(1554309442......) = 362940024450719 * c28531(4282551764......)

n=34179: c22784(9009009009......) = 5433033301745053 * c22769(1658191383......)

n=34183: c34174(1279212368......) = 1074033420527395813 * c34156(1191035906......)

n=34239: c22401(1109999999......) = 113005360961533683991 * c22380(9822542847......)

n=34251: c19475(3535820688......) = 3188392961469871 * c19460(1108966407......)

n=34263: c22349(3131545223......) = 113840593077187 * c22335(2750815977......)

n=34319: c34314(1618775202......) = 8253153854243 * x34301(1961401945......)

n=34319: x34301(1961401945......) = 1938528473203319 * c34286(1011799399......)

n=34329: c22884(9009009009......) = 30796141916329 * c22871(2925369363......)

n=34361: c34346(1039209848......) = 18191250462431 * c34332(5712690565......)

n=34369: c34355(1679232762......) = 8437551006721 * c34342(1990189761......)

n=34407: c22932(9990000009......) = 16325846106373 * c22919(6119131556......)

n=34429: c34417(4502060588......) = 1514013075262333 * x34402(2973594258......)

n=34429: x34402(2973594258......) = 96837922614316681320889 * c34379(3070691913......)

n=34491: c22986(2251713529......) = 199622731948734397 * c22969(1127984527......)

n=34499: c34487(1080746090......) = 41827680701297987 * c34470(2583805920......)

n=34513: c34486(4413694361......) = 814356180919363 * c34471(5419857384......)

n=34521: c22321(1109999999......) = 2061491469666199 * c22305(5384451094......)

n=34569: c21913(1001000999......) = 33239005706773 * c21899(3011525100......)

n=34571: c34193(3828438157......) = 845578776414241 * c34178(4527594902......)

n=34589: c34589(1111111111......) = 384254438812271 * c34574(2891602539......)

# 2551 of 9592 R_prime factorizations are still blank.

n=34603: c34593(3020663182......) = 1152055017146514769 * x34575(2621978236......)

n=34603: x34575(2621978236......) = 1919535431672224016639 * c34554(1365944172......)

n=34607: c34590(3936466253......) = 25465051327319 * c34577(1545830873......)

n=34621: c34144(9000000000......) = 828070481299471 * c34130(1086864005......)

n=34651: c34634(1543308432......) = 365655092688283 * c34619(4220667136......)

n=34701: c22513(1109999999......) = 59916126172957 * x22499(1852589729......)

n=34701: x22499(1852589729......) = 701604793700053 * c22484(2640503238......)

n=34715: c27004(2011997599......) = 1686514816536214601 * c26986(1192991356......)

n=34731: c21680(1237082711......) = 1767608595554194999 * c21661(6998623530......)

n=34745: c27775(9068818645......) = 34800873781951 * c27762(2605916938......)

n=34789: c32934(6467556937......) = 12904066122849467 * c32918(5012030220......)

n=34887: c22401(1109999999......) = 115465113165601 * c22386(9613293310......)

n=34933: c34560(9000000000......) = 1641152485399540299292961 * c34536(5483951113......)

n=34943: c34428(1320953699......) = 97904319722249323 * c34411(1349229230......)

n=34953: c22787(2684870759......) = 355992017391547729 * c22769(7541940910......)

n=34955: c27941(9797771192......) = 12988741103504161 * c27925(7543280072......)

n=34977: c22875(2266791101......) = 96930523173373 * c22861(2338573060......)

n=34987: c34336(9000000000......) = 11742161811801787 * c34320(7664687426......)

n=35041: c34434(1605155283......) = 19425164838203 * c34420(8263277543......)

n=35223: c22940(1138036060......) = 15088409917889323 * c22923(7542451900......)

n=35235: c18118(2843427116......) = 2117393394097591 * c18103(1342890331......)

n=35241: c22081(1109999999......) = 3724370081730315734599 * c22059(2980369768......)

n=35261: c34272(9000000000......) = 4888768090147213 * c34257(1840954578......)

n=35293: c34036(1068698818......) = 75814650678230281 * c34019(1409620448......)

n=35303: c34431(2610389312......) = 5897585878837453 * c34415(4426199747......)

n=35319: c23026(8030247238......) = 2980740379518396769 * c23008(2694044504......)

n=35347: c32607(2833249839......) = 10228173131879 * c32594(2770044858......)

n=35399: c27927(2193598647......) = 213316370503601 * c27913(1028331132......)

n=35451: c21560(3708129623......) = 1236617031988265376962683 * c21536(2998607917......)

n=35467: c34206(4292250879......) = 1613313075897041 * x34191(2660519488......)

n=35467: x34191(2660519488......) = 19142991144238853 * c34175(1389813884......)

n=35477: c32736(9000000000......) = 11531234978563 * x32723(7804888215......)

n=35477: x32723(7804888215......) = 11246623989511249 * c32707(6939760965......)

n=35529: c21830(2571580818......) = 395228118629293 * c21815(6506573538......)

n=35545: c28432(9000090000......) = 12156420193629161 * c28416(7403569354......)

n=35627: c34056(9000000000......) = 79920873795410443 * c34040(1126113813......)

n=35631: c22884(8959720447......) = 3143836110200041 * c22869(2849932418......)

n=35651: c27710(9333194005......) = 362742051119139077 * c27693(2572956175......)

n=35699: c34436(1260521856......) = 2274272633095721 * c34420(5542527477......)

n=35737: c32976(9000000000......) = 1161135554258393923483 * c32955(7751033001......)

n=35795: c28620(6538283073......) = 382190857232213641 * c28603(1710737698......)

n=35841: c22012(3948236178......) = 160093954163053 * c21998(2466199425......)

n=35849: c32571(3445123337......) = 199074522648366641 * c32554(1730569684......)

n=35919: c22027(6967023253......) = 53371975578013 * x22014(1305371063......)

n=35919: x22014(1305371063......) = 9041998838188681 * c21998(1443675327......)

n=35949: c22881(1109999999......) = 34685102736701173 * c22864(3200221168......)

n=35959: c27961(1111110999......) = 1432276125348350129 * c27942(7757659157......)

n=35965: c28768(9000090000......) = 13227312905896951 * c28752(6804171085......)

n=35975: c28743(3957809501......) = 2180839902054091601 * c28725(1814809742......)

n=35981: c32690(4344787341......) = 1760093135680436437 * c32672(2468498543......)

n=36041: c34452(9000000000......) = 10680935464937512001 * c34433(8426228235......)

n=36119: c34178(3561612283......) = 77764115120848991 * c34161(4580020331......)

n=36165: c19274(1763927979......) = 461883075670866589486687351 * c19247(3818992451......)

n=36271: c32473(1111111111......) = 14227552879723701253 * c32453(7809572879......)

n=36295: c23010(6824587961......) = 310062432968401 * c22996(2201036706......)

n=36333: c21961(1001000999......) = 15503930706133 * c21947(6456433655......)

n=36347: c34416(9000000000......) = 86889130339845561601 * c34397(1035802748......)

n=36387: c22315(2750977681......) = 37038617627361013 * x22298(7427322772......)

n=36387: x22298(7427322772......) = 151134086318930516316763 * c22275(4914392876......)

n=36395: c27988(1711879769......) = 218471030263511 * c27973(7835728919......)

n=36423: c22681(1000000001......) = 11716272248637875293 * c22661(8535137966......)

n=36461: c34196(1371309463......) = 17062404630917 * c34182(8037023462......)

n=36495: c19441(1001000999......) = 632932670551681 * c19426(1581528409......)

n=36515: c28505(2623154333......) = 26075361865151 * c28492(1005989618......)

n=36575: c21590(1397534531......) = 253702785732551 * c21575(5508550201......)

n=36621: c22465(1001000999......) = 144309685693213 * c22450(6936478277......)

n=36705: c19569(1109988900......) = 244315307717281 * c19554(4543263827......)

n=36737: c34551(2104208856......) = 2238545650609002323557 * c34529(9399892542......)

n=36815: c28507(1676699297......) = 42718515327845921 * c28490(3924994313......)

n=36945: c19681(1001000999......) = 12592712180026490761 * c19661(7949050098......)

n=36959: c34097(2723859895......) = 20065476107431 * c34084(1357485803......)

n=37095: c19758(9895154259......) = 10632113480071 * x19745(9306855384......)

n=37095: x19745(9306855384......) = 344754076434724111801 * c19725(2699563550......)

n=37141: c34265(1228802256......) = 10814844015640757 * c34249(1136218196......)

n=37155: c19809(1109988900......) = 79089079217542111 * c19792(1403466712......)

n=37281: c22827(2616927045......) = 135729470041987 * c22813(1928046315......)

n=37305: c19845(5139378766......) = 363299815383121 * c19831(1414638419......)

n=37359: c21295(1107126776......) = 4213637509062997 * c21279(2627484622......)

n=37401: c19584(9009009909......) = 20545978628077813 * c19568(4384804478......)

n=37479: c22297(1354804360......) = 13351178650681 * c22284(1014745136......)

n=37653: c19425(4684451362......) = 40137049740481 * c19412(1167114023......)

n=37665: c19429(4684257582......) = 15464805080311 * c19416(3028979387......)

n=37687: c34623(3302017061......) = 341844174418111 * x34608(9659421774......)

n=37687: x34608(9659421774......) = 855230372400866281 * c34591(1129452611......)

n=37825: c28161(1000010000......) = 1561261101178201 * c28145(6405142607......)

n=37863: c21601(1001000999......) = 69728779850311 * c21587(1435563625......)

n=38027: c34551(1699950742......) = 28576412836841 * c34537(5948789836......)

n=38087: c32640(9000000900......) = 48852624912954563 * c32624(1842275807......)

n=38095: c28791(3360202451......) = 175609108988591 * c28777(1913455669......)

n=38233: c33014(1055711860......) = 15651610644309570949591 * c32991(6745068507......)

n=38283: c21865(1109999889......) = 19948930428169 * c21851(5564207529......)

n=38313: c22681(1000000000......) = 1253340228400129 * c22665(7978679510......)

n=38353: c32868(9000000900......) = 25958108868268879 * c32852(3467125030......)

n=38471: c34540(1139097945......) = 10953942651844898557 * c34521(1039897671......)

n=38475: c19441(1000000000......) = 86527973838073273201 * c19421(1155695615......)

n=38493: c19857(1848618879......) = 37597072499533 * c19843(4916922399......)

n=38595: c19675(1458913802......) = 102592597971751 * c19661(1422045869......)

n=38619: c22033(1001000999......) = 2084438278447813 * c22017(4802257808......)

n=38717: c33167(6477475821......) = 45499842824967161 * c33151(1423625977......)

n=38759: c32917(1373884164......) = 334104358981189307603 * c32896(4112140796......)

n=38909: c34553(1548625829......) = 278843128275479 * c34538(5553752890......)

n=38927: c32457(7222770698......) = 440726247730357 * c32443(1638833796......)

n=38985: c19712(9009099100......) = 1834531372553840431 * c19694(4910844935......)

n=38995: c28321(1111099999......) = 264437022868591 * c28306(4201756576......)

n=39014: c19492(1182107104......) = 112397726116019 * c19478(1051717988......)

n=39207: c22385(1952501214......) = 35348160334117 * x22371(5523628942......)

n=39207: x22371(5523628942......) = 9328884052503546579584719 * c22346(5920996457......)

n=39249: c22177(1000000000......) = 11484445795201 * c22163(8707429316......)

n=39273: c22453(2710757235......) = 432739533391236715801 * c22432(6264177470......)

n=39291: c22435(3531331467......) = 420935584823759947373587 * c22411(8389244329......)

n=39459: c22532(1406505263......) = 18592122349137325591 * c22512(7565060283......)

n=39538: c19314(1532781666......) = 22977268348499 * c19300(6670861144......)

n=39753: c22662(1042664045......) = 7887807421052077 * c22646(1321868029......)

n=39765: c19192(7531865254......) = 53396806589697121 * c19176(1410546011......)

n=39781: c34072(7133084904......) = 653462878069919 * c34058(1091582267......)

n=39897: c21595(1043310438......) = 3233720798000551 * c21579(3226346687......)

n=39975: c19200(9999900000......) = 2063565933828974719951 * c19179(4845931906......)

n=40019: c34284(4144240559......) = 5485485259987973129 * c34265(7554920600......)

n=40095: c19425(5568353037......) = 10118468168022310471 * c19406(5503158130......)

n=40173: c22932(3018750961......) = 13151579448245239 * c22916(2295352412......)

n=40201: c34452(9000000900......) = 5355872904400609696561 * c34431(1680398519......)

n=40245: c21450(1379039336......) = 3253474526145031 * c21434(4238666464......)

n=40257: c22660(9661047756......) = 504273864726273601 * c22643(1915833524......)

n=40383: c23024(1739920693......) = 13368946009231 * c23011(1301464373......)

n=40665: c21662(2149331015......) = 452545516349791 * c21647(4749425059......)

n=40725: c21569(8753135260......) = 36213969516505201 * c21553(2417060426......)

n=40735: c32584(9000090000......) = 39051576591241 * c32571(2304667515......)

n=40905: c21601(1000000000......) = 4224554636058550081 * c21582(2367113426......)

n=40935: c21819(2711582236......) = 11419374664718401 * c21803(2374545293......)

n=40965: c21834(4233753191......) = 296995740990785311 * c21817(1425526567......)

n=40995: c21841(1001000999......) = 45833858927281 * c21827(2183977137......)

n=41041: c28780(8818063912......) = 2078573656421510249 * c28762(4242362970......)

n=41085: c19669(6164888845......) = 403329884098681 * c19655(1528497909......)

n=41097: c22026(1370083056......) = 225731542797019477 * c22008(6069524177......)

n=41105: c32851(1656627062......) = 334914527053641481 * c32833(4946417453......)

n=41155: c32910(2272542193......) = 1189708806035008321 * c32892(1910166741......)

n=41295: c21996(7402332531......) = 6660052090627657591 * c21978(1111452647......)

n=41355: c22007(4026281561......) = 148140854848371796561 * c21987(2717873854......)

n=41419: c34561(1111110999......) = 9066329908151587 * c34545(1225535592......)

n=41427: c27583(4247496319......) = 298204092166951 * c27569(1424358830......)

n=41499: c26188(2476507010......) = 208477798689401209 * c26171(1187899635......)

n=41521: c41501(1795451785......) = 660107879756318813 * c41483(2719936908......)

n=41577: c27716(9009009009......) = 5425392695175361 * c27701(1660526622......)

n=41593: c41576(1326434308......) = 1093128734816132053243 * c41555(1213429183......)

n=41603: c41583(7579813934......) = 11440578602072201 * c41567(6625376388......)

n=41619: c27733(2233697280......) = 45566348727769 * c27719(4902076517......)

n=41703: c27800(9009009009......) = 20565455183984839 * c27784(4380651402......)

n=41719: c41707(5255595823......) = 8120516596201748293 * c41688(6471996899......)

n=41729: c41719(1850859359......) = 120064118367043 * x41705(1541559114......)

n=41729: x41705(1541559114......) = 392869430700479717 * c41687(3923845923......)

n=41737: c41737(1111111111......) = 6327402551428142791 * c41718(1756030380......)

# 2550 of 9592 R_prime factorizations are still blank.

n=41759: c41747(2294836267......) = 3620934033210839071 * c41728(6337691452......)

n=41799: c27854(3924937948......) = 6733171941933037 * c27838(5829255487......)

n=41811: c21575(2053010986......) = 503334026931121 * c21560(4078824154......)

n=41841: c27882(2023398099......) = 19772690826079 * c27869(1023329660......)

n=41859: c27883(2571240751......) = 14835103692733 * x27870(1733213872......)

n=41859: x27870(1733213872......) = 237691718847913591 * c27852(7291856361......)

n=41869: c41440(9000000000......) = 879406377950843 * c41426(1023417640......)

n=41913: c27936(9990000009......) = 300618184184567803 * c27919(3323152269......)

n=41915: c32779(6683809832......) = 48241459973561 * c32766(1385490786......)

n=41917: c41484(5177319032......) = 47912924332307521169 * c41465(1080568365......)

n=41953: c41947(1655289037......) = 77320923307382449 * x41930(2140803506......)

n=41953: x41930(2140803506......) = 23678880067700484569 * c41910(9040982936......)

n=41995: c32534(7182935422......) = 53817068303351 * c32521(1334694670......)

n=42013: c41990(9987001271......) = 381825541034563 * c41976(2615592776......)

n=42033: c27992(4143726866......) = 781167172314271 * c27977(5304532773......)

n=42093: c28032(5545204995......) = 164394886755907 * c28018(3373100650......)

n=42101: c42095(2199292399......) = 41272402241223073813 * c42075(5328723990......)

n=42173: c41756(1067020759......) = 24725348890397 * c41742(4315493238......)

n=42179: c42170(8990701680......) = 1328402986551787 * c42155(6768052896......)

n=42209: c42192(9372336009......) = 2145022235373401 * c42177(4369342123......)

n=42213: c28134(6276992125......) = 13672966052803 * x28121(4590805024......)

n=42213: x28121(4590805024......) = 188637468057559 * c28107(2433665523......)

n=42223: c42209(1274419361......) = 17553303201308009 * c42192(7260282280......)

n=42247: c41647(6016858101......) = 69395552947711 * c41633(8670379938......)

n=42255: c22465(1000000001......) = 445733543790001 * c22450(2243492810......)

n=42257: c42240(5610565793......) = 23615697494797 * x42227(2375778142......)

n=42257: x42227(2375778142......) = 3372473354751101471627 * c42205(7044616495......)

n=42273: c21577(5943794267......) = 1645228706996317213 * c21559(3612746508......)

n=42371: c36305(7375327597......) = 17460960631129 * x36292(4223895668......)

n=42371: x36292(4223895668......) = 67311180572917 * c36278(6275176920......)

n=6425: c5120(9999900000......) = 14347869514873211927012551 * c5095(6969606177......)

December 12, 20102010 年 12 月 12 日 (Alfred Reich)

n=82700L: c16512(1144007532......) = 7732652742988151960568776872507813340801 * c16472(1479450288......)

# P-1 = 2^7 * 5^2 * 7 * 41 * 383 * 827 * 1447 * 2909 * 3373 * 32713 * 159763 * 358234307

# 7732652742988151960568776872507813340801 is the largest known factor that appears after n=13020M.

```Largest known factors that appear after the previous one
1  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
2  n=1060M: 22534789481525070481066146802824209631029690388674663333618185041786620876200193924826168812981 (Raman / Sep 22, 2010)
3  n=1220M: 27186363592392725942593454290345801336551729326489701011779461 (Shaopu Lin / Sep 7, 2007)
4  n=1500L: 36605832263463437733314604426708004731796978480010361966001 (Polybius / Nov 3, 2010)
5  n=1860L: 1891014345342089253412148254805092014919223493735583702021 (Yousuke Koide / Aug 14, 2010)
6  n=5100L: 185898550709887865845976723509058449254706894935901 (Frank Boerner / Jun 28, 2010)
7  n=13020M: 38362725655723071852811291205867646748081 (Kurt Beschorner / Sep 2, 2010)
8  n=82700L: 7732652742988151960568776872507813340801 (Alfred Reich / Dec 12, 2010)
9  n=99380M: 6592290434322258947071767721 (Alfred Reich / Apr 26, 2010)
10  n=99874: 20466106492496275108462693 (Alfred Reich / Mar 29, 2010)
11  n=99940M: 17594820928226575015141 (Alfred Reich / Dec 2008)
12  n=99980M: 1848253916056919784641 (Serge Batalov / Nov 21, 2010)
13  n=99992: 371044131599480009569 (Alfred Reich / Jun 17, 2010)
14  n=99999: 1756539274631599 (Alfred Reich / Nov 16, 2010)
15  n=100000: 66489400001 (Kurt Beschorner / Mar 13, 2008)
```

December 12, 20102010 年 12 月 12 日 (Kurt Beschorner)

n=8153: c7842(8057036401......) = 5044011637803267371849 * c7821(1597346909......)

n=8233: c8214(1223267586......) = 3069282722289723269347 * c8192(3985516153......)

# The ratio of factored part of (22*10^8233-13)/9-1 was raised from 0.26% to 0.52%.

n=8237: c8225(2733025379......) = 88616663308720614791 * c8205(3084098720......)

n=12170: c4865(1099989000......) = 21819775047856190898729632041 * c4836(5041248123......)

December 11, 20102010 年 12 月 11 日 (Serge Batalov)

n=30045: c16017(1109988900......) = 11870742882115441 * c16000(9350627092......)

n=30065: c20593(1111099888......) = 380113617901081 * c20578(2923073093......)

n=30107: c21120(9000000900......) = 194863666290679 * c21106(4618614168......)

n=30129: c18041(1000000000......) = 533678088361573 * c18026(1873788753......)

n=30195: c14400(9990000009......) = 189813617620111 * c14386(5263057590......)

n=30219: c17247(2800495094......) = 136388578790773 * c17233(2053320827......)

n=30255: c16102(9320062278......) = 352793414552671 * c16088(2641790320......)

n=30275: c20621(8332674857......) = 542226090776713001 * c20604(1536752841......)

n=30285: c16116(2674956852......) = 5900833902632401 * c16100(4533184455......)

n=30437: c27660(9000000000......) = 371927773388175765311 * c27640(2419824665......)

n=30489: c20313(1700033706......) = 27787042877005723 * c20296(6118080696......)

n=30495: c15253(1629353086......) = 88933853006175720440784721 * c15227(1832095463......)

n=30507: c20328(1102065861......) = 453415707629390689 * x20310(2430585978......)

n=30507: x20310(2430585978......) = 1136161405731050791 * c20292(2139296376......)

n=30537: c18132(4167219801......) = 2040462384497074345627 * c18111(2042291900......)

n=30543: c20350(2011905879......) = 17450510067997 * c20337(1152920958......)

n=30555: c13814(1038444019......) = 636781518627031 * c13799(1630769720......)

n=30741: c20473(6438760283......) = 127809269625917329 * c20456(5037788184......)

n=30801: c20521(1018883185......) = 229335122683430041 * c20503(4442769923......)

n=30813: c20536(1461860711......) = 1457397622345719997 * c20518(1003062369......)

n=30861: c20402(6562226751......) = 47750319221041 * c20389(1374279137......)

n=30975: c13915(1793539963......) = 11220732964351 * c13902(1598416047......)

n=30999: c20664(9009009009......) = 2229388059725350351 * c20646(4041023261......)

n=31011: c20672(9009009009......) = 86863903212652351813 * c20653(1037140708......)

n=31017: c17641(1000000100......) = 181539846615511609 * c17623(5508433099......)

n=31113: c20698(8229493107......) = 20619310468483 * c20685(3991158249......)

n=31131: c20736(9999999990......) = 337801817473867 * c20722(2960315626......)

n=31137: c20353(1109999999......) = 14524936906231 * c20339(7642029753......)

n=31161: c17660(1445535197......) = 182191310489591209 * x17642(7934161037......)

n=31161: x17642(7934161037......) = 26563398123728238235711 * c17620(2986877281......)

n=31221: c20777(9101848384......) = 61821123010344883 * c20761(1472287778......)

n=31241: c26772(9000000900......) = 60359512702441 * c26759(1491065864......)

n=31299: c20864(9009009009......) = 68602653854733079 * c20848(1313215816......)

n=31311: c17641(1000000000......) = 31969422220711123 * c17624(3127988967......)

n=31323: c20379(1362968274......) = 9843076731466483 * c20363(1384697398......)

n=31591: c27067(4748163199......) = 1479905095244717 * c27052(3208424117......)

n=31599: c21035(6808399629......) = 36381436541083 * c21022(1871393841......)

n=31623: c20659(8775189140......) = 78311903963361427 * c20643(1120543454......)

n=31703: c27124(3264619431......) = 10724359641572921 * c27108(3044115957......)

n=31839: c21217(1445123315......) = 813101075359508797 * c21199(1777298491......)

n=31887: c21240(9999999990......) = 1556669739484723933 * c21222(6423970182......)

n=31899: c17619(2916746674......) = 47657200191260760349868653483 * c17590(6120264436......)

n=31923: c21271(2607830804......) = 7626507831393935166667 * c21249(3419429786......)

n=31989: c21324(9009009009......) = 127427212069600430597041 * c21301(7069925538......)

n=32013: c21323(2045478636......) = 510138494950595482603 * c21302(4009653567......)

n=32014: c16006(9090909090......) = 19050723251773769 * c15990(4771949584......)

n=32024: c16008(9999000099......) = 6915902704452529 * c15993(1445798260......)

n=32049: c21340(2890700525......) = 5706134399431 * c21327(5065952400......)

n=32073: c21380(9009009009......) = 22050042914917 * c21367(4085710419......)

n=32127: c21403(1420079092......) = 179334395568733 * c21388(7918609745......)

n=32128: c16000(9999999999......) = 1451436313547009 * c15985(6889727028......)

n=32163: c21001(1109999999......) = 1853442182963548357 * c20982(5988856896......)

n=32186: c11876(1553446320......) = 15741016671997 * c11862(9868780098......)

n=32198: c15116(1719789594......) = 38038218581773 * c15102(4521214868......)

n=32205: c16128(9009099100......) = 97109420550080639881 * c16108(9277265839......)

n=32207: c26702(8134305310......) = 5637001084284907 * c26687(1443020001......)

n=32221: c27593(4067942843......) = 3384313037658281 * c27578(1201999578......)

n=32242: c13519(7753801301......) = 1988077044431927 * c13504(3900151315......)

n=32277: c17472(9009009909......) = 101338406555769391 * c17455(8890025229......)

n=32308: c15665(4088488114......) = 1602735417139921 * c15650(2550943886......)

n=32336: c15450(6185053138......) = 7688707505535401281 * c15431(8044334024......)

n=32350: c12908(7283138029......) = 56359261320851 * c12895(1292269958......)

n=32351: c27515(1908079782......) = 37061065490879 * c27501(5148475246......)

n=32355: c17218(2147945932......) = 7979493128414761 * x17202(2691832549......)

n=32355: x17202(2691832549......) = 170500795147488135241 * c17182(1578780055......)

n=32391: c20881(1001000999......) = 374257484653681 * c20866(2674631880......)

n=32433: c20449(1109999999......) = 152052901817119117 * c20431(7300090867......)

n=32450: c11593(2304886470......) = 9592402492088691001 * c11574(2402825019......)

n=32461: c27096(5637126656......) = 7128074803775641 * c27080(7908343854......)

n=32487: c16111(1412643044......) = 6474713288317 * c16098(2181784708......)

n=32510: c12988(1343964587......) = 2631989937280831051 * c12969(5106267955......)

n=32542: c15895(1386687574......) = 1935278079263567 * c15879(7165314323......)

n=32600: c12961(1000000000......) = 19682476178801 * c12947(5080661553......)

n=32605: c26067(1134679269......) = 6802027927706624135170001 * c26042(1668148501......)

n=32619: c21307(3804032643......) = 22862753652241 * x21294(1663855850......)

n=32619: x21294(1663855850......) = 61122722048191 * c21280(2722156008......)

n=32627: c27145(1111110999......) = 669847183866253 * c27130(1658752961......)

n=32631: c21307(5669426468......) = 321867179709841 * c21293(1761418009......)

n=32654: c15719(2878449952......) = 17160603250810235009 * c15700(1677359420......)

n=32661: c20507(2970241666......) = 14231322920809 * c20494(2087115641......)

n=32680: c12096(9999000099......) = 90615948255121 * c12083(1103448155......)

n=32685: c17389(4803727536......) = 987250226519305111591 * c17368(4865764937......)

n=32775: c15836(1525514484......) = 44477864435551 * c15822(3429828532......)

n=32800: c12791(1102242419......) = 15606742076356801 * c12774(7062604187......)

n=32809: c27204(9101673257......) = 3044456856105001 * c27189(2989588516......)

n=32853: c21332(2231972724......) = 4272579371302597 * c21316(5223946778......)

n=32995: c26363(2833861452......) = 462551505764191 * c26348(6126585725......)

n=33003: c20737(1001000999......) = 815723693278727466529 * c20716(1227132432......)

n=33014: c15521(1099999999......) = 867375889255459 * c15506(1268192964......)

n=33033: c15826(4514769527......) = 304158658033231 * c15812(1484346872......)

n=33044: c14996(1528242218......) = 62019736447039141 * c14979(2464122400......)

n=33045: c17617(1109988900......) = 20277507529906856191 * c17597(5473990816......)

n=33049: c33043(1528184848......) = 174003734817720311056321 * c33019(8782483028......)

n=33068: c14148(1087846549......) = 2351792397455501281 * c14129(4625606199......)

n=33075: c15115(3779275210......) = 8814213220468951 * c15099(4287705681......)

n=33098: c14245(6408388564......) = 123371615552771 * c14231(5194378411......)

n=33117: c17712(9009009909......) = 215383080058609 * c17698(4182784417......)

n=33118: c15929(8215418428......) = 11958865121178940186496891 * c15904(6869730819......)

n=33136: c15553(1000000009......) = 3627520690543327793 * c15534(2756703807......)

n=33184: c15335(1854728143......) = 134475586348513 * x15321(1379230382......)

n=33184: x15321(1379230382......) = 2223446716722337 * c15305(6203118661......)

n=33218: c15617(1099999999......) = 36930332964407 * c15603(2978581322......)

n=33242: c15076(1675270460......) = 72005643134958721 * c15059(2326582177......)

n=33247: c33219(3930717930......) = 3232197227775889 * c33204(1216113266......)

n=33255: c17698(1048281401......) = 97837096245751 * c17684(1071455962......)

n=33280: c12289(1000000000......) = 72591121008641 * c12275(1377578946......)

n=33295: c26623(3011716029......) = 16966809438041 * c26610(1775063273......)

n=33304: c15822(2731807632......) = 27294720923273 * c15809(1000855674......)

n=33305: c26631(5455272880......) = 1527734267212511 * c26616(3570825762......)

n=33315: c17747(3168037399......) = 3774393981892869031 * c17728(8393499498......)

n=33364: c15769(1009999999......) = 155354151181529 * c15754(6501274618......)

n=33368: c16115(5956755193......) = 206446476942161 * c16101(2885375077......)

n=33370: c12864(1485144460......) = 7890344195608000681 * c12845(1882230259......)

n=33376: c14204(2996075141......) = 207618760888544321 * c14187(1443065707......)

n=33388: c15681(1009999999......) = 1023713634188029 * c15665(9866040328......)

n=33391: c33384(9243260715......) = 72905610216641 * c33371(1267839427......)

n=33408: c10730(2543330658......) = 666563556940924033 * c10712(3815586124......)

n=33413: c33396(2062751016......) = 152251659410659243 * c33379(1354829907......)

n=33427: c33414(2044299645......) = 874585346294027 * c33399(2337450146......)

n=33436: c15409(1009999999......) = 20566262186809 * c15395(4910955577......)

n=33457: c33449(1346720331......) = 26727390884016533 * c33432(5038727263......)

n=33470: c13354(4577074511......) = 3599311663690095481 * c13336(1271652732......)

n=33478: c15841(1099999999......) = 14411968809390133 * x15824(7632544966......)

n=33478: x15824(7632544966......) = 3485124844104899 * c15809(2190034879......)

n=33502: c14342(5158030749......) = 63336917294702423 * c14325(8143798230......)

n=33506: c15221(1099999999......) = 2763134811726917 * x15205(3980985637......)

n=33506: x15205(3980985637......) = 171263924417348291920249 * c15182(2324474141......)

n=33515: c26808(9000090000......) = 608064294625459681 * c26791(1480121441......)

n=33529: c33529(1111111111......) = 2981543823014435333 * c33510(3726630152......)

# 2554 of 9592 R_prime factorizations are still blank.

n=33550: c11994(3104786666......) = 373669015574801 * c11979(8308921899......)

n=33564: c11180(1504564331......) = 37188167114149 * c11166(4045814698......)

n=33572: c12960(9900990099......) = 38761778112289 * c12947(2554317830......)

n=33581: c33550(1306070907......) = 271710575513813 * c33535(4806846051......)

n=33595: c26872(9000090000......) = 3972872866509312881 * c26854(2265385856......)

n=33624: c11177(2052495570......) = 158594164515649 * c11163(1294181016......)

n=33625: c26781(1121294518......) = 9879631057001 * c26768(1134955861......)

n=33626: c14766(2940006771......) = 710582820601007 * c14751(4137458275......)

n=33627: c20353(1292450613......) = 729566716460020759 * c20335(1771531765......)

n=33645: c17931(1499597941......) = 6111742101001 * c17918(2453634195......)

n=33648: c11190(1619855960......) = 914587994626561 * c11175(1771131886......)

n=33657: c20689(1109999999......) = 852745618636632631 * c20671(1301677752......)

n=33682: c15292(2661428826......) = 20671420915289 * c15279(1287491961......)

n=33703: c33690(7579705829......) = 46770754293352757 * c33674(1620607993......)

n=33705: c15264(9990000009......) = 20582784696601 * c15251(4853570669......)

n=33706: c15938(4414980585......) = 3768529833931 * x15926(1171539242......)

n=33706: x15926(1171539242......) = 858684987611463619 * c15908(1364341125......)

n=33713: c33708(1647872678......) = 181707194707582879 * c33690(9068835614......)

n=33728: c15344(6957862320......) = 11016037666561 * c15331(6316120669......)

n=33754: c14445(3398097345......) = 3600039739677541671743 * c14423(9439055097......)

n=33764: c16099(1994230552......) = 75047460982969 * c16085(2657292500......)

n=33795: c17990(7501683160......) = 67406682402001 * c17977(1112899032......)

n=33805: c27035(1210159591......) = 3418610940707892991 * c27016(3539916102......)

n=33811: c33794(6227672997......) = 3041935307780641 * c33779(2047273320......)

n=33815: c27044(1330763998......) = 622629614069600351 * c27026(2137328467......)

n=33824: c14401(1000000000......) = 58268623132609 * c14387(1716189513......)

n=33825: c15990(2362463849......) = 4570638161476201 * c15974(5168783364......)

n=33827: c33808(1780537123......) = 49930155136573 * c33794(3566055659......)

n=33828: c11256(7534558360......) = 22023537405361 * x11243(3421139039......)

n=33828: x11243(3421139039......) = 31411903691914596785199841 * c11218(1089121841......)

n=33848: c16900(8589034735......) = 14105005435817 * c16887(6089352304......)

n=33855: c17280(9009099100......) = 32012685713591521 * c17264(2814227828......)

n=33886: c16915(4387719142......) = 1530454090205281 * c16900(2866939407......)

n=33888: c11265(1000000000......) = 11776409967457 * x11251(8491552202......)

n=33888: x11251(8491552202......) = 343520030000783809 * c11234(2471923457......)

n=33893: c33893(1111111111......) = 46942777581733237 * c33876(2366947948......)

# 2553 of 9592 R_prime factorizations are still blank.

n=33905: c27109(2330116922......) = 865104163995601 * c27094(2693452441......)

n=33906: c11283(2664220599......) = 7756029522860761 * c11267(3435031534......)

n=33910: c13561(1099989000......) = 12668854637291 * c13547(8682623896......)

n=33911: c33905(4095673289......) = 7231457983858813 * c33889(5663689533......)

n=33922: c14533(1099999890......) = 5795421859632637 * c14517(1898049730......)

n=33932: c15925(5375968153......) = 380912701536608209 * c15908(1411338643......)

n=33941: c33936(1636803192......) = 245938437659497613 * c33918(6655337034......)

n=33945: c17263(1189041152......) = 8557469306996533451041 * c17241(1389477554......)

n=33946: c15414(7715329588......) = 439289074124539 * c15400(1756321757......)

n=33947: c33446(3310323271......) = 14651960061071 * c33433(2259304050......)

n=33950: c11520(9999900000......) = 2098698155681226401 * c11502(4764810972......)

n=33954: c11317(1098901098......) = 99200264416447 * c11303(1107760251......)

n=33968: c15361(1000000009......) = 27239871180017 * c15347(3671089350......)

n=34005: c18086(3781500072......) = 7171620425795200321 * c18067(5272867006......)

n=34015: c27201(4021151762......) = 1408263073085471 * c27186(2855398141......)

n=34023: c20585(1201189409......) = 48235374753722773 * c20568(2490266564......)

n=34025: c27177(9831237912......) = 13912889448134401 * c27161(7066280480......)

n=34043: c33408(9000000000......) = 238565470522827911032253 * c33385(3772549304......)

n=34049: c33518(6460664509......) = 25715851628812559761 * c33499(2512327650......)

n=34065: c18119(1784100294......) = 1027566970423831 * c18104(1736237486......)

n=34093: c33635(8835917758......) = 174678107733297719 * c33618(5058400204......)

n=34125: c14400(9999999999......) = 19380254370751 * c14387(5159890994......)

n=34207: c33696(9000000000......) = 13759558729237 * c33683(6540907435......)

n=34241: c33765(1865220748......) = 3179549179630121 * c33749(5866305703......)

n=34277: c33893(1683120069......) = 3802275369579054959 * x33874(4426612766......)

n=34277: x33874(4426612766......) = 12995086166617170308732161 * c33849(3406374309......)

n=34291: c33581(1747586543......) = 203028824494976923 * x33563(8607578495......)

n=34291: x33563(8607578495......) = 380065094753685427 * c33546(2264764277......)

n=34315: c27426(2597617833......) = 17318494175641 * c27413(1499909753......)

n=34373: c33408(9000000000......) = 20503573944993230307871 * c33386(4389478646......)

n=34387: c34000(9000000000......) = 13436861374249 * c33987(6697992744......)

n=34393: c34013(1048402055......) = 45749124448799 * c33999(2291633048......)

n=34399: c33512(6124426752......) = 103952496706049 * c33498(5891562922......)

n=34435: c26881(1111099999......) = 28385546673935932772671 * c26858(3914316017......)

n=34445: c27224(9999999999......) = 64846943723801 * c27211(1542092722......)

n=34465: c26867(4954438096......) = 825839318855981932361 * c26846(5999276109......)

n=34495: c27583(5173295531......) = 859612561268471 * c27568(6018171167......)

n=34551: c20881(1001000999......) = 728975419763354083 * c20863(1373161526......)

n=34555: c27640(9000090000......) = 8136459349321 * c27628(1106143300......)

n=34565: c26641(1111099999......) = 1481454969353136641 * c26622(7500059218......)

n=34573: c26881(1111110999......) = 303679771997449 * c26866(3658824533......)

n=34597: c33367(5780848046......) = 4074841740760409 * c33352(1418668113......)

n=34609: c33904(9000000000......) = 166833393945737921 * c33887(5394603434......)

n=34655: c26657(1111099999......) = 44798080323193381511 * c26637(2480240206......)

n=34671: c18144(9009009909......) = 394188201896416201 * c18127(2285459043......)

n=34683: c20988(1674094999......) = 10688143575121 * c20975(1566310358......)

n=34715: c27018(2254418396......) = 112048761786641 * c27004(2011997599......)

n=34755: c15823(3545681099......) = 41406443856805441 * c15806(8563114262......)

n=34875: c18001(1000000000......) = 4549400614346307751 * c17982(2198091759......)

n=34945: c26881(1111099999......) = 1049799779988601 * c26866(1058392296......)

n=34983: c20586(1570621339......) = 12443403494107 * c20573(1262212014......)

n=35013: c21201(1109999999......) = 29515241583631 * c21187(3760768811......)

n=35045: c27217(1111099999......) = 532595300745421481764321 * c27193(2086199405......)

n=35213: c33660(9000000000......) = 4329190519920037 * c33645(2078910585......)

n=35405: c27636(7241897835......) = 811704356687317081 * c27618(8921841771......)

n=35418: c11764(6103580681......) = 32795738479117 * c11751(1861089569......)

n=35422: c17402(1437231571......) = 3376922896211 * c17389(4256039050......)

n=35443: c33391(2351187467......) = 375989509477717 * c33376(6253332627......)

n=35485: c27591(1256211360......) = 7675454133469961 * c27575(1636660631......)

n=35513: c33408(9000000000......) = 432723964640707 * x33394(2079847832......)

n=35513: x33394(2079847832......) = 3270475355864279 * c33378(6359466457......)

n=35557: c33480(9999999999......) = 3313494112785551 * c33465(3017962205......)

n=35587: c33696(9000000000......) = 87380684765878126111 * c33677(1029975906......)

n=35663: c33768(9000000000......) = 47572278947110787 * c33752(1891858073......)

n=35685: c17270(8313028830......) = 49167876111121 * c17257(1690743934......)

n=35891: c33979(1393104750......) = 1077316033779520921 * c33961(1293125421......)

n=35955: c17664(9990000009......) = 3433403391505561 * x17649(2909649368......)

n=35955: x17649(2909649368......) = 147384042276500274452671 * c17626(1974195661......)

n=36135: c17271(3412789637......) = 5725476260227351 * c17255(5960708738......)

n=36141: c20641(1109999889......) = 408283589699792689 * c20623(2718698270......)

n=36332: c17469(3843606238......) = 3145025921596189 * c17454(1222122276......)

n=36385: c27505(1111099999......) = 5001072159446791 * c27489(2221723591......)

n=36477: c20729(7969340996......) = 1552500043538288671 * c20711(5133230771......)

n=36532: c18264(9900990099......) = 12049037061923075029 * c18245(8217245949......)

n=36588: c12193(1009998990......) = 12481775574361 * c12179(8091789377......)

n=36635: c27521(1111099999......) = 2052530143006164751 * c27502(5413318794......)

n=36687: c20933(6700130193......) = 277545142906368751 * c20916(2414068617......)

n=36756: c12207(1773775758......) = 63996031488601 * c12193(2771696489......)

n=36813: c21008(1584584645......) = 65423916495253 * c20994(2422026577......)

n=36817: c33460(9000000000......) = 354778568274043 * c33446(2536793596......)

n=36971: c33584(2350205439......) = 5388857689667 * c33571(4361231218......)

n=37103: c33720(9000000000......) = 3908066867261572027 * c33702(2302928866......)

n=37125: c18001(1000000000......) = 1252871452800001 * c17985(7981664820......)

n=37146: c11953(2176762848......) = 7284437097583 * c11940(2988237552......)

n=37147: c33650(9846838301......) = 13454284124963967586643 * c33628(7318738188......)

n=37235: c27019(6823370263......) = 1768149192588241 * c27004(3859046675......)

n=37259: c33697(1111111111......) = 5986645340911 * c33684(1855982854......)

n=37359: c21313(1001000999......) = 904143068006564359 * c21295(1107126776......)

n=37374: c12457(1098901098......) = 4069202057545441 * c12441(2700532151......)

n=37417: c33601(1111111111......) = 33594343605959 * c33587(3307435097......)

n=37485: c16107(8926491323......) = 261625487894013601 * c16090(3411934897......)

n=37494: c12468(3490835779......) = 28375554485339407 * c12452(1230226454......)

n=37505: c27622(6846866758......) = 58575035588551 * c27609(1168905266......)

n=37565: c27281(1111099999......) = 4129205555527361 * c27265(2690832376......)

n=38325: c17280(9999900000......) = 140618146510801 * c17266(7111386579......)

n=38385: c20449(1001000999......) = 298592252796111423031 * c20428(3352401110......)

n=38533: c33589(7960643314......) = 100851811385099180751912227 * c33563(7893406380......)

n=38625: c20394(6813144736......) = 5279488407001 * c20382(1290493360......)

n=38685: c20618(2608454390......) = 2205831398166722551 * c20600(1182526639......)

n=38703: c20736(9009009909......) = 33911742453877 * c20723(2656604838......)

n=38913: c20719(5828316371......) = 1251072324082267 * c20704(4658656625......)

n=38955: c17460(1560088683......) = 40489654734181600921 * c17440(3853055042......)

n=38983: c33400(1183583969......) = 52523513070821227 * c33383(2253436414......)

n=39160: c14049(2867038195......) = 3594022648663921 * x14033(7977240199......)

n=39160: x14033(7977240199......) = 236160887684927041 * c14016(3377883729......)

n=39375: c18001(1000000000......) = 17597042111191803751 * c17981(5682773239......)

n=39400: c15639(3096069318......) = 77792051018239601 * c15622(3979930182......)

n=39457: c33601(1111111111......) = 588352726209799 * c33586(1888511876......)

n=39529: c33859(8756573313......) = 5354242183711 * c33847(1635445878......)

n=39557: c33891(9058759519......) = 498706544738837 * c33877(1816450899......)

n=39825: c20839(9533424659......) = 1486189455058351 * c20824(6414676558......)

n=39855: c21238(1964056959......) = 101334458624761 * c21224(1938192581......)

n=39927: c26616(9009009009......) = 4281255872544043 * c26601(2104291188......)

n=39935: c27217(1000000100......) = 26663773005241 * c27203(3750407340......)

n=39939: c26616(8550766343......) = 2934490173138961 * c26601(2913884810......)

n=39945: c21297(1109988900......) = 57205090698001 * c21283(1940367345......)

n=39963: c20633(7773577742......) = 2477291270539933 * c20618(3137934499......)

n=40005: c18144(9990000009......) = 152570301565202641 * c18127(6547801182......)

n=40023: c26661(2804719530......) = 7355161223043772431547 * c26639(3813267235......)

n=40065: c21361(1109988900......) = 113239499228518385911 * c21340(9802135364......)

n=40101: c26724(4974711307......) = 10210801866032191 * c26708(4872008459......)

n=40131: c21169(1000000000......) = 2332407469917799 * x21153(4287415526......)

n=40131: x21153(4287415526......) = 422631193813341787 * c21136(1014457898......)

n=40143: c26760(9009009009......) = 5214981702127129 * c26745(1727524567......)

n=40155: c21409(1109988900......) = 123072198146423401 * c21391(9019006052......)

n=40183: c33601(1111111111......) = 14217479382679 * x33587(7815106188......)

n=40183: x33587(7815106188......) = 873603644235323 * c33572(8945825993......)

n=40205: c26871(3554607995......) = 34164116008111 * c26858(1040450744......)

n=40369: c33686(2798085057......) = 654486976942093 * c33671(4275234123......)

n=40419: c26892(9999999999......) = 742424500998673474159 * c26872(1346938306......)

n=40515: c20736(9009099100......) = 344465691673850819154001 * c20713(2615383568......)

n=40617: c27055(6552200228......) = 7143810708783595519 * c27036(9171855883......)

n=40671: c27108(9990000009......) = 1744938426011041 * c27093(5725130389......)

n=40683: c26601(1109999999......) = 191836530731551 * c26586(5786176364......)

n=40731: c27139(5387226890......) = 625864906330717 * c27124(8607651325......)

n=41007: c27327(5411992366......) = 50324548235112397 * c27311(1075417973......)

n=41079: c27377(3930275014......) = 24909536601121 * c27364(1577819401......)

n=41103: c27378(6741582253......) = 137382660048079 * c27364(4907156588......)

n=41169: c27432(1398782338......) = 37710950067613 * c27418(3709220626......)

n=41187: c27450(7811931987......) = 165223425034069471 * c27433(4728101953......)

n=41205: c21112(1270724860......) = 88270208640871 * c21098(1439585200......)

n=41229: c27422(7712659668......) = 33841135910161 * c27409(2279078246......)

n=41373: c27566(1366816614......) = 200204779263491355841 * c27545(6827092838......)

n=41385: c21112(5716648139......) = 541783925848111 * c21098(1055152777......)

n=41427: c27599(1489815315......) = 3507514081430041 * c27583(4247496319......)

n=41511: c27191(1074426632......) = 112414704479839 * c27176(9557705441......)

n=41531: c33403(4458944487......) = 11809061675363 * c33390(3775866880......)

n=41565: c20725(4806319845......) = 194951713716394081 * c20708(2465389892......)

n=41595: c21332(3616058919......) = 766408583403511 * c21317(4718186875......)

n=41815: c33426(1690545222......) = 75431165020961 * x33412(2241176073......)

n=41815: x33412(2241176073......) = 8461666422377819351 * c33393(2648622577......)

n=41856: c13811(4942745791......) = 168938210573953 * c13797(2925771366......)

n=41919: c27450(2135454371......) = 108804715365751 * c27436(1962648736......)

n=41961: c27441(1109999999......) = 37729046433452797 * c27424(2942030358......)

n=42117: c27575(1461446643......) = 60803614860338827 * c27558(2403552233......)

n=42245: c26880(9000090900......) = 27992612980151 * c26867(3215166410......)

n=42299: c42286(7202806127......) = 96637904755128881 * x42269(7453396413......)

n=42299: x42269(7453396413......) = 11931152812771725094049 * c42247(6247004401......)

December 10, 20102010 年 12 月 10 日 (Serge Batalov)

n=32184: c10620(5629084982......) = 84380889754390609 * p10603(6671042459......)

# Phi_32184(10) is the 1011th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

```Primality testing 6671042459...... [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 12+sqrt(13)
Calling N-1 BLS with factored part 0.07% and helper 0.03% (0.26% proof)
6671042459...... is Fermat and Lucas PRP! (46.3540s+0.0849s)
```

n=18967: c17452(2537641746......) = 195795560630856161 * c17435(1296067050......)

n=18905: c14233(2474865681......) = 10011473155121627641 * c14214(2472029483......)

n=18901: c18364(8089244528......) = 363280422116171549042467 * c18341(2226721848......)

n=18683: c14936(1044431853......) = 6986932161202867512563 * x14914(1494836115......)

n=18683: x14914(1494836115......) = 99400047550117990369 * c14894(1503858551......)

n=33674: c16577(1099999999......) = 355360745420327 * c16562(3095446005......)

n=30879: c19862(1742616566......) = 7607169871712569 * c19846(2290755426......)

n=32010: c7681(1098890109......) = 14652498759881401 * c7664(7499677208......)

n=32640: c8175(1412744251......) = 950905911486721 * c8160(1485682478......)

n=32802: c8387(2925116849......) = 2581089042293139379 * c8369(1133287849......)

n=33120: c8448(9999999999......) = 9480975047175792961 * c8430(1054743837......)

n=32850: c8609(3180540683......) = 89227225973147851 * c8592(3564540586......)

n=37800: c8633(1193818869......) = 12188562355077847201 * c8613(9794583104......)

n=33510: c8928(9100090999......) = 3593218194090211 * c8913(2532574007......)

n=33750: c9001(1000000000......) = 26495963561251 * c8987(3774159779......)

n=32634: c9058(7151879120......) = 13020319190101416607 * c9039(5492860057......)

n=33348: c9495(1780548644......) = 226045822683289729 * c9477(7876936733......)

n=33768: c9496(7228175584......) = 12398242248257731993 * c9477(5830000285......)

n=33642: c9504(9999999990......) = 759402805555939655881 * c9484(1316824209......)

n=33474: c9552(9100000909......) = 4605942028927 * c9540(1975708954......)

n=33894: c9648(9990010000......) = 5075563641586303699 * c9630(1968256277......)

n=33198: c10040(9100000000......) = 31235461554331 * c10027(2913355381......)

n=33384: c10165(3647037486......) = 34990334589601 * c10152(1042298545......)

n=33924: c10222(5007241926......) = 37287095261461 * c10209(1342888710......)

n=32712: c10300(3056583040......) = 108658863546721 * c10286(2813008474......)

n=33744: c10345(1796043717......) = 535213056345073 * c10330(3355754678......)

n=33252: c10368(9901000000......) = 75836447098189 * x10355(1305572765......)

n=33252: x10355(1305572765......) = 78872426356249 * c10341(1655296820......)

n=32200: c10536(1347329646......) = 651512753497201 * c10521(2068001953......)

n=32574: c10546(2222062361......) = 12622395149023531 * c10530(1760412612......)

n=33234: c10623(4797659001......) = 41778662598637 * c10610(1148351503......)

n=33078: c10656(9100000000......) = 5442318113677 * c10644(1672081603......)

n=32562: c10688(1023677664......) = 5371915839175341952453 * c10666(1905610018......)

n=37632: c10714(1294434276......) = 5413928323112622571777 * c10692(2390933531......)

n=33582: c10726(1359359442......) = 17593080707496739 * c10709(7726670869......)

n=33756: c10733(1464640471......) = 4940491416357709 * c10717(2964564347......)

n=33408: c10744(1018959360......) = 40063975028353 * c10730(2543330658......)

n=32352: c10745(1298193603......) = 58674140753525569 * c10728(2212548129......)

n=32484: c10814(5269891020......) = 1181629848707041 * c10799(4459849272......)

n=32622: c10873(1098901098......) = 43168218471853 * c10859(2545625318......)

n=33654: c10920(9100000000......) = 259389157340893 * c10906(3508242246......)

n=33156: c10989(2129564947......) = 774090019480501 * c10974(2751055941......)

n=33084: c11012(1511283229......) = 6219668573686621 * c10996(2429845274......)

n=33126: c11032(1071387504......) = 9212061472274383 * c11016(1163026872......)

n=33186: c11050(2147682230......) = 4838355880891675663 * c11031(4438867837......)

n=33204: c11065(1009998990......) = 14458927540546129 * c11048(6985296711......)

n=33318: c11080(6385916210......) = 7100795997289 * c11067(8993239931......)

n=33378: c11108(9370684858......) = 47995531110406651 * c11092(1952407784......)

n=33438: c11122(1448154216......) = 7982985992574127 * c11106(1814050804......)

n=33468: c11147(6035574007......) = 80692351370641 * c11133(7479734950......)

n=33160: c13249(1000099999......) = 102135482470693172881 * c13228(9791895782......)

n=33920: c13300(1256004276......) = 6818608499680001 * c13284(1842024331......)

n=33470: c13370(1440359323......) = 3146899444344001 * c13354(4577074511......)

n=30135: c13440(9999999000......) = 893333882578127761 * c13423(1119402184......)

n=33680: c13441(1000000009......) = 2181737247571201 * c13425(4583503403......)

n=33710: c13463(4091833804......) = 12928403878976107601 * c13444(3164995340......)

n=33916: c16555(9926387482......) = 371054365717649701 * c16538(2675184123......)

n=33148: c16540(6337244151......) = 89298344238361 * c16526(7096709581......)

n=33122: c16536(1014632242......) = 84875831627601062837 * c16516(1195431282......)

n=31035: c16533(5087531522......) = 93601539889321 * c16519(5435307504......)

n=33104: c16529(7179577847......) = 190123315878124289 * c16512(3776274264......)

n=33562: c16501(8539948884......) = 436433405010259 * c16487(1956758760......)

n=33056: c16487(3725518317......) = 36800243322796609 * c16471(1012362414......)

n=33008: c16481(9297959200......) = 15364439264408177 * c16465(6051609850......)

n=32932: c16464(9900990099......) = 8716968480712963129 * c16446(1135829516......)

n=33818: c16410(1758218994......) = 9139254168689 * c16397(1923810151......)

n=37905: c16406(1008593652......) = 7195029456721 * c16393(1401792249......)

n=30795: c16398(1225243231......) = 153959523078278431 * c16380(7958216595......)

n=30735: c16364(1628411771......) = 36913019729041 * c16350(4411483491......)

n=33394: c16357(1099999999......) = 2670789894679757863 * c16338(4118631728......)

n=32684: c16335(2524416854......) = 12666905372629 * c16322(1992923117......)

n=33976: c16321(1000099999......) = 3634693181939437443668510929 * c16293(2751538988......)

n=31647: c16313(1353003049......) = 3128845675850203 * c16297(4324288220......)

n=33454: c16297(1099999999......) = 62322563927401 * c16283(1765010825......)

n=30645: c16273(1000000001......) = 4011371807413506751 * c16254(2492912771......)

n=30465: c16225(1001000999......) = 1569431241792721 * c16209(6378113123......)

n=33178: c16220(3315350070......) = 41279046176955186920183 * c16197(8031556874......)

n=33284: c16215(1259647590......) = 2550287025274141 * c16199(4939238518......)

n=33496: c16213(2176631835......) = 14737735614227073841 * c16194(1476910627......)

n=33182: c16185(7517120412......) = 32633466333899 * c16172(2303500442......)

n=32918: c16168(5417568959......) = 2630945429915717 * c16153(2059171922......)

n=33248: c16586(7471362492......) = 5474470053761 * c16574(1364764519......)

n=33272: c16614(1759863379......) = 442563519119737 * c16599(3976521568......)

n=33536: c16635(1754038234......) = 42838872918529 * c16621(4094501360......)

n=32595: c16640(9009099100......) = 29786616103801 * c16627(3024546013......)

n=33386: c16672(8478844050......) = 1608290408798216743 * c16654(5271960837......)

n=34515: c16691(1907766755......) = 2279838106296271 * x16675(8367992228......)

n=34515: x16675(8367992228......) = 93292106303011591 * c16658(8969668024......)

n=32745: c16694(6043842341......) = 1119944168313121 * c16679(5396556821......)

n=33416: c16695(2252204709......) = 23100987085817 * c16681(9749387336......)

n=36645: c16699(1756053727......) = 16902766282921 * c16686(1038914990......)

n=33476: c16736(9900990099......) = 212376422271001 * c16722(4662000608......)

n=31485: c16779(5875724018......) = 60751424776711 * c16765(9671746859......)

n=33574: c16786(9090909090......) = 16326256811260354201 * c16767(5568275199......)

n=32625: c16801(1000000000......) = 2386407099942001 * x16785(4190399869......)

n=32625: x16785(4190399869......) = 191972191414644001 * c16768(2182816083......)

n=31521: c16848(9009009909......) = 4825257077435677 * c16833(1867052835......)

n=33736: c16848(1794176587......) = 1483698227610317569 * c16830(1209259776......)

n=33772: c16876(4462276466......) = 49743498481321 * c16862(8970572241......)

n=33766: c16878(2692246599......) = 33473861193536809 * c16861(8042832535......)

n=37065: c16878(1710136301......) = 51774051320888648641 * c16858(3303076073......)

n=33776: c16880(9999999900......) = 90750490221233 * c16867(1101922411......)

n=33808: c16896(9999999900......) = 9828354942920777729 * c16878(1017464261......)

n=33832: c16899(4263218988......) = 909675285385169 * c16884(4686528321......)

n=33848: c16914(6285291575......) = 73178090080633 * c16900(8589034735......)

n=33842: c16920(9090909090......) = 30118377148135459 * c16904(3018392739......)

n=33886: c16931(1999259579......) = 4556489408163437 * c16915(4387719142......)

n=33868: c16932(9900990099......) = 8853930274842869 * c16917(1118259325......)

n=33952: c16954(3236630370......) = 11157237788388193 * c16938(2900924432......)

n=33962: c16980(9090909090......) = 15372813036521 * c16967(5913627564......)

n=33974: c16980(4955262158......) = 267356378749489 * c16966(1853429561......)

n=32055: c17089(1109988900......) = 16771908764478001 * c17072(6618142965......)

n=32115: c17113(3630561073......) = 618704938905121 * c17098(5868000795......)

n=37947: c19866(6594726647......) = 2199487090970443 * c19851(2998302047......)

n=40185: c19872(9990000009......) = 11084444224502401 * c19856(9012630500......)

n=34797: c19873(1109999889......) = 25445424003049 * c19859(4362277039......)

n=38577: c19902(4653399854......) = 424245068589338997001 * c19882(1096865985......)

n=41415: c19988(1562929460......) = 673806883827001 * c19973(2319551043......)

n=31749: c20017(1109999999......) = 1026234696792592405081 * c19996(1081623924......)

n=30117: c20050(4628992884......) = 391880317012369 * c20036(1181226176......)

n=30123: c20069(8208917028......) = 2029585146002173 * c20054(4044628058......)

n=30111: c20072(9009009009......) = 1832115672223729 * c20057(4917270861......)

n=37725: c20081(1000010000......) = 4443767774479658682601 * c20059(2250365119......)

n=30213: c20084(1654889370......) = 99706636621207910467 * c20064(1659758494......)

n=30207: c20136(9009009009......) = 256337102409163 * c20122(3514516207......)

n=32283: c20140(3885398488......) = 93139111761769 * x20126(4171607839......)

n=32283: x20126(4171607839......) = 336348766644679 * x20112(1240262564......)

n=32283: x20112(1240262564......) = 80233212760553130121 * c20092(1545821888......)

n=41535: c20145(3616002753......) = 72215651887471 * c20131(5007228570......)

n=33561: c20148(3472957544......) = 128450560499119 * c20134(2703730938......)

n=30237: c20149(6505382123......) = 85917400562477761 * c20132(7571670093......)

n=32877: c20152(4377062565......) = 3900335755206934369 * x20134(1122227121......)

n=32877: x20134(1122227121......) = 94441403737082274002443 * c20111(1188278738......)

n=31191: c20153(1412190006......) = 60853163840083 * c20139(2320651741......)

n=37023: c20160(9009009909......) = 3690764481915253 * c20145(2440960390......)

n=37323: c20160(9990000009......) = 1446716894470849 * c20145(6905290211......)

n=40455: c20160(9990000009......) = 29297179016368557841 * c20141(3409884618......)

n=35469: c20233(1001000999......) = 12642810768883 * c20219(7917551075......)

n=33111: c20295(1193625739......) = 233409425873599 * c20280(5113871192......)

n=35553: c20305(1109999889......) = 173980468477201 * c20290(6380025865......)

n=39027: c26009(8244299902......) = 785629529646853 * c25995(1049387731......)

n=39051: c26017(2979410236......) = 144692475122577871 * c26000(2059132815......)

n=40119: c26041(1109999999......) = 257549234972137729 * c26023(4309855550......)

n=40917: c26049(1109999999......) = 63357425534569 * c26035(1751965125......)

n=32605: c26080(9000090000......) = 79318361066831 * c26067(1134679269......)

n=32039: c26113(3691027352......) = 56703140267105711 * c26096(6509387901......)

n=32675: c26120(9999900000......) = 4708876628178137801 * c26102(2123627520......)

n=39279: c26175(3250466665......) = 5295264914959 * c26162(6138440130......)

n=39309: c26185(5065322046......) = 1670672425366667359477 * c26164(3031906177......)

n=33755: c26194(6372516075......) = 4108831689969161 * c26179(1550931397......)

n=38255: c26194(1182440148......) = 2120918902025071 * c26178(5575131361......)

n=32755: c26195(1526497182......) = 14884950818681 * c26182(1025530551......)

n=38465: c26196(7801541786......) = 154817773128955726441 * c26176(5039177110......)

n=33761: c26198(1218512963......) = 2141707783207721 * c26182(5689445465......)

n=41499: c26203(2409690814......) = 973019985471307 * c26188(2476507010......)

n=41871: c26231(3134754869......) = 23442369192493 * c26218(1337217600......)

n=39609: c26244(9999999999......) = 27177383981107 * c26231(3679530011......)

n=39453: c26300(9009009009......) = 4502907106611391 * c26285(2000709496......)

n=41973: c26305(1109999999......) = 10173037983001 * c26292(1091119488......)

n=40737: c26325(1709488503......) = 21493106234923 * c26311(7953659580......)

n=30737: c26340(9000000900......) = 4200543919415201 * c26325(2142579883......)

n=41781: c26353(1109999999......) = 139245404890147 * c26338(7971537738......)

n=39549: c26364(9009009009......) = 12534733226253913231 * c26345(7187236334......)

n=30349: c26370(7909175861......) = 74526128284169 * c26357(1061262143......)

n=32995: c26379(4613295333......) = 16279184465251921 * c26363(2833861452......)

n=35075: c26382(8693003867......) = 98669481447751 * c26368(8810225552......)

n=39215: c26388(9885967377......) = 18992228164151441 * c26372(5205269909......)

n=30199: c26392(9581504333......) = 20663894448832658609 * c26373(4636833757......)

n=34111: c26513(3457897211......) = 90241554100391 * c26499(3831823649......)

n=30947: c26515(4846970858......) = 135109467211867 * c26501(3587439843......)

n=39807: c26532(9990000009......) = 255127958754695722369 * c26512(3915682177......)

n=39891: c26578(3439003857......) = 53511067581973 * c26564(6426715094......)

n=34003: c33043(6617014550......) = 151200595575959 * c33029(4376315136......)

n=33491: c33050(2603843786......) = 259984470220105458467 * c33030(1001538201......)

n=41345: c33054(6654314280......) = 22701343674182431 * c33038(2931242474......)

n=36517: c33071(1886792452......) = 13841395941828599 * c33055(1363151853......)

n=41365: c33077(5176776240......) = 16700204666231 * c33064(3099828022......)

n=33107: c33107(1111111111......) = 27120974615325347 * c33090(4096870141......)

n=33701: c33112(2028832339......) = 9877620207761 * c33099(2053968766......)

n=38647: c33114(2042781028......) = 541156274528773 * c33099(3774844946......)

n=33149: c33131(1637055952......) = 69130484056981439 * c33114(2368066670......)

n=33161: c33138(8096279624......) = 15098816230216027 * c33122(5362194956......)

n=38689: c33146(1041877133......) = 646628991098231 * c33131(1611244078......)

n=38717: c33180(9000000900......) = 13894302577289 * c33167(6477475821......)

n=33659: c33216(9000000000......) = 47159934630119 * c33203(1908399591......)

n=33247: c33232(6307731064......) = 16047274765439 * c33219(3930717930......)

n=37973: c33245(8580774135......) = 2434174366465391161 * c33227(3525127145......)

n=33667: c33269(4319928474......) = 212271143286347 * c33255(2035099263......)

n=41675: c33320(9999900000......) = 167982092959024424551 * c33300(5952955951......)

n=33329: c33329(1111111111......) = 100416525950966443 * c33312(1106502242......)

n=38899: c33329(2203508886......) = 3917901473168703663825001 * c33304(5624206994......)

n=33359: c33352(2108081018......) = 39829804018841 * c33338(5292722549......)

n=38941: c33356(2245338735......) = 96562383746822762231 * c33336(2325272687......)

December 9, 20102010 年 12 月 9 日 (Kurt Beschorner)

n=8083: c7846(1347818048......) = 7267026788765657483272147 * c7821(1854703563......)

n=11313: c7502(2182872934......) = 342837206057487733201 * c7481(6367082966......)

n=11481: c7379(3614563150......) = 1222860207186302454542413 * c7355(2955826945......)

December 9, 20102010 年 12 月 9 日 (Serge Batalov)

n=8639: c8414(1076696545......) = 729377770607137999 * c8396(1476185028......)

n=8713: c8693(1533454258......) = 260719178850594761951 * c8672(5881631973......)

n=8929: c8887(2304886774......) = 9170422397484779479 * c8868(2513392158......)

n=9459: c6296(5280405946......) = 950587642557703686186015733 * c6269(5554885956......)

n=9563: c9360(9000000000......) = 2321066266088618287995799 * c9336(3877528242......)

n=9707: c9105(2900713855......) = 30819013866243047738641 * c9082(9412091729......)

n=22899: c14327(3818272454......) = 66533244672982441 * c14310(5738894101......)

n=22911: c13064(1045241470......) = 3734756967986773 * c13048(2798686714......)

n=22917: c15276(9009009009......) = 222470436886561 * c15262(4049530865......)

n=22933: c20156(1211244711......) = 19675991127601 * c20142(6155952722......)

n=22959: c15288(1571996511......) = 24453321727769317 * c15271(6428560214......)

n=22961: c22951(7840954276......) = 145174459730266163 * c22934(5401056281......)

n=22963: c22951(1003411242......) = 124359027346626102460580551 * c22924(8068664288......)

n=22979: c20864(1558228956......) = 33184654217422951 * c20847(4695631136......)

n=22997: c20161(1111111111......) = 1039093307161729 * c20146(1069308312......)

n=22999: c22675(9782927704......) = 504025237108427 * c22661(1940959893......)

n=23003: c22987(8783745291......) = 29944105011449 * x22974(2933380472......)

n=23003: x22974(2933380472......) = 1399957667065267 * c22959(2095335124......)

n=23005: c17803(1006211506......) = 74479582302481 * x17789(1350989728......)

n=23005: x17789(1350989728......) = 3167842776156601 * c17773(4264699429......)

n=23037: c13146(2769157492......) = 162685920626209 * c13132(1702149443......)

n=23055: c11641(3672608135......) = 3870795028362511 * c11625(9487994349......)

n=23065: c15774(4341786409......) = 225806145367321 * c15760(1922793731......)

n=23085: c11665(1000000000......) = 923612125443034510081 * c11644(1082705577......)

n=23101: c21312(9000000000......) = 2336875761902181319 * c21294(3851295882......)

n=23105: c18466(4541983734......) = 45921014424511481 * c18449(9890861060......)

n=23113: c22283(6489807396......) = 37193812344414199 * c22267(1744862112......)

n=23129: c22795(1297071069......) = 297605138101559 * c22780(4358362485......)

n=23135: c15836(2401287823......) = 476023065420281 * c15821(5044477879......)

n=23147: c22768(1929241265......) = 282677150430836081 * c22750(6824892858......)

n=23153: c21185(3493679040......) = 57998649432413 * c21171(6023724819......)

n=23155: c16760(1520948118......) = 369009812468449681 * c16742(4121701015......)

n=23167: c23158(2077490276......) = 143744157105221587 * c23141(1445269371......)

n=23169: c15426(2442720849......) = 51925070837988769 * c15409(4704318761......)

n=23177: c17624(1128464854......) = 17886629449075176791 * c17604(6308985480......)

n=23207: c22176(9000000000......) = 815393463056761 * c22162(1103761608......)

n=23229: c14785(1001000999......) = 3117252469245586271569 * c14763(3211164350......)

n=23231: c21421(4169116180......) = 949901858852831 * x21406(4388996759......)

n=23231: x21406(4388996759......) = 8968988534217443161 * c21387(4893524774......)

n=23233: c19891(2251812851......) = 13279297658831 * c19878(1695731889......)

n=23259: c15499(2766665236......) = 13479531326551 * c15486(2052493643......)

n=23265: c11035(2683745210......) = 400735215072721 * c11020(6697053590......)

n=23275: c15113(3836120767......) = 2569026398467201 * c15098(1493219676......)

n=23285: c18624(9000090000......) = 3606709568639950725047761 * c18600(2495374199......)

n=23303: c19951(5292515513......) = 941294149206470921 * c19933(5622594720......)

n=23313: c14673(1114489608......) = 124780526657797 * c14658(8931598853......)

n=23333: c23317(1209908758......) = 20234228035471 * c23303(5979515286......)

n=22390: c8953(1099989000......) = 9104983072295781961 * c8934(1208117567......)

n=22365: c10032(4439317497......) = 10465789404230352991 * c10013(4241741665......)

n=23407: c23013(1798776527......) = 367432385988846799 * c22995(4895530703......)

n=23469: c15623(1468759538......) = 75907177099407397 * c15606(1934941588......)

n=23819: c23760(5619465096......) = 649786447451597 * c23745(8648172208......)

n=23965: c19142(2247982364......) = 3762433527651341281 * c19123(5974809517......)

December 9, 20102010 年 12 月 9 日 (Makoto Kamada)

n=72600: c17594(2550759475......) = 5942020761601 * c17581(4292747498......)

n=72631: c64801(1111111111......) = 6387510924653 * c64788(1739505613......)

n=72636: c24201(4634978723......) = 7548291209029 * c24188(6140434430......)

n=36321: c24202(4062756101......) = 5814704365039 * c24189(6987038113......)

n=72753: c48481(8641290140......) = 6538856738959 * c48469(1321529203......)

n=36379: c31176(9000000900......) = 8807735842277 * c31164(1021829112......)

n=72768: c24193(1000000000......) = 7533905061889 * c24180(1327332892......)

n=72792: c24183(6046555181......) = 5442183527329 * c24171(1111053155......)

n=72850: c27577(1251951416......) = 8409869346451 * c27564(1488669281......)

n=36465: c15351(4776525808......) = 6350736523561 * c15338(7521215516......)

n=36489: c24317(3663153735......) = 5580586135519 * c24304(6564102133......)

n=72995: c53842(1571138550......) = 7487090288471 * c53829(2098463475......)

n=18261: c12135(1566141254......) = 9831580840729 * c12122(1592969919......)

n=73088: c36480(9999999999......) = 7831195456769 * c36468(1276944248......)

n=73181: c73173(1311144586......) = 7559266521881 * c73160(1734486518......)

n=73195: c58541(2929363621......) = 5531965672481 * c58528(5295339478......)

n=73307: c67656(9000000000......) = 5975373353639 * c67644(1506182035......)

n=73535: c45593(3708846346......) = 5517568862191 * c45580(6721885016......)

n=73554: c21108(3142053813......) = 5208783808567 * c21095(6032221588......)

n=36785: c25180(8786836708......) = 9532796185711 * c25167(9217480933......)

n=73607: c73587(1455780619......) = 6981679596893 * c73574(2085143838......)

December 8, 20102010 年 12 月 8 日 (Serge Batalov)

n=22351: c18351(9463888671......) = 3640727722708987 * c18336(2599449723......)

n=22361: c21919(5031052775......) = 13043059495001 * x21906(3857264300......)

n=22363: c19069(2086536781......) = 167644843230173 * c19055(1244617335......)

n=22365: c10067(5074250834......) = 134077275483054751 * x10050(3784571856......)

n=22377: c14916(9009009009......) = 73588643264282479 * c14900(1224239041......)

n=22383: c14896(3587342493......) = 30470090038831 * c14883(1177332422......)

n=22403: c21830(1480322199......) = 23226740645368919 * x21813(6373353118......)

n=22403: x21813(6373353118......) = 153912368609020129 * c21796(4140897301......)

n=22409: c22400(2634324335......) = 117265932181481 * x22386(2246453242......)

n=22409: x22386(2246453242......) = 15662795130387283 * c22370(1434260758......)

n=22413: c14394(8843712478......) = 27930511038826831 * c14378(3166326769......)

n=22417: c21609(8061867126......) = 5072953353626597 * c21594(1589186133......)

n=22435: c15361(1111099888......) = 1373207912428591 * c15345(8091272114......)

n=22437: c14889(6080388108......) = 4650521652303011479 * c14871(1307463670......)

n=22449: c12817(1109999889......) = 617352098247347569 * c12799(1798001322......)

n=22451: c18710(3061602320......) = 16358336208887490533 * c18691(1871585399......)

n=22463: c19232(7721975893......) = 68391700383959 * x19219(1129080846......)

n=22465: c17968(9000090000......) = 31829720672986194674502641 * c17943(2827574295......)

n=22471: c21441(4152799921......) = 47505623135351 * c21427(8741701817......)

n=22475: c16801(1000010000......) = 36505702864852944011551 * c16778(2739325424......)

n=22482: c7477(1589957444......) = 29274933126299554056277 * c7454(5431122380......)

n=22493: c22126(9288037406......) = 13746410573003 * c22113(6756700126......)

n=22515: c11215(6210287762......) = 888417345689510431 * c11197(6990281980......)

n=22517: c19354(1265267364......) = 50748748760293 * x19340(2493199133......)

n=22519: c19275(4016819439......) = 18955132070729 * c19262(2119119732......)

n=22525: c16627(7313076378......) = 834909935397001 * c16612(8759120078......)

n=22531: c22515(2968040449......) = 35360729320151 * c22501(8393606429......)

n=22551: c15016(1597304903......) = 77747136323191 * c15002(2054487122......)

n=22565: c18041(5617630094......) = 1801940837718871 * c18026(3117544137......)

n=22571: c22558(5569659738......) = 318559512745488319 * c22541(1748389081......)

n=22577: c22243(7761939084......) = 10492096234693 * c22230(7397891623......)

n=22585: c18052(7160855553......) = 713254670721431 * c18038(1003968967......)

n=22589: c19309(4688731136......) = 327933072423881 * c19295(1429782943......)

n=22595: c18068(1991566905......) = 355937392433881 * c18053(5595273066......)

n=22599: c14574(1324842506......) = 5000426016962239 * x14558(2649459269......)

n=22599: x14558(2649459269......) = 18443865548430667 * c14542(1436498906......)

n=22607: c19862(3293527753......) = 197361493410797 * c19848(1668779302......)

n=22609: c21598(5528768331......) = 55149410524682471 * c21582(1002507239......)

n=22617: c12889(1001000999......) = 2462360830695490004281 * c12867(4065208427......)

n=22629: c14257(1109999999......) = 45878036270653813 * c14240(2419458394......)

n=22631: c18713(4675891069......) = 23402559769289 * c18700(1998025478......)

n=22639: c22627(2701564926......) = 11758750315904031157 * x22608(2297493231......)

n=22639: x22608(2297493231......) = 157426741969397991001 * c22588(1459404674......)

n=22647: c15096(9009009009......) = 35939931994671877 * c15080(2506685046......)

n=22655: c17241(4279612493......) = 169259109546431 * c17227(2528438501......)

n=22659: c11787(1076077920......) = 578795880748222957 * c11769(1859166514......)

n=22681: c22025(1838776148......) = 1338081482838982036721 * c22004(1374188471......)

n=22685: c16692(2516447493......) = 705036005160761 * c16677(3569246782......)

n=22689: c15103(2227429325......) = 5452782288109777333 * c15084(4084940876......)

n=22695: c11252(8553468986......) = 10582085969098976534071 * c11230(8082970608......)

n=22719: c15112(3945043610......) = 34764263999192041 * c15096(1134798542......)

n=22729: c18241(1111110999......) = 53337336880549877 * x18224(2083176748......)

n=22729: x18224(2083176748......) = 84222917959966717 * c18207(2473408424......)

n=22733: c22410(7499980678......) = 8192332610430281 * c22394(9154878146......)

n=22739: c22721(1445395275......) = 53636865075881 * c22707(2694779557......)

n=22759: c20680(9000000000......) = 6997501848110533 * c20665(1286173293......)

n=22765: c17473(1111099999......) = 22768505737833310921 * c17453(4879986472......)

n=22771: c19512(9000000900......) = 214615407199572443 * c19495(4193548365......)

n=22789: c21017(2345174388......) = 979992270157213 * c21002(2393053965......)

n=22793: c21764(2051051277......) = 10633903059724649 * c21748(1928785005......)

n=22837: c22232(5493410870......) = 123712768819351 * c22218(4440455842......)

n=22851: c15223(3643153318......) = 5705655300355951 * c15207(6385161961......)

n=22873: c22518(7167655052......) = 278968881541409 * c22504(2569338563......)

n=22875: c11995(2428652267......) = 662377944447001 * c11980(3666565724......)

n=19309: c19281(6643497832......) = 272535065299529 * x19267(2437667176......)

n=19309: x19267(2437667176......) = 417534968733479 * c19252(5838234781......)

n=19653: c13071(2535418284......) = 142015521967830529 * c13054(1785310682......)

n=19955: c14669(1269367516......) = 364785432286601 * c14654(3479764825......)

n=19989: c13296(1165892848......) = 377955945475399 * c13281(3084732129......)

n=20419: c17463(6241608078......) = 282602010355409711 * c17446(2208621258......)

n=20507: c20480(8995143200......) = 843074626353067 * c20466(1066945074......)

n=20631: c12113(1579029799......) = 153274386291079 * c12099(1030198089......)

n=20721: c13785(3492335217......) = 6331598067511 * c13772(5515724750......)

n=20775: c11017(5263957620......) = 10802746269811192201 * c10998(4872795758......)

n=20907: c13174(1832993604......) = 134062038818963641 * c13157(1367272660......)

n=21059: c21038(1325544910......) = 27989661238387 * c21024(4735837635......)

n=21159: c14055(1358028973......) = 1524678419443223570923 * c14033(8906986261......)

n=21229: c18457(6256865952......) = 7511864499345649 * c18441(8329311521......)

n=21567: c11214(6703264274......) = 16565327156888329 * c11198(4046563168......)

n=21715: c16765(8055387045......) = 15604646184494231 * c16749(5162172182......)

n=21785: c17396(6262134778......) = 30821842322478761 * c17380(2031719815......)

n=21793: c19390(1761827085......) = 41287207980919231 * c19373(4267246857......)

n=21885: c11632(3061696042......) = 15299588993515951 * c11616(2001162282......)

n=22045: c17611(3441771038......) = 7614506675439271 * c17595(4520018413......)

n=22209: c13421(2913486617......) = 19352741241307 * c13408(1505464564......)

n=22361: x21906(3857264300......) = 160575660477889 * c21892(2402147553......)

n=13459: c13076(3291394214......) = 1361122379206040161 * c13058(2418147159......)

n=13533: c8280(5917831490......) = 614718324224707 * c8265(9626899438......)

n=14031: c9328(3318941311......) = 159385171829020561 * c9311(2082340077......)

n=14127: c8802(2278126283......) = 2892522909104947 * c8786(7875914400......)

n=14171: c13702(1036328424......) = 25826245156969 * c13688(4012694909......)

n=14217: c8067(3878996958......) = 105613054401623707 * c8050(3672838533......)

n=15127: c12942(1415137128......) = 445025960320272382801 * c12921(3179897927......)

n=15413: c15380(9060455410......) = 736695697182510052093 * c15360(1229877606......)

n=15809: c15778(5459563313......) = 13257698340807511 * c15762(4118032537......)

n=15863: c15257(7117584201......) = 11275472154972787 * c15241(6312448918......)

n=15869: c13570(1434796043......) = 665126113829544347 * c13552(2157178938......)

n=15959: c15923(7388960806......) = 26449912150389557 * c15907(2793567239......)

n=16105: c12847(2624231821......) = 13472393469361 * c12834(1947858654......)

n=16241: c15940(2854538592......) = 1157310839640973 * c15925(2466527137......)

n=16259: c15918(7240936327......) = 14076789267874559 * c15902(5143883445......)

n=16503: c10966(2138463993......) = 69231815339551 * c10952(3088845761......)

n=16817: c16480(4781690118......) = 10840261144173049 * c16464(4411046979......)

n=16945: c13529(4326969791......) = 17131106348296321 * c13513(2525797052......)

n=17039: c15450(4799091614......) = 48069702134167501125889 * c15427(9983610052......)

n=17457: c10077(1493675155......) = 115662159665723315569 * c10057(1291412126......)

n=18083: c16508(1525651477......) = 10960696275959 * x16495(1391929343......)

n=18085: c14443(5913638242......) = 23611122335761 * c14430(2504598535......)

n=18447: c10062(6760604775......) = 1988596619377369 * c10047(3399686346......)

n=18765: c9914(3050379578......) = 227910598263937711 * c9897(1338410588......)

n=18793: c18774(5951316336......) = 1367749366738133 * c18759(4351174624......)

n=18901: c18380(1064359851......) = 1315771636584037 * c18364(8089244528......)

n=18967: c17469(6107241855......) = 240666038190112471 * c17452(2537641746......)

n=19045: c13993(6048851991......) = 136571172709921 * c13979(4429084023......)

n=23407: c23026(2380618305......) = 13234652941427 * c23013(1798776527......)

n=23747: c23713(6525546082......) = 50944926800912756597 * c23694(1280902043......)

n=23819: c23774(9704263719......) = 172690168057243 * c23760(5619465096......)

n=22365: x10050(3784571856......) = 852512094227684521 * c10032(4439317497......)

n=22463: x19219(1129080846......) = 68723269314169 * x19205(1642938203......)

n=22463: x19205(1642938203......) = 116367922041911 * c19191(1411848020......)

n=15099: c8591(1743983407......) = 48001010408668843 * x8574(3633222285......)

n=18083: x16495(1391929343......) = 62207782834289 * c16481(2237548551......)

n=13671: c7538(1086231766......) = 26922104640649 * c7524(4034720839......)

n=15099: x8574(3633222285......) = 76607792009498359 * c8557(4742627597......)

n=14993: c12863(1509025302......) = 17305754270773 * c12849(8719789260......)

n=22517: x19340(2493199133......) = 969184826440370644979711 * c19316(2572470250......)

December 8, 20102010 年 12 月 8 日 (Makoto Kamada)

n=71572: c34486(5671343511......) = 6535673404181 * c34473(8677519760......)

n=35815: c24169(2531944451......) = 5125974599201 * c24156(4939440106......)

n=71646: c23860(1148050124......) = 5937090944797 * c23847(1933691323......)

n=35845: c27976(1884795673......) = 6913762093001 * c27963(2726150608......)

n=71720: c25920(9999000099......) = 7869938446481 * c25908(1270530915......)

n=71726: c35857(1584309254......) = 9922950469063 * c35844(1596611068......)

n=71742: c21703(1319945763......) = 8694708628783 * c21690(1518102354......)

n=71775: c33595(1741550432......) = 7666801802551 * c33582(2271547481......)

n=71787: c47834(4246660479......) = 8194689494359 * c47821(5182210360......)

n=71833: c69328(9000000000......) = 9254864015797 * c69315(9724616141......)

n=71834: c30731(1505070897......) = 6425436293767 * c30718(2342363737......)

n=71894: c35490(2550049946......) = 6047832127517 * c35477(4216469459......)

n=71902: c35942(2002767585......) = 7694178302579 * c35929(2602964874......)

n=71904: c20352(9999999999......) = 6075589095073 * c20340(1645930928......)

n=23969: c21755(5643545270......) = 5336704129879 * c21743(1057496374......)

n=71962: c32701(1099999999......) = 7692064667453 * c32688(1430045179......)

n=71965: c55860(2323405796......) = 7082403810401 * c55847(3280532795......)

n=36039: c23354(2026313228......) = 5685175242883 * c23341(3564205398......)

n=36087: c22961(2028957686......) = 9916906728067 * c22948(2045958222......)

n=72178: c35701(1099999999......) = 5700351381401 * c35688(1929705603......)

n=72205: c49489(1111099888......) = 9464725988551 * c49476(1173937724......)

n=72212: c30937(1009999999......) = 8470734712189 * c30924(1192340492......)

n=36137: c36129(1327598749......) = 9314251690307 * c36116(1425341287......)

n=72287: c72280(4269673063......) = 5842516536431 * c72267(7307934922......)

n=72347: c65750(1593982595......) = 8728243043521 * c65737(1826235346......)

n=72412: c35281(1009999999......) = 6038046017261 * c35268(1672726569......)

n=72446: c31675(1568563724......) = 5297909329681 * c31662(2960722101......)

n=72463: c71915(3105022200......) = 5241135747721 * c71902(5924330813......)

n=72493: c72487(3831774375......) = 5412912688483 * c72474(7078951012......)

n=72573: c45498(9559332017......) = 6063589831363 * c45486(1576513630......)

n=36297: c23321(4055597527......) = 6860781554797 * c23308(5911276280......)

December 7, 20102010 年 12 月 7 日 (Serge Batalov)

n=6205: c4581(2818575650......) = 11872454117195694875805995641 * c4553(2374046362......)

n=6239: c5852(7212116355......) = 26105217517838673323732559031 * c5824(2762710692......)

n=6439: c6249(7279856531......) = 10975588170657365114403960761 * c6221(6632771217......)

n=7849: c7593(1137643025......) = 631874365840719075990619351 * c7566(1800425981......)

# The ratio of factored part of (4*10^15698-7)/3+1 was raised from 3.10% to 3.27%.

n=14569: c13688(1737204769......) = 15994671606944065667 * c13669(1086114683......)

n=14573: c12517(5011227330......) = 1505109363688373 * c12502(3329477213......)

n=14577: c9394(1485925386......) = 8430380561638663597 * c9375(1762583996......)

n=14605: c11084(1267930298......) = 73192300859201 * c11070(1732327422......)

n=14607: c9712(2247253381......) = 176836874084677 * c9698(1270805873......)

n=14637: c7671(2006780571......) = 1636564415989231 * c7656(1226215449......)

n=14645: c11189(7036741770......) = 53826610486825321 * c11173(1307297953......)

n=14683: c14678(1891800369......) = 430141924522117 * c14663(4398084124......)

n=14705: c11002(1076343678......) = 19273798796801 * c10988(5584491619......)

n=14725: c10786(3177601091......) = 97882615222351 * c10772(3246338570......)

n=14787: c9349(1129213909......) = 88827226968269557 * c9332(1271247508......)

n=17735: c14171(5246648828......) = 134854235341561 * c14157(3890607376......)

n=17741: c17456(6866148140......) = 50239620926641 * c17443(1366679925......)

n=17743: c16115(4226999253......) = 3406684525066241 * c16100(1240795624......)

n=17761: c17752(1995503667......) = 5186886050765893 * c17736(3847209381......)

n=17763: c11393(8901629535......) = 5062563870466156815601 * c11372(1758324391......)

n=17785: c14209(1464565266......) = 351008411900761 * c14194(4172450621......)

n=17809: c16168(1922279666......) = 2926945629243241 * c16152(6567527758......)

n=17827: c17822(1038780803......) = 138278870310929 * c17807(7512216446......)

n=17829: c10142(1124646594......) = 8088020908507 * c10129(1390509009......)

n=17845: c13777(1111099999......) = 1051590809043488671 * c13759(1056589683......)

n=17851: c17839(1412910332......) = 8017810832844199 * c17823(1762214601......)

n=17853: c10801(1109999999......) = 299390983816453 * c10786(3707526478......)

n=17871: c9492(2286938236......) = 2102461894788529 * c9477(1087743012......)

n=17873: c17504(5758280636......) = 532995488647841 * c17490(1080361984......)

n=17921: c17908(4432582313......) = 1499520859311997 * c17893(2955999101......)

n=17927: c14108(1032986249......) = 5937815323987 * c14095(1739673926......)

n=17953: c16560(9000000000......) = 27100404267656653987093 * c16538(3320983669......)

n=17959: c17944(6845389785......) = 75346842911746853 * c17927(9085171349......)

n=17965: c14362(2319347208......) = 23099280263431 * c14349(1004077695......)

n=17975: c14356(2781535979......) = 14562461924201 * c14343(1910072619......)

n=17977: c17968(9118821280......) = 21661721672729 * c17955(4209647514......)

n=17987: c17975(2232436004......) = 9246123749141479 * x17959(2414456116......)

n=17987: x17959(2414456116......) = 144662674300636747 * c17942(1669024942......)

n=18031: c15553(1111111111......) = 752023468421083 * c15538(1477495261......)

n=18041: c18029(1622476753......) = 41575019258693 * c18015(3902527965......)

n=18043: c18013(2198604079......) = 3472300362786797 * c17997(6331837252......)

n=18045: c9601(1001000999......) = 131484765427111 * c9586(7613056894......)

n=18051: c10897(9027093454......) = 44446822963951 * x10884(2030987335......)

n=18051: x10884(2030987335......) = 58920825835368157 * x10867(3446977035......)

n=18051: x10867(3446977035......) = 1606461323260598839 * c10849(2145695626......)

n=18073: c15595(1536974456......) = 46024906603237 * c15581(3339440685......)

n=18075: c9596(2766202871......) = 104397400815751 * x9582(2649685576......)

n=18075: x9582(2649685576......) = 607154516904151 * c9567(4364104198......)

n=18083: c16521(1529925422......) = 10028013905911 * c16508(1525651477......)

n=18085: c14459(1658846818......) = 2805120553881031 * c14443(5913638242......)

n=18107: c17136(9000000000......) = 4182211234003440041 * c17118(2151971647......)

n=18109: c14243(1347130212......) = 152655870046198203049 * c14222(8824621106......)

n=18117: c10801(1000000001......) = 321617700782173703161 * c10780(3109281605......)

n=18123: c10331(2217890977......) = 25156507484431 * c10317(8816370788......)

n=18125: c13982(5551148142......) = 8856376414464985001 * c13963(6267967713......)

n=18133: c18128(1531869784......) = 473325763589747 * c18113(3236396373......)

n=18167: c17640(9000000000......) = 94362438497137249 * c17623(9537693327......)

n=18191: c18181(7809776951......) = 51300215168791 * c18168(1522367289......)

n=18197: c17563(6551975403......) = 684189920456347 * c17548(9576252451......)

n=18199: c18185(2025602306......) = 128274535391729 * c18171(1579114904......)

n=18207: c9779(1539098053......) = 13544833747436839 * c9763(1136298962......)

n=18229: c18220(7007695775......) = 7811664224912294750119 * c18198(8970810282......)

n=18233: c18228(3046894757......) = 122281514451533 * x18214(2491705120......)

n=18233: x18214(2491705120......) = 16287775298138301051005533 * c18189(1529800770......)

n=18237: c12140(4411502597......) = 60770885984870599 * c12123(7259236928......)

n=18241: c16120(2017248632......) = 22453798595536631 * c16103(8983997179......)

n=18261: c12152(3746858830......) = 239241436254997453 * c12135(1566141254......)

n=18267: c12168(5899341159......) = 61945036353649 * x12154(9523509075......)

n=18267: x12154(9523509075......) = 94220060679733 * c12141(1010772972......)

n=18295: c14632(9000090000......) = 2852753933701656871 * c14614(3154877781......)

n=18313: c18303(7370068610......) = 305198976736074054467 * c18283(2414840537......)

n=18317: c16889(3342495360......) = 26761379704169839 * c16873(1248999639......)

n=18327: c11841(1109999999......) = 28339228825501161049 * c11821(3916832059......)

# The ratio of factored part of (35*10^18328-359)/9+1 was raised from 1.96% to 2.07%.

n=18329: c18319(2039716993......) = 21629187803666340991 * c18299(9430391062......)

n=18347: c15708(2078415838......) = 374084018672260373 * c15690(5556013448......)

n=18357: c11748(6367845265......) = 9279747923359 * c11735(6862088623......)

n=18373: c17373(1061683684......) = 442253475325719271254197 * c17349(2400622592......)

n=18421: c16836(1286726027......) = 13961000924214952609 * c16816(9216574327......)

n=18439: c18434(1506448352......) = 622256388671573 * c18419(2420944773......)

n=18447: c10080(9009009009......) = 1332574423152774517 * c10062(6760604775......)

n=18451: c18443(3935918848......) = 23877010851399443480471 * c18421(1648413561......)

n=18455: c14738(8985838450......) = 2174900373942601 * c14723(4131609226......)

n=18459: c10499(1321620079......) = 29446818220163107 * c10482(4488159195......)

n=18461: c18449(1848147700......) = 172750897801923391 * c18432(1069833919......)

n=18477: c12304(7909189340......) = 8715915341587 * x12291(9074421940......)

n=18477: x12291(9074421940......) = 1334201406151231 * c12276(6801388379......)

n=18495: c9793(1000000001......) = 1386889187155731001 * c9774(7210381407......)

n=18515: c12136(1255760564......) = 24907003788670151 * x12119(5041796978......)

n=18515: x12119(5041796978......) = 27905971529113341721 * c12100(1806708995......)

n=18519: c12340(1216168177......) = 470897725840182889 * c12322(2582658846......)

n=18525: c8632(2095518893......) = 2389859471307751 * c8616(8768377046......)

n=18533: c18060(9000000000......) = 10783780045569005107 * c18041(8345867554......)

n=18547: c17411(1026339309......) = 5355357716785757 * c17395(1916471996......)

n=18567: c12366(4638371829......) = 121588004024438293 * c12349(3814826854......)

n=18579: c11236(2987163271......) = 36236112100849 * c11222(8243608649......)

n=18595: c14841(6607312635......) = 99262775254114391 * c14824(6656385154......)

n=18603: c11213(2886129519......) = 38561108847396643 * c11196(7484560495......)

n=18607: c17766(3685305179......) = 1736459238369923 * c17751(2122310215......)

n=18621: c12392(8356768392......) = 1655599322710441 * c12377(5047579011......)

n=18623: c16912(1380307811......) = 95621498286667 * c16898(1443512009......)

n=18627: c10625(4433847326......) = 46243059272719 * c10611(9588135812......)

n=18637: c18629(1222694007......) = 82724844375434698277 * c18609(1478025152......)

n=18643: c18346(1467893976......) = 82827210818551 * c18332(1772236396......)

n=18653: c17816(2412415900......) = 11564380058311 * c17803(2086074556......)

n=18657: c12420(9999999990......) = 29820448604227681 * x12404(3353403606......)

n=18657: x12404(3353403606......) = 5337254778638788441 * c12385(6283012045......)

n=18659: c18205(8553436821......) = 9431034889037 * c18192(9069457299......)

n=18665: c14910(8122304183......) = 42060396789431 * c14897(1931104983......)

n=18679: c18649(2260183337......) = 5734518264427 * c18636(3941365661......)

n=18683: c14955(1038018949......) = 9938599122095782517 * c14936(1044431853......)

n=18687: c12442(2397291972......) = 685089569583841 * x12427(3499238754......)

n=18687: x12427(3499238754......) = 741549669225679 * c12412(4718819116......)

n=18701: c18695(1237801313......) = 477055222743929 * c18680(2594670919......)

n=18745: c14257(1111099999......) = 325793957403521591 * c14239(3410437716......)

n=18747: c12473(4082645732......) = 8504451536827270987 * c12454(4800598503......)

n=18759: c11221(2336930116......) = 433533184027711 * c11206(5390429621......)

n=18765: c9927(2392657382......) = 7843802125681 * c9914(3050379578......)

n=18769: c18620(5790105691......) = 4224284491079803 * c18605(1370671341......)

n=18783: c12497(1399849418......) = 2352593896103071 * c12481(5950238250......)

n=18793: c18787(9853857440......) = 16557441888307 * c18774(5951316336......)

n=18795: c8535(9379597077......) = 10689144574921 * c8522(8774880919......)

n=18803: c18791(4695372854......) = 29625393333323 * c18778(1584914941......)

n=18811: c17347(3987011203......) = 7779349395689 * c17334(5125121653......)

n=18815: c14551(1505671612......) = 25547072476201 * c14537(5893714881......)

n=18819: c11510(6239231339......) = 10096297861843 * c11497(6179721938......)

n=18849: c12241(1109999999......) = 6616251271321597 * c12225(1677687189......)

n=18859: c18854(1472899387......) = 90896484645395215628239 * c18831(1620414027......)

n=18873: c12504(1376491664......) = 825054507901441 * c12489(1668364515......)

n=18875: c14987(5662241020......) = 3800505145751 * c14975(1489865374......)

n=18901: c18394(5806889939......) = 545575815609427 * c18380(1064359851......)

n=18905: c14247(2012450484......) = 81315543681481 * c14233(2474865681......)

n=18907: c15543(5807033216......) = 51023545096631801 * c15527(1138108535......)

n=18949: c16221(5669219657......) = 5032462584658972849 * c16203(1126529916......)

n=18961: c18607(1582192250......) = 324607910181331862843 * c18586(4874164186......)

n=18967: c17483(2269068766......) = 37153740106081 * c17469(6107241855......)

n=18971: c18576(1219325476......) = 71852595708613018289 * c18556(1696981806......)

n=18997: c17148(2517273149......) = 79923933452683 * c17134(3149586163......)

n=19007: c18684(2871388737......) = 249898295657917 * c18670(1149022937......)

n=19017: c12650(3326238158......) = 185899835037529 * c12636(1789263641......)

n=19025: c15194(1775739287......) = 101693936133151 * c15180(1746160444......)

n=19035: c9927(8113232682......) = 321750273227401 * c9913(2521593097......)

n=19041: c11509(6074372793......) = 1391065450649658631 * c11491(4366705240......)

n=19045: c14009(3592411943......) = 5938997927485351 * c13993(6048851991......)

n=19053: c12082(5331451477......) = 5924951113632157 * c12066(8998304585......)

n=19061: c16277(2200347254......) = 134809430856871 * x16263(1632190893......)

n=19061: x16263(1632190893......) = 1406501787492026516201 * c16242(1160461300......)

n=19063: c17316(1180281431......) = 6499392145178791 * c17300(1815987411......)

n=19071: c11652(5869226030......) = 7386142469489820973 * c11633(7946267019......)

n=19087: c19081(5821267301......) = 3089127842027 * c19069(1884437161......)

n=19091: c17935(1840589820......) = 154003028967537601 * c17918(1195164687......)

n=19093: c18693(4721761157......) = 255673071722653511 * c18676(1846796428......)

n=19103: c16362(5234777356......) = 7440397333527467 * c16346(7035615332......)

n=19125: c9601(1000000000......) = 54712370177406001 * c9584(1827740229......)

n=19139: c19131(6310305658......) = 2121929903639321 * x19116(2973852080......)

n=19139: x19116(2973852080......) = 2921505720378517 * c19101(1017917596......)

n=19141: c19132(1304290416......) = 5035838191006774909129 * c19110(2590016531......)

n=19147: c18634(1073167741......) = 633174063022867 * c18619(1694901614......)

n=19159: c14777(3624638492......) = 7570211221572889 * c14761(4788028214......)

n=19161: c12768(9990000009......) = 417797559660733831 * c12751(2391110186......)

n=19185: c10216(3743343850......) = 18150077913841 * c10203(2062439549......)

n=19217: c17460(9000000000......) = 24111287854122198467 * c17441(3732691532......)

n=21038: c10262(8910237083......) = 280595955955309698623 * c10242(3175468817......)

n=21059: c21051(8973097460......) = 67693651010597 * c21038(1325544910......)

n=21063: c11136(9009009909......) = 108053677229317 * x11122(8337531994......)

n=21063: x11122(8337531994......) = 14286371915467471 * c11106(5836003740......)

n=21067: c21037(3453133340......) = 6828278384671 * x21024(5057106851......)

n=21067: x21024(5057106851......) = 45965571562986401 * c21008(1100194488......)

n=21073: c19435(3559042538......) = 11252794746291359 * c19419(3162807656......)

n=21117: c14076(9009009009......) = 2234236090356757 * c14061(4032254714......)

n=21119: c18040(6993275563......) = 8708346451547 * c18027(8030543574......)

n=21123: c14064(3907272928......) = 12589075266787 * c14051(3103701301......)

n=21131: c17921(1111111111......) = 81572104666522377293 * c17901(1362121420......)

# The ratio of factored part of (4*10^42262-7)/3+1 was raised from 1.62% to 1.67%.

n=21147: c11232(9009009909......) = 31630318787677 * c11219(2848219763......)

n=21151: c19501(1117940111......) = 359810696111231 * c19486(3107023007......)

n=21157: c21150(7502483884......) = 375658735958067043 * c21133(1997154110......)

n=21159: c14081(4274690074......) = 17308598634559 * x14068(2469691605......)

n=21159: x14068(2469691605......) = 18185853567547 * c14055(1358028973......)

n=21161: c18121(2871189243......) = 29669336965199 * c18107(9677294934......)

n=21173: c20442(2255443007......) = 398659487542907 * c20427(5657567618......)

n=21183: c13449(2930818759......) = 54792013890961 * c13435(5348988934......)

n=21191: c21185(2912945742......) = 1669998051300307 * c21170(1744280923......)

n=21199: c18817(1111111111......) = 2530666141550213 * c18801(4390587493......)

n=21201: c13669(6498548134......) = 2186943693186877 * x13654(2971520553......)

n=21201: x13654(2971520553......) = 42680367902759516659627 * c13631(6962265556......)

n=21209: c20906(7161268969......) = 633279464446159 * c20892(1130822862......)

n=21213: c14122(6402732838......) = 527518662793062841 * c14105(1213745273......)

n=21229: c18471(9539131224......) = 152458615820213 * c18457(6256865952......)

n=21231: c12079(4537836035......) = 12029800984363 * c12066(3772162183......)

n=21237: c14149(1313352561......) = 6873048981888787 * c14133(1910873274......)

n=21241: c19291(1861670964......) = 6652320161540197 * c19275(2798528813......)

n=21243: c13825(1109999999......) = 39365097041835787 * c13808(2819756798......)

n=21249: c14148(9999999990......) = 18124284455440003 * c14132(5517459193......)

n=21267: c13235(2510655083......) = 206518543398886120453 * x13215(1215704431......)

n=21267: x13215(1215704431......) = 832078383390465445387 * c13194(1461045564......)

n=21275: c15826(2293496896......) = 21726782794601 * c15813(1055608148......)

n=21281: c19606(1095804187......) = 125595190185557 * c19591(8724889753......)

n=21287: c18240(9000000900......) = 231095948303835203 * c18223(3894486669......)

n=21299: c19829(1139023787......) = 2600515979692711 * c19813(4379991495......)

n=21337: c20173(2060662083......) = 35549349845861647702117 * c20150(5796623826......)

n=21349: c20713(5625564301......) = 120299462608977791 * c20696(4676300442......)

n=21365: c17064(4026641761......) = 32161793691241 * c17051(1251995395......)

n=21373: c18468(2316508092......) = 12158019974383163 * c18452(1905333349......)

n=21377: c21359(7741167708......) = 7735883247491089 * c21344(1000683110......)

n=21379: c21374(1299286821......) = 235259449375283 * c21359(5522782718......)

n=21381: c14252(9009009009......) = 1057550535582493 * c14237(8518750363......)

n=21387: c14256(9009009009......) = 2872011453909547 * x14241(3136829066......)

n=21387: x14241(3136829066......) = 657744722948841498831769 * c14217(4769067629......)

n=21405: c11403(8642686734......) = 10544449932241 * c11390(8196432047......)

n=21441: c12228(2950295544......) = 8314245824431 * c12215(3548482455......)

n=21449: c21108(2575123343......) = 5242481743963 * c21095(4912031113......)

n=21451: c20295(3799957064......) = 38879236732983133 * c20278(9773743993......)

n=21455: c14672(1375154725......) = 1300615832916401 * c14657(1057310460......)

n=21461: c19496(2096777951......) = 583163591678379119 * c19478(3595522733......)

n=21463: c19615(1288779527......) = 8759887831847413 * c19599(1471228344......)

n=21472: c9595(2217722709......) = 11325998397885526081 * c9576(1958081425......)

n=21505: c14080(9000090000......) = 44711374956601 * x14067(2012930716......)

n=21505: x14067(2012930716......) = 230442439401791 * c14052(8735069466......)

n=21515: c15832(1938989248......) = 431512914665561 * c15817(4493467478......)

n=21541: c19859(1883831755......) = 113814627559933 * c19845(1655175433......)

n=21555: c11460(8657812813......) = 887552932241071 * x11445(9754700254......)

n=21555: x11445(9754700254......) = 834389768977974795871 * c11425(1169081958......)

n=21567: c11232(9009009909......) = 1343973553916633641 * c11214(6703264274......)

n=21575: c17236(2317420222......) = 317809256333351 * c17221(7291858798......)

n=21581: c18480(2951200185......) = 94515623835733787 * c18463(3122446920......)

n=21589: c21563(1438834301......) = 8408834809817161 * c21547(1711098307......)

n=21595: c14769(2091045655......) = 19231542178591 * c14756(1087300038......)

n=21609: c12348(9999999999......) = 4416223265996599 * c12333(2264378270......)

n=21645: c10351(2477730462......) = 1999036492115448241 * c10333(1239462347......)

n=21653: c21213(2293293297......) = 354163969995377167081597 * c21189(6475230379......)

n=21665: c14824(4157383120......) = 10421534665151 * c14811(3989223520......)

n=21667: c21149(3457201734......) = 34160699207801 * x21136(1012040682......)

n=21667: x21136(1012040682......) = 1789971172465332631 * c21117(5653949618......)

n=21681: c12945(5743163150......) = 154520833202209 * c12931(3716756524......)

n=21685: c17334(1055257384......) = 4832674745838418601 * c17315(2183588675......)

n=21687: c14443(7431251420......) = 18920582120683 * c14430(3927601895......)

n=21689: c20228(2280976308......) = 242891703224321 * x20213(9390918989......)

n=21689: x20213(9390918989......) = 10187928779493649 * c20197(9217692027......)

n=21711: c14464(2302982353......) = 1189687624485069049 * c14446(1935787433......)

n=21715: c16780(2116592334......) = 262754889624641 * c16765(8055387045......)

n=21765: c11590(5549041715......) = 143592029740046524561 * c11570(3864449666......)

n=21769: c19759(1986413580......) = 284318635481665357 * c19741(6986575386......)

n=21783: c14134(1029051903......) = 29996593520239 * c14120(3430562550......)

n=21785: c17411(4503243945......) = 719122807824241 * c17396(6262134778......)

n=21791: c16907(5626995953......) = 20095067281400284001182201 * c16882(2800187665......)

n=21793: c19408(1865945684......) = 1059096945519528961 * c19390(1761827085......)

n=21841: c21834(4239391843......) = 426289941145133209 * c21816(9944855448......)

n=21849: c14541(1279843487......) = 663726164313198872581279 * c14517(1928270357......)

n=21853: c19664(2567665169......) = 154031175349351 * c19650(1666977586......)

n=21857: c19848(8675357202......) = 1251947619670628761 * c19830(6929488954......)

n=21871: c21865(5080270819......) = 120994789854517 * c21851(4198751719......)

n=21885: c11645(7181230503......) = 23455073276071 * c11632(3061696042......)

n=21913: c20599(1592622711......) = 1345974743754241 * c20584(1183248585......)

n=21955: c17553(2033400253......) = 462874421037121 * c17538(4392984708......)

n=21967: c19960(9000000000......) = 5842825737902077 * c19945(1540350577......)

n=21973: c18121(6228903335......) = 664821663859711 * c18106(9369284538......)

n=21997: c21988(1434998250......) = 7868926758191 * c21975(1823626391......)

n=22009: c20290(6292376341......) = 24804198166628885707 * c20271(2536819089......)

n=22013: c22001(1904419585......) = 2091573251846053 * c21985(9105201475......)

n=22015: c13818(7048551420......) = 19980745045497601 * c13802(3527671968......)

n=22045: c17626(4639314914......) = 1347944085394481 * c17611(3441771038......)

n=22049: c20727(1692576616......) = 7202796566987653 * c20711(2349888131......)

n=22051: c22038(5874503928......) = 11550074678957 * c22025(5086117702......)

n=22053: c14690(8765389924......) = 132033994743407587 * c14673(6638737199......)

n=22077: c13293(6864589131......) = 42670650432169 * c13280(1608737870......)

n=22097: c20901(9066296004......) = 11559762443237 * c20888(7842977784......)

n=22103: c20460(9999999999......) = 17658525289750014089587 * c20438(5662987047......)

n=22113: c11636(5361652517......) = 315264701123191 * c11622(1700682790......)

n=22163: c21513(5806586405......) = 145790986458323 * c21499(3982815773......)

n=22175: c17707(3284821942......) = 777820051544951 * x17692(4223112963......)

n=22175: x17692(4223112963......) = 96077201392181951 * c17675(4395541191......)

n=22183: c18995(2713896354......) = 52618313801761 * c18981(5157703009......)

n=22185: c10730(3355196489......) = 835060871308681 * c10715(4017906484......)

n=22201: c22040(8043480759......) = 88552671625813 * c22026(9083272827......)

n=22205: c17754(5196383815......) = 573776606113465834315081 * c17730(9056458140......)

n=22207: c21714(2142221734......) = 15102107431933 * c21701(1418491918......)

n=22209: c13434(3123732742......) = 10721630653999 * c13421(2913486617......)

n=22215: c11835(4996551444......) = 1387405328364841 * c11820(3601363885......)

n=22239: c12649(4112535437......) = 55392947768467 * c12635(7424294252......)

n=22243: c19476(1493215883......) = 12192924223637 * x19463(1224657724......)

n=22243: x19463(1224657724......) = 892439707662361 * c19448(1372258219......)

n=22287: c12672(9009009009......) = 419106551461249 * c12658(2149574846......)

n=22289: c21540(9000000000......) = 631725113897671 * c21526(1424670288......)

n=22295: c14090(5337075165......) = 47470306728718320721 * c14071(1124297594......)

n=22301: c21496(3114922393......) = 64429233609547 * c21482(4834641386......)

n=22305: c11883(8293959545......) = 19143337552081231 * c11867(4332556704......)

n=22309: c19092(1181934898......) = 385630781199698707 * c19074(3064939201......)

n=22315: c17837(1933734982......) = 1827545928894841 * c17822(1058104725......)

n=22333: c21333(3109499039......) = 50431949260439 * c21319(6165732407......)

December 7, 20102010 年 12 月 7 日 (Polybius)

n=1002: c247(6679009732......) = 3991682749552894902673962957124418797917278009299 * p199(1673231604......)

# Phi_1002(10) is the 1010th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

n=1003: c892(2517941865......) = 312364786492896451349063229952945673957 * c853(8060901786......)

# The ratio of factored part of (16*10^10030-13)/3-1 was raised from 8.26% to 8.64%.

December 7, 20102010 年 12 月 7 日 (Kurt Beschorner)

n=8083: c7871(4649633602......) = 34497487309629844984585027 * c7846(1347818048......)

n=9149: c7836(9000000900......) = 1784979815364680208613039 * x7812(5042074326......)

n=9149: x7812(5042074326......) = 15344882085978134643684347 * c7787(3285834519......)

n=9269: c7909(6594132609......) = 23457097561973848815599129 * c7884(2811146004......)

n=11163: c7320(9999999999......) = 1432991000756549796770917 * c7296(6978410886......)

December 7, 20102010 年 12 月 7 日 (Makoto Kamada)

n=70791: c40441(1109999889......) = 9018491510239 * c40428(1230804384......)

n=35439: c23609(1092587710......) = 5568415318519 * c23596(1962116056......)

n=70888: c35431(6782396218......) = 7855689493489 * c35418(8633737654......)

n=70950: c16789(5518162583......) = 5337237021601 * c16777(1033898730......)

n=70960: c28353(1000000009......) = 9163314295361 * c28340(1091308207......)

n=70973: c60817(2481545259......) = 5130289408679 * c60804(4837047312......)

n=70977: c46401(1109999999......) = 9555263435923 * c46388(1161663419......)

n=71001: c38809(1000000000......) = 9400916657413 * c38796(1063726056......)

n=71021: c65510(5483870659......) = 7090927118323 * c65497(7733644088......)

n=71026: c33400(5866396311......) = 5023431113927 * c33388(1167806660......)

n=35515: c28408(9000090000......) = 7032942329671 * c28396(1279704791......)

n=71062: c35519(1321939015......) = 5083936151183 * c35506(2600227415......)

n=71096: c35536(1083435982......) = 7353047634161 * c35523(1473451603......)

n=35551: c34992(9000000000......) = 8357915387093 * c34980(1076823535......)

n=17777: c17125(6756974820......) = 8235771722557 * c17112(8204422181......)

n=71131: c70179(1878734498......) = 8423327898569 * c70166(2230394590......)

n=71139: c45321(1109999999......) = 7637355132079 * c45308(1453382723......)

n=71151: c46081(1109999999......) = 7026260861401 * c46068(1579787630......)

n=71272: c34801(1000099999......) = 5663126299681 * c34788(1765985688......)

n=71349: c44737(1109999999......) = 6377159350201 * c44724(1740586896......)

n=71423: c63001(1111111111......) = 5010746988391 * c62988(2217456027......)

n=71541: c47680(1025861051......) = 9360040837159 * c47667(1096000614......)

n=71550: c18699(9027607037......) = 5659852849201 * c18687(1595025043......)

December 6, 20102010 年 12 月 6 日 (Yousuke Koide)

n=932: c450(3733444597......) = 31306780512964774446383151831688280696877739051661 * c401(1192535462......)

December 6, 20102010 年 12 月 6 日 (Serge Batalov)

n=3239: c3045(3112075485......) = 256377141792571210231161560761 * c3016(1213866206......)

n=3733: c3711(4337512649......) = 97386479305325794709276117 * c3685(4453916683......)

n=8953: c7668(9000000900......) = 118031337987560068961 * c7648(7625094363......)

n=9077: c8731(2754205518......) = 420520997323761588281 * c8710(6549507721......)

n=9161: c9142(1611646913......) = 2317797912939305405661067 * c9117(6953353888......)

n=9319: c9313(1324784235......) = 142518922598227205734821329 * c9286(9295497128......)

n=9335: c7464(9000090000......) = 3533604963736138915665769508551 * c7434(2546999478......)

n=9559: c8580(9999999999......) = 6586439721548214683 * c8562(1518270935......)

n=9787: c9776(5676010162......) = 180846550393397188801 * c9756(3138578065......)

n=9791: c9784(5205635350......) = 66209822992717 * c9770(7862330866......)

n=9797: c9588(1269328299......) = 36366789534119441077 * c9568(3490350166......)

n=13017: c8657(3372456263......) = 443549126276464963 * c8639(7603343268......)

n=13023: c8668(6308423928......) = 69681131031961 * c8654(9053274301......)

n=13053: c8196(6930892562......) = 60743896088641 * c8183(1141002307......)

n=13055: c8924(4255294277......) = 40524614332721 * c8911(1050051764......)

n=13077: c8704(2381645721......) = 83274589190861509249 * c8684(2859990958......)

n=13079: c11192(2285917216......) = 18699709693039 * c11179(1222434601......)

n=13111: c11227(6864413283......) = 723725078745089 * x11212(9484835450......)

n=13111: x11212(9484835450......) = 1087087393012013 * c11197(8724998111......)

# The ratio of factored part of (2*10^26223-17)/3-1 was raised from 0.50% to 0.61%.

n=13115: c10081(1111099999......) = 531676790061542161 * c10063(2089803468......)

n=13117: c12086(7004282401......) = 2547973817018761 * c12071(2748961686......)

n=13133: c12536(3426352457......) = 17911729588708679 * c12520(1912909884......)

n=16051: c13736(1349455139......) = 46390035280913843 * c13719(2908933202......)

n=16067: c16055(1276327851......) = 601422757262226293 * c16037(2122180839......)

n=16075: c12831(8940981946......) = 1493462000198951 * c12816(5986748873......)

n=16085: c12864(9000090000......) = 1606891189191185671 * c12846(5600933069......)

n=16101: c10718(1264082801......) = 117636538320289 * c10704(1074566473......)

n=16105: c12862(1815474559......) = 691811807385001 * c12847(2624231821......)

n=16117: c15802(1933344359......) = 56049696581479 * c15788(3449339562......)

n=16121: c13517(5680484236......) = 22165149932969 * c13504(2562799824......)

n=16133: c13811(2067454849......) = 706897513439573 * c13796(2924688246......)

n=16135: c11041(1111099888......) = 69366719582205070068655921 * c11015(1601776609......)

n=16153: c15563(3482311790......) = 5978805689598587 * c15547(5824427103......)

n=16177: c13855(1854481126......) = 16537930806013 * c13842(1121350154......)

n=16203: c9801(1109999999......) = 2318986462815199 * c9785(4786573866......)

n=16233: c9244(6003966691......) = 22506738286577536489 * x9225(2667630740......)

n=16233: x9225(2667630740......) = 67053805497904621478083 * c9202(3978343541......)

n=16241: c15955(2946274929......) = 1032137010857401 * c15940(2854538592......)

n=16249: c16238(5844717841......) = 20356858789585027 * c16222(2871129530......)

n=16259: c15941(1320595407......) = 18237909399730909275031 * c15918(7240936327......)

n=16267: c16260(7589396065......) = 103343322284294086693 * c16240(7343866925......)

n=16269: c8947(2243959235......) = 2738832973862437 * c8931(8193121876......)

n=16291: c14800(9000000000......) = 2011809705394382587 * c14782(4473584144......)

n=16293: c10856(2764602144......) = 12263443914376561 * c10840(2254344019......)

n=16295: c13024(1293070618......) = 194243592876750871 * c13006(6656953773......)

n=16305: c8681(3473295612......) = 14062927592431 * c8668(2469824003......)

n=16317: c9073(1000000000......) = 22292391782728117 * c9056(4485835390......)

n=16319: c16311(2320618924......) = 1968418832848159 * c16296(1178925382......)

n=16343: c16008(9000000000......) = 16887547464555763 * c15992(5329370661......)

n=16357: c14846(1938091597......) = 16701454800493 * c14833(1160432800......)

n=16385: c12545(1111099999......) = 2359243094099413031 * c12526(4709561311......)

n=16387: c14019(4052993577......) = 25892128932743517809 * c14000(1565338094......)

n=16403: c16008(9000000000......) = 911734884910133 * c15993(9871290600......)

n=16411: c16399(7054117589......) = 355759615701013 * c16385(1982832586......)

n=16443: c9054(4448886555......) = 10387390441933 * c9041(4282968450......)

n=16447: c16427(2890546294......) = 21719365251637 * c16414(1330861312......)

n=16497: c9937(1000000001......) = 148364145807685471 * c9919(6740172941......)

n=16503: c10980(2832451134......) = 132452598818893 * c10966(2138463993......)

n=16513: c14107(1513956255......) = 241530031361893 * c14092(6268190531......)

n=16515: c8779(1515288351......) = 46217270736271 * c8765(3278619284......)

n=16523: c14378(1480100098......) = 150432760705317335726521 * c14354(9838947922......)

n=16525: c13181(1505104074......) = 14258808166601 * c13168(1055560925......)

n=16551: c11011(7552356705......) = 48012077090071 * x10998(1573011867......)

n=16551: x10998(1573011867......) = 577935901640809 * c10983(2721775655......)

n=16559: c15943(2304336786......) = 423300049690042489 * c15925(5443743246......)

n=16563: c11029(2409308046......) = 657304249188751 * c11014(3665438112......)

n=16605: c8641(1000000000......) = 4286553956172001 * c8625(2332876268......)

n=16613: c16115(1363370969......) = 170719572637292719 * c16097(7986026139......)

n=16615: c13277(1983133777......) = 115459475257362311 * c13260(1717601585......)

n=16617: c10631(2254759742......) = 243982636306215403 * c10613(9241476266......)

n=16619: c16607(2801249692......) = 30190039669151 * c16593(9278721468......)

n=16621: c15087(1385124191......) = 52854105818999 * c15073(2620655802......)

n=16637: c16364(1405682144......) = 19831652545151 * c16350(7088073682......)

n=16683: c10825(1109999999......) = 4064530606240681 * c10809(2730942653......)

n=16689: c11112(3521676248......) = 6851222945384075518801 * c11090(5140215515......)

n=16697: c16346(3111572711......) = 119359421332271 * c16332(2606893261......)

n=16703: c16696(1314656948......) = 54816287798483 * c16682(2398296202......)

n=16723: c14312(1805154514......) = 4212985052384809 * c14296(4284739897......)

n=16741: c16715(2114405551......) = 54038236165787 * c16701(3912795274......)

n=16765: c11464(3900822293......) = 3551756432554961 * c11449(1098279785......)

n=16787: c16764(9414505979......) = 84909535005947 * c16751(1108768994......)

n=19873: c15926(4395859254......) = 61538209537561 * c15912(7143300541......)

n=19905: c10603(2323508700......) = 20863460424511 * x10590(1113673692......)

n=19905: x10590(1113673692......) = 68014191456391 * c10576(1637413705......)

n=19907: c18715(1883755538......) = 7407170960449321 * c18699(2543151155......)

n=19921: c18095(3764855492......) = 8605925562708277 * c18079(4374724676......)

n=19951: c19586(2974350278......) = 4005511231623293209 * c19567(7425644584......)

n=19955: c14682(9942898358......) = 78329547839791 * c14669(1269367516......)

n=19959: c13304(9009009009......) = 6917466574312123 * c13289(1302356709......)

n=19975: c14715(5006282822......) = 354590761087151 * c14701(1411848071......)

n=19979: c19973(3972410812......) = 33812752505097420409 * c19954(1174826217......)

n=19987: c17153(1395373731......) = 2824157179810627 * c17137(4940850110......)

n=19989: c13309(6354061269......) = 54499530363121 * c13296(1165892848......)

n=20005: c15991(1509056603......) = 1682582707741801 * c15975(8968691976......)

n=20019: c13326(6543593729......) = 66764193511418827 * c13309(9801052608......)

n=20033: c17407(2540168187......) = 24554413082317 * c17394(1034505764......)

n=20047: c20034(9985917652......) = 24148792533413 * c20021(4135162301......)

n=20051: c20040(5176927789......) = 16330025970317 * c20027(3170189563......)

n=20085: c9792(9009099100......) = 9422007072901059391 * c9773(9561762191......)

n=20107: c20094(5835206812......) = 130149280597163 * c20080(4483472198......)

n=20109: c13398(1445189453......) = 2326393587458203 * x13382(6212145104......)

n=20109: x13382(6212145104......) = 513896543093291203 * c13365(1208831853......)

n=20113: c20101(2288870794......) = 57513457697609 * c20087(3979713420......)

n=20141: c18296(2234193083......) = 25088650144471 * c18282(8905194464......)

n=20149: c20136(6045198216......) = 62082077285999 * c20122(9737429030......)

n=20153: c17261(5845335744......) = 855487542562507 * c17246(6832753784......)

n=20161: c20154(2811831162......) = 376287444890831 * c20139(7472561734......)

n=20169: c13250(1794532886......) = 1762882175190201299947 * c13229(1017953957......)

n=20171: c19266(3541150330......) = 8168216959999 * c19253(4335279471......)

n=20177: c20165(2296955055......) = 39543702736997 * c20151(5808649408......)

n=20185: c14634(3876465274......) = 488903913549164521 * c14616(7928889844......)

n=20211: c13472(9009009009......) = 41776167538174249 * c13456(2156494848......)

n=20253: c13093(8680469350......) = 759553944821063089 * c13076(1142837768......)

n=20287: c20280(2340581200......) = 44202252680359678237 * c20260(5295162709......)

n=20307: c11583(2572933774......) = 36011723014387 * x11569(7144711664......)

n=20307: x11569(7144711664......) = 1400966396805991 * c11554(5099845136......)

n=20309: c19404(9000000000......) = 1302340523849161 * c19389(6910634995......)

n=20317: c18448(3417379695......) = 40431928458923 * c18434(8452180803......)

n=20373: c13570(1704266715......) = 291578644719871 * c13555(5844964116......)

n=23819: c23790(1985883930......) = 2046403506280249 * c23774(9704263719......)

n=23849: c20436(9000000900......) = 260074242771757 * c20422(3460550650......)

n=23865: c12096(9009099100......) = 5261069883179055991 * c12078(1712408179......)

n=23879: c23862(1653559185......) = 58934168582195113312489 * c23839(2805773331......)

n=23883: c15041(8096963398......) = 16678798135201 * c15028(4854644400......)

n=23889: c15916(2340903490......) = 3182554757629959157 * c15897(7355422510......)

n=23897: c22836(9000000000......) = 2712261949751933083 * x22818(3318263562......)

n=23897: x22818(3318263562......) = 12285015011990797711 * c22799(2701065940......)

n=23901: c15348(7784749682......) = 363190308386662698757 * c15328(2143435411......)

n=23915: c19128(9000090000......) = 17210202844481 * c19115(5229508380......)

n=23921: c22627(5791799742......) = 2860265254171139053 * c22609(2024917001......)

n=23923: c23351(1630316947......) = 3179213332087147 * c23335(5128051430......)

n=23927: c23514(4822357736......) = 73048675142797 * c23500(6601567690......)

n=23931: c15942(3478750202......) = 5139955897350751 * c15926(6768054574......)

n=23953: c22512(6821557199......) = 7242451563004391 * c22496(9418850978......)

n=23955: c12751(2735920589......) = 15659070743521 * c12738(1747179404......)

n=23957: c23950(3461147631......) = 4966342442743397 * c23934(6969208570......)

n=23965: c19157(1603657448......) = 713376347602081 * c19142(2247982364......)

n=23969: c21771(1270977901......) = 2252091266366041 * c21755(5643545270......)

n=23971: c23955(1866535102......) = 11461245840151 * c23942(1628562137......)

n=23981: c23960(9008278526......) = 1183861496382757 * c23945(7609233473......)

n=23985: c11509(1779815027......) = 152882599401728060671 * c11489(1164171092......)

n=23987: c22299(1097084279......) = 253520648467439 * c22284(4327396153......)

n=27948: c8671(5631469798......) = 218644429704175429 * c8654(2575629210......)

n=35780M: c7153(2824060999......) = 100011353647048185642241 * c7130(2823740402......)

n=38380M: c7201(2796100002......) = 5553956469079554661 * c7182(5034429092......)

n=48540M: c6465(2529932837......) = 19641111035794921 * c6449(1288080308......)

n=48940L: c9784(3576409999......) = 3699237914504634593248501 * c9759(9667964273......)

n=52980L: c7056(3913542626......) = 530492611172491369081 * c7035(7377185929......)

n=61620M: c7488(3952678052......) = 2092097946229230799357926481 * c7461(1889336997......)

n=68220L: c9073(1105096689......) = 139304946573500401 * c9055(7932932154......)

n=75180L: c8545(2557786117......) = 326172033828481 * c8530(7841831463......)

n=26895: c12956(1674833912......) = 59373189852241 * c12942(2820858904......)

n=13179: c8348(2681169335......) = 5048705366951839 * c8332(5310607651......)

n=13241: c13234(6878228597......) = 226583516440653121 * c13217(3035626203......)

n=13247: c12209(6385329520......) = 5049234411045152811757 * c12188(1264613404......)

n=13261: c13007(1705770357......) = 24872761864905332197 * c12987(6857985319......)

n=13277: c11191(3440564328......) = 11783450327947 * x11178(2919827582......)

n=13277: x11178(2919827582......) = 4691858138448757 * x11162(6223179594......)

n=13277: x11162(6223179594......) = 26569348772687711 * c11146(2342240168......)

n=13303: c12994(4974549651......) = 302039258813111 * c12980(1646987769......)

n=13307: c11400(9000000900......) = 542575792856461799 * c11383(1658754595......)

n=13313: c13292(5358605784......) = 27433864951169009 * c13276(1953281389......)

n=13329: c8880(9990000009......) = 343570832671249 * c8866(2907697353......)

n=13331: c13314(5608932699......) = 39536206199276591969 * c13295(1418682579......)

n=13335: c6033(9183614594......) = 418910889454783763311 * c6013(2192259696......)

n=13361: c12879(2734529344......) = 75625853573881973 * c12862(3615865759......)

n=13383: c8911(4665411975......) = 50788789597081 * c8897(9185908963......)

n=13395: c6608(7201908632......) = 188271899251997881 * c6591(3825270080......)

n=13413: c8357(2035398763......) = 8815796123983957711 * c8338(2308808795......)

n=13437: c8929(8179485656......) = 570224485958311 * c8915(1434432553......)

n=13453: c12206(2175867187......) = 351270361657843 * c12191(6194280602......)

n=13459: c13089(9422294656......) = 28627062097397 * c13076(3291394214......)

n=13493: c13256(3334939044......) = 14633405533244237 * c13240(2278990380......)

n=13495: c10769(2694849671......) = 42805275777501001 * c10752(6295601705......)

n=13511: c13198(3574692392......) = 313819692975479 * c13184(1139091163......)

n=13527: c8957(5600471022......) = 37691974167373 * c8944(1485852398......)

n=13533: c8300(2050505237......) = 34649605019493105409 * c8280(5917831490......)

n=13535: c10801(2040135721......) = 50272647942031 * c10787(4058142558......)

n=13537: c13522(1079772976......) = 43107730967608921 * c13505(2504824431......)

n=13541: c12290(1844747418......) = 688113656825849 * c12275(2680876044......)

n=13545: c6048(9990000009......) = 210190354156441 * c6034(4752834662......)

n=13549: c12729(5078406935......) = 28965838018018271 * c12713(1753240121......)

n=13559: c10657(1111110999......) = 131721822447671 * c10642(8435284141......)

n=13571: c13200(9000000000......) = 227524129184598401 * c13183(3955624413......)

n=13585: c8640(9000090000......) = 762164931030361 * x8626(1180858582......)

n=13585: x8626(1180858582......) = 1034921231534603178481 * c8605(1141013003......)

n=13599: c9049(1756114439......) = 35723031988519 * c9035(4915916542......)

n=13605: c7233(2895356179......) = 13273389226681 * c7220(2181323948......)

n=13611: c8344(7985868150......) = 3974098269172201 * c8329(2009479285......)

# The ratio of factored part of (53*10^13612-521)/9-1 was raised from 3.21% to 3.32%.

n=13617: c8442(1336565745......) = 77334218028428293 * c8425(1728298002......)

n=13653: c8632(8320164808......) = 273478916237821420519 * c8612(3042342321......)

# The ratio of factored part of (44*10^27306-53)/9+1 was raised from 5.70% to 5.77%.

n=13671: c7552(1461430881......) = 134541349884523 * c7538(1086231766......)

n=13675: c10915(7312487660......) = 405808509686551 * c10901(1801955229......)

n=13711: c13702(3266341540......) = 2818710102762189521 * c13684(1158807192......)

n=13729: c13724(2023255296......) = 1210507530412319 * c13709(1671410747......)

n=13745: c10988(1091303609......) = 14438940626161 * c10974(7558058711......)

n=13765: c10999(2445335592......) = 45371630568239191 * c10982(5389569564......)

n=13779: c9164(2964460293......) = 375358041388167391 * c9146(7897686918......)

n=13781: c13769(3217972665......) = 204788159487533 * c13755(1571366564......)

n=13791: c9192(9009009009......) = 3804686673972187 * c9177(2367871465......)

n=13795: c10555(5033956895......) = 110753511645241 * c10541(4545189422......)

n=13801: c13392(9000000000......) = 6310424057573 * c13380(1426211601......)

n=13811: c11825(2380038445......) = 29233251724559 * x11811(8141545345......)

n=13811: x11811(8141545345......) = 7782266836560091639 * c11793(1046166305......)

n=13835: c11059(8131558262......) = 225642882798481 * c11045(3603729114......)

n=13853: c11861(1462581774......) = 2266881253063799 * c11845(6451955843......)

n=13867: c11835(4597618353......) = 40414345536180829061521 * c11813(1137620390......)

n=13871: c11521(1111111111......) = 12805274535769 * c11507(8676980005......)

n=13875: c7188(1033814784......) = 64291630939762866001 * c7168(1608008335......)

n=13919: c13430(8726845654......) = 19153080215557 * c13417(4556366681......)

n=13925: c11120(9999900000......) = 13506102926454001 * c11104(7403986223......)

n=13931: c13921(1181252565......) = 36247403745517 * c13907(3258861168......)

n=13939: c13624(9000000000......) = 97439937029217290071 * c13604(9236459171......)

n=13941: c9277(9178546661......) = 36450703294834545991 * c9258(2518071211......)

n=13957: c13102(4005060509......) = 244292338640956769 * c13085(1639453996......)

n=13961: c13326(8264773972......) = 190288016004275471 * c13309(4343297148......)

n=13963: c13948(3280076972......) = 20595357614563 * c13935(1592629287......)

n=13987: c13704(2979165552......) = 264988820199053 * c13690(1124260846......)

n=14001: c8587(6606631629......) = 20640350477449 * c8574(3200833065......)

n=14005: c11200(9000090000......) = 4120099842681733831 * c11182(2184434927......)

n=14007: c7373(1154830255......) = 16701612649009 * x7359(6914483525......)

n=14007: x7359(6914483525......) = 47584329486500267161 * c7340(1453100968......)

n=14019: c9332(1947386770......) = 2029105730372041 * c9316(9597266130......)

n=14027: c12788(1188170573......) = 208457671763329 * x12773(5699816963......)

n=14027: x12773(5699816963......) = 12143482138191119 * c12757(4693725324......)

n=14031: c9343(8899856577......) = 2681534785679569 * c9328(3318941311......)

n=14063: c11760(9999999999......) = 1300724616413923 * c11745(7688022409......)

n=14069: c12771(7360537497......) = 14355681621271 * c12758(5127264376......)

n=14109: c9400(1596294808......) = 66320397645387751 * c9383(2406943964......)

n=14111: c13863(5166131779......) = 206605448275019879 * c13846(2500481871......)

n=14115: c7497(3916491837......) = 29396865493684921 * c7481(1332282123......)

n=14119: c12092(1593569222......) = 138871267889467 * c12078(1147515427......)

n=14125: c11200(9999999999......) = 657560684752001 * c11186(1520772186......)

n=14127: c8816(3504247365......) = 153821471209111 * c8802(2278126283......)

n=14141: c13880(3182123537......) = 20768549691689 * c13867(1532183799......)

n=14143: c14136(4223795079......) = 75744783199093 * c14122(5576351136......)

n=14163: c9428(2965673457......) = 130157607427201 * c9414(2278524871......)

n=14171: c13715(6897304870......) = 66555203011831 * c13702(1036328424......)

n=14173: c14158(2634820771......) = 47157827492053 * c14144(5587239513......)

n=14175: c6476(3527212444......) = 6520790283956551 * c6460(5409179394......)

n=14191: c13543(8649111871......) = 51718572275969 * c13530(1672341576......)

n=14201: c12879(1079822244......) = 6268494335541910432841 * c12857(1722618202......)

n=14203: c12164(1584144632......) = 33246019513351 * c12150(4764915185......)

n=14207: c14189(9212985541......) = 250704035572089641 * c14172(3674845329......)

n=14209: c13104(9000000000......) = 3219868160062373 * x13089(2795145500......)

n=14209: x13089(2795145500......) = 104348355195250501427 * c13069(2678667522......)

n=14211: c9462(2440890265......) = 302528467549279 * c9447(8068299439......)

n=14217: c8082(1309602838......) = 337613783425507 * c8067(3878996958......)

n=14239: c13700(8798335724......) = 3481673229246439 * c13685(2527042357......)

n=14243: c14236(2349729345......) = 3432230880787671161 * c14217(6846070170......)

n=14257: c13928(1974319287......) = 212817242094481 * c13913(9277064527......)

n=14259: c8060(1753248067......) = 225968287034323 * c8045(7758823550......)

n=14263: c13400(1249363034......) = 89140925526637 * c13386(1401559415......)

n=14275: c11400(9999900000......) = 388541884838951 * c11386(2573699359......)

n=14277: c9500(4543444708......) = 16021774152427 * c9487(2835793755......)

n=14295: c7603(3031182781......) = 3428436606277681 * c7587(8841297447......)

n=14325: c7601(1000010000......) = 145371652132630351 * c7583(6878989028......)

n=14343: c8167(8089833360......) = 954274389647587 * c8152(8477470890......)

n=14347: c14320(3205296712......) = 25407807643053089 * c14304(1261540057......)

n=14371: c12306(4970324899......) = 4600848815019800813 * c12288(1080306069......)

n=14399: c10551(5951910053......) = 313063084465363 * c10537(1901185527......)

n=14415: c7432(2350643016......) = 37031954062921 * c7418(6347607291......)

n=14419: c14401(1365112008......) = 7681021421627987 * c14385(1777253223......)

n=14421: c7912(3438543489......) = 12361789138498796840119 * c7890(2781590472......)

n=14457: c9334(1115557388......) = 14570681029231 * c9320(7656178779......)

n=14467: c12667(7680261497......) = 10786137751637159 * c12651(7120492686......)

n=14473: c14080(9000000000......) = 85399545797877556481 * c14061(1053869773......)

n=14477: c13962(3613025241......) = 145242007223709516121 * c13942(2487589720......)

n=14517: c9657(4607708236......) = 17753816526373 * c9644(2595333927......)

n=14529: c9288(3651956311......) = 1411216939852036064569 * c9267(2587806458......)

n=14545: c11623(8838892719......) = 307525911958561 * c11609(2874194458......)

n=16789: c16504(2614602110......) = 45561263960990067067 * c16484(5738651396......)

n=16817: c16494(5460943032......) = 114205289284027 * c16480(4781690118......)

n=16821: c9495(4748362434......) = 9370846012249 * c9482(5067165150......)

n=16827: c10921(1109999999......) = 87590797067089 * c10907(1267256420......)

n=16845: c8961(7259015499......) = 158199471032041 * c8947(4588520715......)

n=16851: c10876(1097846835......) = 97395815362386157 * c10859(1127201236......)

n=16861: c15522(2834344308......) = 3839217090827 * c15509(7382610156......)

n=16863: c8628(4299872512......) = 3729482273540668794997 * c8607(1152940863......)

n=16877: c14453(1281899463......) = 342249663823733 * c14438(3745509780......)

n=16883: c16872(7124684584......) = 10290355742999 * c16859(6923652362......)

n=16885: c12241(1111099999......) = 113208200545991 * c12226(9814660021......)

n=16889: c16883(1061112548......) = 15796715867921239 * c16866(6717298442......)

n=16901: c16876(1442004572......) = 15631068105286427 * c16859(9225246558......)

n=16905: c7386(3080941264......) = 754840977505231 * c7371(4081576592......)

n=16913: c15591(6739298931......) = 94391255481766283 * c15574(7139749225......)

n=16933: c13909(7123347484......) = 6671930562294936569 * c13891(1067659115......)

n=16945: c13543(2832450421......) = 65460369669041 * c13529(4326969791......)

n=16973: c15388(7881961178......) = 16150141491881 * x15375(4880428559......)

n=16973: x15375(4880428559......) = 24084053771317 * c15362(2026414907......)

n=16979: c16969(1479980893......) = 84472442356767053 * c16952(1752028060......)

n=16989: c9692(1633385654......) = 1154217424808449 * c9677(1415145551......)

n=17001: c11328(9990000009......) = 293785265709721 * c11314(3400442832......)

n=17015: c13088(1725966941......) = 10324281721366831 * c13072(1671754983......)

n=17039: c15463(2864904596......) = 5969680988129 * c15450(4799091614......)

n=17071: c16623(9032825404......) = 32024699682218603 * c16607(2820580831......)

n=17083: c15510(5711592188......) = 2106255675268867 * c15495(2711727856......)

n=17147: c15811(2186966167......) = 1057699566502333 * c15796(2067662913......)

# The ratio of factored part of (28*10^17147-37)/9+1 was raised from 0.42% to 0.51%.

n=17155: c13218(1596601384......) = 5850742464655841 * c13202(2728886793......)

n=17159: c17154(3237597573......) = 78449213763240559 * c17137(4126998114......)

n=17177: c16878(1709234988......) = 199873201719715187 * c16860(8551596579......)

n=17179: c16710(5851501407......) = 165254795810917 * c16696(3540896576......)

n=17185: c11750(5192589460......) = 66583768796213955791 * c11730(7798581477......)

n=17193: c10378(2039398221......) = 3837076693627 * c10365(5314979044......)

n=17199: c9063(5710923804......) = 23246671333159 * c9050(2456663030......)

n=17245: c13775(7175338817......) = 140211863247030041 * c13758(5117497657......)

n=17249: c16814(4462269410......) = 7047915043529 * c16801(6331332575......)

n=17257: c17246(2727284344......) = 6528243959399 * c17233(4177669158......)

n=17269: c14796(9000000900......) = 203516879302910913209 * c14776(4422238062......)

n=17301: c11222(1571288021......) = 39654252044329009 * c11205(3962470456......)

n=17327: c17316(6728601516......) = 501197992920908117 * c17299(1342503683......)

n=17339: c14836(9314504592......) = 617381468141909563 * c14819(1508711400......)

n=17351: c17344(7446192140......) = 4933942956827 * c17332(1509176779......)

n=17365: c13201(1111099999......) = 11770201677643081 * c13184(9439940201......)

n=17367: c9903(1361704281......) = 26004926386951 * c9889(5236331998......)

n=17371: c16725(9499518920......) = 19120282317043 * c16712(4968294276......)

n=17381: c13666(2344989035......) = 30772737943403 * c13652(7620345773......)

n=17385: c8619(2781178154......) = 377863723044839761 * x8601(7360267696......)

n=17385: x8601(7360267696......) = 2362336215980784751 * c8583(3115673225......)

n=17395: c11755(1437192674......) = 224784188804911 * x11740(6393655541......)

n=17395: x11740(6393655541......) = 4487831987495431 * c11725(1424664639......)

n=17403: c11593(4006732677......) = 1980242718148333 * c11578(2023354329......)

n=17417: c17396(3647404249......) = 126007404654448679 * c17379(2894595170......)

n=17423: c14027(7073673555......) = 5922685134461467 * c14012(1194335575......)

n=17435: c12632(4236679485......) = 321165989549791 * c12618(1319155708......)

n=17443: c17434(1587725371......) = 9012832044079 * c17421(1761627603......)

n=17447: c17131(8597384484......) = 252557715520759243253 * c17111(3404126643......)

n=17455: c13950(3985430991......) = 53516668472041 * c13936(7447083508......)

n=17457: c10091(1083636205......) = 72548318269879 * c10077(1493675155......)

n=17463: c11631(1343375855......) = 20383365186319 * c11617(6590549907......)

n=17465: c11947(7952275526......) = 1040521513770551 * c11932(7642586358......)

n=17475: c9281(1000010000......) = 3641777089889401 * c9265(2745939620......)

n=17501: c15108(3778853113......) = 4109759407857818969 * c15089(9194828062......)

n=17503: c16707(1584726928......) = 5396504989357049 * c16691(2936580123......)

n=17517: c11667(1025328966......) = 18303381502093 * c11653(5601855406......)

n=17547: c11688(4556457298......) = 73928507403087249769 * c11668(6163329220......)

n=17589: c9600(9009009009......) = 425426547692719 * c9586(2117641472......)

n=17601: c11726(1752898390......) = 728090792249449 * c11711(2407527205......)

n=17607: c11720(2372096353......) = 1001688010440723871 * c11702(2368098978......)

n=17621: c17282(5426812361......) = 2039370822452791 * c17267(2661022851......)

n=17625: c9175(2637435936......) = 45201788037001 * c9161(5834804442......)

n=17633: c13676(3150568520......) = 50810153127194693 * c13659(6200667241......)

n=17639: c17009(2287106649......) = 1472169884976250723843 * c16988(1553561632......)

n=17641: c15294(4562209875......) = 1774015551173893 * c15279(2571685390......)

n=17669: c17661(3163218029......) = 24209511113681 * c17648(1306601366......)

n=17671: c17189(1948810360......) = 2520820330296464717 * c17170(7730857836......)

n=17699: c16047(5838115898......) = 175381776117241 * c16033(3328804182......)

n=17719: c15452(1567661034......) = 1151182572398093 * c15437(1361783153......)

n=20381: c20060(2207884601......) = 45542491338871 * x20046(4847966231......)

n=20381: x20046(4847966231......) = 90594907877471 * c20032(5351256870......)

n=20385: c10784(1050932221......) = 5241363032944711 * c10768(2005074280......)

n=20409: c13578(1427174952......) = 739677193644043 * x13563(1929456477......)

n=20409: x13563(1929456477......) = 1717282117272013 * c13548(1123552419......)

n=20419: c17482(1189552355......) = 1905842758739162363 * c17463(6241608078......)

n=20445: c10295(2419029872......) = 12617253604677481 * c10279(1917239637......)

n=20463: c12876(2054381186......) = 856348572520662121 * c12858(2399001122......)

n=20497: c20184(1994698422......) = 40121243711677969 * c20167(4971676442......)

n=20507: c20498(5725067681......) = 636462094490425603 * c20480(8995143200......)

n=20509: c20494(5743457033......) = 48931076889241 * c20481(1173785127......)

n=20525: c16392(6992047117......) = 45433176597551 * c16379(1538973860......)

n=20527: c18917(3075061683......) = 133337062443634453 * c18900(2306231760......)

n=20547: c13671(1966309193......) = 9827652496231 * c13658(2000792350......)

n=20553: c11520(9009009009......) = 2181442221478027 * c11505(4129840763......)

n=20559: c10560(9009009910......) = 185002043100799 * c10546(4869681306......)

n=20563: c20553(2787380440......) = 3647769563271037681 * c20534(7641328193......)

n=20573: c17628(9000000900......) = 12600324677177830601 * c17609(7142673804......)

n=20579: c18968(6786035844......) = 31912152017899921 * c18952(2126473902......)

n=20593: c20581(7797824395......) = 4370093857505741191 * c20563(1784360851......)

n=20597: c20066(4554366352......) = 404385981866847763 * c20049(1126242391......)

n=20611: c20605(8984701748......) = 145682567056702477 * c20588(6167314270......)

n=20619: c13105(1001000999......) = 23327859724427809 * c13088(4291010884......)

n=20631: c12129(8220540913......) = 52060707882505999 * c12113(1579029799......)

n=20637: c13742(4257439927......) = 1973566745713603 * c13727(2157231285......)

n=20643: c11779(3360692875......) = 297251433277681 * c11765(1130589292......)

n=20671: c17705(5469756231......) = 8507673811799 * c17692(6429203038......)

n=20687: c20390(8886162081......) = 14859841652569 * c20377(5979984369......)

n=20697: c13779(1465808836......) = 223862404263527923 * c13761(6547811552......)

n=20721: c13802(3496980183......) = 100133004600891721 * c13785(3492335217......)

n=20743: c20729(3280220049......) = 461689516611569 * c20714(7104818133......)

n=20753: c20739(1387135899......) = 44090854468877 * c20725(3146085318......)

n=20763: c13813(4891201702......) = 62025810280908373 * c13796(7885752205......)

n=20775: c11034(2005635378......) = 38101282774593001 * c11017(5263957620......)

n=20777: c20423(2615350108......) = 3872142403352471 * c20407(6754271501......)

n=20793: c13329(1109999999......) = 16514833656119182369 * c13309(6721230277......)

n=20817: c13824(9999999999......) = 206162313315405076834218631 * c13798(4850547046......)

n=20825: c13431(4493151401......) = 4018260002986601 * c13416(1118183342......)

n=20843: c19728(9000000000......) = 177339425933795173133 * c19708(5075013608......)

n=20867: c16186(5407386058......) = 1933037048724013 * c16171(2797352519......)

n=20881: c16839(1407274446......) = 27559233417689 * c16825(5106362810......)

n=20895: c9490(5027537800......) = 117733282017443205121 * c9470(4270277456......)

n=20907: c13190(1374862129......) = 7500637896687361 * c13174(1832993604......)

n=20911: c19000(9000000000......) = 3951614315173801 * c18985(2277550206......)

n=20915: c16193(1111099999......) = 2662082697692109151 * c16174(4173799713......)

n=20929: c20924(1327222799......) = 76013378365079 * c20910(1746038431......)

n=20931: c13945(4154581358......) = 10636704821467 * c13932(3905891371......)

n=20941: c20407(1023281938......) = 86048918004908849 * c20390(1189186292......)

n=20945: c16241(1111099999......) = 1456811478678991 * c16225(7626930568......)

n=20949: c13964(9009009009......) = 1998238735161801679 * c13946(4508474813......)

n=20969: c19333(5301344526......) = 10179305911592039 * c19317(5207962676......)

n=20985: c11179(3778158282......) = 7267573171711 * c11166(5198651865......)

n=20989: c20684(6541977401......) = 312855475441237 * c20670(2091054149......)

n=21015: c11177(1164613456......) = 370241232741631 * c11162(3145553098......)

n=21017: c21008(4527856748......) = 137006703614827 * c20994(3304843214......)

December 6, 20102010 年 12 月 6 日 (Makoto Kamada)

n=70006: c31351(1180300295......) = 5956660937179 * c31338(1981479737......)

n=70056: c19854(2725014558......) = 7355672424073 * c19841(3704643710......)

n=70121: c70110(6376714572......) = 7100056837319 * c70097(8981216233......)

n=35071: c32992(9000000000......) = 6987687095563 * c32980(1287979824......)

n=70156: c35076(9900990099......) = 9047887987969 * c35064(1094287430......)

n=70161: c36852(3271439469......) = 6635684391883 * c36839(4930070926......)

n=70213: c58801(1111111111......) = 9336937097489 * c58788(1190016704......)

n=70227: c44064(9999999999......) = 8902938736711 * c44052(1123224622......)

n=70344: c23419(7107876237......) = 9449632539649 * c23406(7521854641......)

n=70392: c20060(1420453752......) = 5534366370457 * c20047(2566605926......)

n=70401: c45352(6761072640......) = 6725858659609 * c45340(1005235611......)

n=70425: c37435(2366578235......) = 9040537252801 * c37422(2617740704......)

n=70430: c28162(7809088592......) = 6490553841281 * c28150(1203146724......)

n=70437: c45969(1109999999......) = 5319571007053 * c45956(2086634426......)

n=70468: c34633(1009999999......) = 5273833223821 * c34620(1915115547......)

n=35235: c18131(2129305178......) = 7488516818521 * c18118(2843427116......)

n=70480: c28134(8626797528......) = 5965209557761 * c28122(1446185158......)

n=70483: c60401(2391205513......) = 6285113741117 * c60388(3804554081......)

n=70569: c47040(9990000009......) = 7527419654329 * c47028(1327148009......)

n=35293: c34048(9000000000......) = 8421455923883 * c34036(1068698818......)

n=70597: c70060(9000000000......) = 5226767497961 * c70048(1721905557......)

n=70767: c47153(1072145678......) = 5896300495573 * c47140(1818336225......)

December 5, 20102010 年 12 月 5 日 (Serge Batalov)

n=14801: c13680(9999999999......) = 2863885332722040553627 * c13659(3491759912......)

n=14805: c6607(8584366966......) = 45412702716710071 * x6591(1890300830......)

n=14805: x6591(1890300830......) = 8469088941716551 * c6575(2232000211......)

n=14819: c12089(1028515916......) = 36766987592441 * c12075(2797389679......)

n=14823: c9709(1519090836......) = 41421558551671 * x9695(3667391788......)

n=14823: x9695(3667391788......) = 24307982158977058357 * c9676(1508719137......)

n=14925: c7909(1464067023......) = 75337778359201 * c7895(1943337134......)

n=14947: c14916(2515103628......) = 151752925522748440169 * c14896(1657367474......)

n=14967: c9955(1395819030......) = 15704132532841 * c9941(8888227527......)

n=14999: c14653(2248777019......) = 40289337545089 * c14639(5581568613......)

n=15003: c9991(3026658226......) = 979354640201689 * c9976(3090461925......)

n=15013: c15006(4458427857......) = 18218038294601 * c14993(2447260119......)

n=15017: c14999(2270930810......) = 81835717451205761 * c14982(2774987354......)

n=15027: c9988(9498870221......) = 1288103527963627 * c9973(7374306502......)

n=15047: c14625(5755907185......) = 6503268851340203 * c14609(8850790760......)

n=15049: c14783(7703539264......) = 634513381596881 * c14769(1214086178......)

n=15063: c10035(1495219089......) = 3567336465129721 * c10019(4191415931......)

n=15071: c12903(1431185115......) = 1338213476552093 * c12888(1069474445......)

n=15087: c9742(1648891502......) = 367450036823794027 * c9724(4487389677......)

n=15099: c8605(2535842699......) = 145405207880479 * c8591(1743983407......)

n=8353: c8341(1569821485......) = 23954115005702173483 * c8321(6553452235......)

n=10247: c10214(1921189673......) = 19766308625769803159483 * c10191(9719516727......)

n=10381: c8880(2766703923......) = 13567552596461552963 * c8861(2039206337......)

n=10387: c8833(1111111111......) = 205368643751377751347 * c8812(5410325017......)

# The ratio of factored part of 2*10^10388-19-1 was raised from 3.31% to 3.50%.

n=10527: c6142(4666089461......) = 608021651595300612018654069733 * c6112(7674215958......)

n=10661: c9088(6753019814......) = 177298469153936214449 * c9068(3808842708......)

n=11605: c8384(2604880331......) = 9363503873481529201 * c8365(2781950396......)

n=11643: c7741(5340448943......) = 34543546296670475209 * c7722(1546004830......)

n=11717: c11686(1293292044......) = 632369516845613544961 * c11665(2045152415......)

n=11751: c7790(6608283833......) = 1201797437204330107 * c7772(5498666937......)

n=11771: c11540(1274300196......) = 74690040958184100587 * c11520(1706117951......)

n=11797: c11457(2809293274......) = 645110091948711329 * x11439(4354750157......)

n=11797: x11439(4354750157......) = 4814988277246469083 * c11420(9044155263......)

n=11833: c11813(9969867049......) = 6227407238592928991 * c11795(1600965966......)

n=11857: c11620(9000000000......) = 5237086216895966959 * c11602(1718512857......)

n=15101: c15096(3678810419......) = 45784706738597 * c15082(8035020167......)

n=15115: c12088(9000090000......) = 48871025022059940041 * c12069(1841600415......)

n=15127: c12955(2124861801......) = 15015236036249 * c12942(1415137128......)

n=15153: c10087(8090872306......) = 6264436793994146827 * c10069(1291556220......)

n=15165: c8042(9514658671......) = 21094117313041 * c8029(4510574455......)

n=15175: c12107(3159818827......) = 1119410675843236184201 * c12086(2822752092......)

n=15201: c10099(3451696535......) = 15692734108801 * c10086(2199550767......)

n=15223: c14027(1819675218......) = 65587165799495471 * c14010(2774437951......)

n=15231: c10140(5236583603......) = 70913443996500997 * c10123(7384472263......)

n=15233: c15228(3646933111......) = 84683999373080056968241 * c15205(4306519695......)

n=15241: c15231(2095232293......) = 281474981580777908477 * c15210(7443760300......)

n=15249: c8428(4144032906......) = 66668877959122413001 * c8408(6215843184......)

n=15261: c10147(7510342913......) = 548465374422439 * c10133(1369337658......)

n=15281: c12516(8545821789......) = 496129665431093 * c12502(1722497642......)

n=15303: c10194(6262853998......) = 158737631160769 * c10180(3945412283......)

n=15313: c15302(7879418487......) = 1029385555438802867 * c15284(7654487131......)

n=15317: c14144(9999999999......) = 443246676987991 * c14130(2256080083......)

n=15319: c15310(1236684898......) = 165951266259439 * c15295(7452096788......)

n=15333: c9634(7582153198......) = 58985659272517 * c9621(1285423150......)

n=15351: c8064(9009009909......) = 66648175799563 * c8051(1351726405......)

n=15371: c14538(2788180962......) = 400169553629231 * c14523(6967498995......)

n=15373: c15365(1150904306......) = 16219960584683 * c15351(7095604829......)

n=15383: c15374(1203549276......) = 22574195311047241 * c15357(5331526815......)

n=15405: c7483(9746837208......) = 3767851242871 * c7471(2586842361......)

n=15413: c15396(2586299634......) = 2854491873809119 * c15380(9060455410......)

n=15417: c10252(4764467609......) = 96622172097877 * c10238(4931029292......)

n=15419: c14484(1551408551......) = 70778886474013 * c14470(2191908673......)

n=15429: c9937(1109999999......) = 4344899970003667 * c9921(2554719343......)

n=15439: c15434(1799166266......) = 80591289850550081 * c15417(2232457464......)

n=15461: c15430(1460174570......) = 233713741861991 * c15415(6247705241......)

n=15471: c10254(1709974916......) = 40772464095547 * c10240(4193945483......)

n=15523: c14359(6442012226......) = 4554586385747 * x14347(1414401151......)

n=15523: x14347(1414401151......) = 793007944969105037 * c14329(1783590139......)

n=15543: c9339(2473348009......) = 287363646433711 * x9324(8607031684......)

n=15543: x9324(8607031684......) = 1933339747754449 * c9309(4451898169......)

n=15567: c10376(9009009009......) = 99608119941978908641 * c10356(9044452414......)

n=15573: c9963(1697073847......) = 21547902783283 * c9949(7875819119......)

n=15579: c10356(6606946517......) = 3058817190166961479 * c10338(2159967760......)

n=15613: c14395(1441104462......) = 420282683951664587 * c14377(3428893260......)

n=15615: c8290(2393484280......) = 3316853683640900881 * c8271(7216128622......)

n=15623: c14670(5338712497......) = 3036402836369653 * c14655(1758235907......)

n=15693: c10443(6719842196......) = 40001104284133 * c10430(1679914171......)

n=15695: c12092(3539549552......) = 323038453678081 * c12078(1095705329......)

n=15705: c8342(2839817986......) = 172169364821761 * c8328(1649432806......)

n=15709: c14999(2046138141......) = 12798342011572151 * c14983(1598752510......)

n=15717: c9361(1000000000......) = 26184457292509443126854355637 * c9332(3819059485......)

n=15721: c15426(1855553619......) = 9308864380192609 * c15410(1993318994......)

n=15731: c15725(3923983031......) = 891649792111009 * c15710(4400811917......)

n=15747: c10074(2136048591......) = 16905026419482079 * c10058(1263558268......)

n=15751: c14872(4467108771......) = 211690888684523 * c14858(2110203608......)

n=15765: c8392(4767634734......) = 94933434399603841 * c8375(5022081803......)

n=15809: c15792(1880883324......) = 34451167914679 * c15778(5459563313......)

n=15817: c15809(1059546066......) = 639884741500518667 * c15791(1655838930......)

n=15831: c10536(8827259380......) = 178298379194959 * c10522(4950835459......)

n=15847: c13721(2909332635......) = 403826573245031 * x13706(7204411072......)

n=15847: x13706(7204411072......) = 4496710473707862027427552627 * c13679(1602151420......)

n=15863: c15274(5973413812......) = 83924736872980637 * c15257(7117584201......)

n=15869: c13588(7144665400......) = 4979568650796366719 * c13570(1434796043......)

n=15899: c14659(4043362819......) = 1888840950465068107 * c14641(2140658173......)

n=15907: c15891(3461103310......) = 50567410246798267 * c15874(6844533453......)

n=15917: c14454(1234570102......) = 73965192227323 * c14440(1669123091......)

n=15953: c13100(3482342432......) = 23863021487957 * c13087(1459304905......)

n=15959: c15953(1657684503......) = 140532851401751 * x15939(1179570816......)

n=15959: x15939(1179570816......) = 1596396093781763 * c15923(7388960806......)

n=15963: c9979(6953536593......) = 10923471325392601 * c9963(6365683935......)

n=15965: c12229(1340479513......) = 58669509617471 * c12215(2284797541......)

n=15979: c14609(7783847535......) = 24154324424911 * c14596(3222548227......)

n=15985: c12122(1675380990......) = 133854260776923241 * x12105(1251645619......)

n=15985: x12105(1251645619......) = 114758221297108600031 * c12085(1090680567......)

n=15997: c15032(9859892785......) = 13192534348498643 * c15016(7473842800......)

n=16003: c14756(1405964413......) = 160314061580105603 * c14738(8770062960......)

n=16005: c7680(9009099100......) = 3557811735937471 * c7665(2532202311......)

n=16013: c15693(4807889684......) = 170610247840387 * c15679(2818054451......)

n=16025: c12795(4457256709......) = 2141270736225151 * c12780(2081594183......)

n=16037: c13105(1111110999......) = 38139150228397 * x13091(2913308223......)

n=16037: x13091(2913308223......) = 288963237453103631321 * c13071(1008193377......)

n=19239: c11422(9299104771......) = 68435802107707 * x11409(1358807011......)

n=19239: x11409(1358807011......) = 924377087456397037 * c11391(1469970458......)

n=19243: c16488(9000000900......) = 3176091929336369 * c16473(2833671411......)

n=19283: c17499(9792752482......) = 11995135572011747 * c17483(8163936475......)

n=19299: c10995(4555310292......) = 1111628365977067 * c10980(4097871583......)

n=19309: c19295(4468735070......) = 67264793086877 * c19281(6643497832......)

n=19311: c12481(1109999999......) = 1903529958309223879 * c12462(5831271502......)

n=19317: c12505(1970587717......) = 32199754720621262689 * c12485(6119884250......)

n=19323: c12091(4316948209......) = 828437746555999 * c12076(5210950644......)

n=19347: c12886(2747746798......) = 7619640163159 * c12873(3606137218......)

n=19351: c18787(7751470626......) = 968654368962083 * c18772(8002308020......)

n=19355: c13085(4101498193......) = 26277034134751 * c13072(1560868008......)

n=19361: c18310(1226969375......) = 18583435173323 * c18296(6602489604......)

n=19373: c19368(2867605520......) = 121601516680759 * c19354(2358198811......)

n=19389: c12313(1993348000......) = 28702713302077 * c12299(6944806852......)

n=19399: c18353(1260025621......) = 999514319098025329 * c18335(1260637889......)

n=19431: c12090(4441004136......) = 2553082239489013 * c12075(1739467717......)

n=19433: c19417(3490912766......) = 92523581898227 * c19403(3772997861......)

n=19451: c19016(2193455965......) = 7567010689459029242123 * c18994(2898708691......)

n=19461: c11948(2851784292......) = 7882119285769 * c11935(3618042544......)

n=19465: c14586(1274150343......) = 37672372660981231 * c14569(3382187671......)

n=19471: c19465(9510739050......) = 796830462544321 * c19451(1193571217......)

n=19473: c12973(2514353418......) = 28334264283133 * c12959(8873896965......)

n=19483: c19478(1425726086......) = 45645563793498203 * x19461(3123471304......)

n=19483: x19461(3123471304......) = 732622095533399453 * c19443(4263414007......)

n=19493: c19183(1768968081......) = 30614072452080014587 * c19163(5778284101......)

n=19525: c13995(3201046091......) = 6301891303951 * c13982(5079500640......)

n=19541: c19530(2219242690......) = 106264466113054729 * c19513(2088414661......)

n=19545: c10417(1109988900......) = 6593800038087751 * c10401(1683382713......)

n=19553: c19548(2841207740......) = 28330721888533 * x19535(1002871635......)

n=19553: x19535(1002871635......) = 555248001861802973 * c19517(1806168833......)

n=19561: c18900(9000000000......) = 1896845702879949121 * c18882(4744719080......)

n=19563: c13032(2451882923......) = 12330918350563 * c13019(1988402528......)

n=19571: c19563(5840878682......) = 2181403495169359 * c19548(2677578309......)

n=19575: c10062(4465388838......) = 2503893289262401 * c10047(1783378252......)

n=19589: c18540(9000000000......) = 6672467002907271733 * c18522(1348826452......)

n=19613: c17816(2294338083......) = 129969602115893 * c17802(1765288225......)

n=19627: c18571(7642468347......) = 54076548161479 * c18558(1413268525......)

n=19635: c7648(6196368461......) = 3499672978651081 * c7633(1770556420......)

n=19641: c13062(5906558844......) = 51639567212719 * c13049(1143804869......)

n=19649: c16784(1686333594......) = 11604912395161 * c16771(1453120486......)

n=19653: c13084(1330331302......) = 5246989463413 * c13071(2535418284......)

n=19659: c13085(7741223201......) = 772120551285649 * c13071(1002592560......)

n=19667: c19313(7704029010......) = 69209416741081 * c19300(1113147512......)

n=19677: c11216(1051157739......) = 14834468773363 * c11202(7085914270......)

# The ratio of factored part of (14*10^19677-11)/3-1 was raised from 0.70% to 0.77%.

n=19693: c19221(5785001945......) = 116021483263067402467 * c19201(4986147205......)

n=19707: c13127(1812567557......) = 139847391276020191 * c13110(1296103946......)

n=19719: c11220(1038178656......) = 299520135198397 * c11205(3466139781......)

n=19735: c15771(4782003726......) = 7010086817134792441 * c15752(6821604141......)

n=19737: c12086(2150447412......) = 227278490590286911 * c12068(9461728676......)

n=19747: c15111(8351574750......) = 10324775228951 * c15098(8088868343......)

n=19753: c19745(3336313428......) = 864652278838373 * c19730(3858560846......)

n=19755: c10507(1266767569......) = 20355815956076911 * c10490(6223123514......)

n=19761: c11266(2838680467......) = 39294704828191 * c11252(7224078867......)

n=19769: c19344(9000000000......) = 604496646389520217631 * c19324(1488842006......)

n=19777: c19762(7982570171......) = 17582241208495591 * c19746(4540132328......)

n=19783: c19432(3062305160......) = 280758096010477 * c19418(1090727285......)

n=19793: c19775(1612032170......) = 6300853949529877187 * c19756(2558434433......)

n=19799: c18259(1082304442......) = 106332131397493 * c18245(1017852673......)

n=19821: c13196(2631177330......) = 15352167607279 * c13183(1713880018......)

n=19825: c14380(1277498345......) = 943398809384201 * c14365(1354144538......)

n=19835: c15841(3032767132......) = 1225916796290911 * c15826(2473876809......)

n=19839: c12411(5595011870......) = 5388145509757 * x12399(1038392868......)

n=19839: x12399(1038392868......) = 593017916404507831 * c12381(1751031190......)

n=19843: c19830(2649529649......) = 83874107906723 * c19816(3158936310......)

n=19849: c18957(1249788698......) = 543178686667009 * c18942(2300879488......)

n=19853: c19847(4663889786......) = 4922337123662317 * c19831(9474949946......)

n=19863: c13236(9990000009......) = 11810336201310277 * c13220(8458692318......)

n=19869: c12808(6794687599......) = 11076811327077031 * c12792(6134154856......)

n=23359: c19305(8675993176......) = 1451008668928635881 * c19287(5979284177......)

n=23369: c23358(7394067746......) = 45968770806151 * c23345(1608498033......)

n=23379: c15570(3709974962......) = 169098054001119049 * c15553(2193978508......)

n=23407: c23041(2837218259......) = 1191798892049587 * c23026(2380618305......)

n=23465: c16399(1567488327......) = 383522570146335881 * c16381(4087082349......)

n=23467: c22674(3551084520......) = 56684469037681 * c22660(6264651643......)

n=23469: c15636(7550520494......) = 51407465273809 * c15623(1468759538......)

n=23477: c22080(9000000000......) = 755684870057111 * c22066(1190972633......)

n=23479: c22979(3833196332......) = 66764059207067 * c22965(5741406944......)

n=23511: c14692(4996966674......) = 11398122643249 * c14679(4384026063......)

n=23553: c15691(7069113148......) = 1226077606878121 * x15676(5765632704......)

n=23553: x15676(5765632704......) = 6748760798734879 * c15660(8543246495......)

n=23555: c16124(2358472307......) = 10492932267791 * c16111(2247677053......)

n=23569: c18126(7535313354......) = 580902598490761 * c18112(1297173290......)

n=23587: c23241(2034801666......) = 1364861588145563 * c23226(1490848364......)

n=23589: c15712(1168476106......) = 337032583370911 * c15697(3466952940......)

n=23605: c18875(2382987230......) = 13024019990591 * c18862(1829686403......)

n=23621: c20586(9799808531......) = 56251292662360071667 * c20567(1742148147......)

n=23633: c23622(1519952697......) = 24826184509247893 * c23605(6122377351......)

n=23641: c23081(2294795544......) = 53205767482800787 * c23064(4313057874......)

n=23649: c15759(9523567353......) = 819476706252961 * c15745(1162152295......)

n=23651: c23209(1952546087......) = 2786435673036066757 * c23190(7007325186......)

n=23655: c11800(1901037751......) = 37075246266151 * c11786(5127512136......)

n=23657: c23022(1283553844......) = 22334630309308441 * c23005(5746922276......)

n=23665: c18922(7042814406......) = 47179503994391 * c18909(1492769912......)

n=23679: c15768(9999999990......) = 17678702067590718361 * c15749(5656523850......)

n=23691: c15384(1628771304......) = 4624581900496561 * c15368(3521986071......)

n=23715: c11516(2106217454......) = 248096689615351 * c11501(8489502452......)

n=23717: c23025(5750883010......) = 9455450347627 * c23012(6082082607......)

n=23735: c18383(1799537837......) = 48387969021191 * c18369(3718977825......)

n=23741: c23735(5850139321......) = 20872368085111 * c23722(2802815328......)

n=23747: c23734(5907065770......) = 905221677349232086609 * c23713(6525546082......)

n=23773: c23768(1168446795......) = 388745604629449 * c23753(3005684904......)

December 5, 20102010 年 12 月 5 日 (Kurt Beschorner)

n=8081: c8046(3290136222......) = 570150005031274421866526837 * x8019(5770650168......)

n=8081: x8019(5770650168......) = 950854642126763033066863523 * c7992(6068908866......)

# The ratio of factored part of (52*10^16162-43)/9-1 was raised from 0.32% to 0.65%.

n=8203: c7546(7080005760......) = 640149892472211026933 * x7526(1105991868......)

n=8203: x7526(1105991868......) = 416610158340049632533173 * c7502(2654740521......)

n=8261: c7495(3026257830......) = 120569397439193867209519 * c7472(2509971762......)

n=10531: c10531(1111111111......) = 18781035401346912791 * c10511(5916133415......)

# 2557 of 9592 R_prime factorizations are still blank.

n=11031: c7352(9009009009......) = 39193807949002909288774384387 * c7324(2298579668......)

n=11091: c7363(5344171382......) = 665711724244435719079 * c7342(8027756141......)

December 5, 20102010 年 12 月 5 日 (Makoto Kamada)

n=89522: c42104(1220085631......) = 5621244296809 * c42091(2170490316......)

n=89523: c49393(1000000000......) = 8327353007359 * c49380(1200861785......)

n=89539: c80251(3102301814......) = 5172719425387 * c80238(5997429127......)

n=89560: c35801(9970370026......) = 6296937985841 * c35789(1583367987......)

n=44789: c44780(2028760093......) = 6485609425759 * c44767(3128094772......)

n=44815: c35848(9000090000......) = 9939072940751 * c35835(9055261043......)

n=89645: c71704(3588170480......) = 7932999448921 * c71691(4523094326......)

n=29915: c23035(2063435171......) = 5541174894751 * c23022(3723822492......)

n=44885: c34951(3153905345......) = 8960412568711 * c34938(3519821572......)

n=29945: c23278(7055023890......) = 7432562687521 * c23265(9492047611......)

n=89845: c57594(1043474161......) = 6910489269601 * c57581(1509985936......)

n=89859: c46560(9009009910......) = 5543034905563 * c46548(1625284715......)

n=44953: c44909(1240652943......) = 8220180651511 * c44896(1509276980......)

n=89914: c39600(9090909091......) = 9180526366397 * c39587(9902383292......)

n=89924: c44955(5505168279......) = 8702684655281 * c44942(6325827600......)

n=14993: c12876(1235130571......) = 8184956010529 * c12863(1509025302......)

n=44989: c38549(2696077019......) = 5738953131787 * c38536(4697855092......)

n=44991: c29981(2891203159......) = 9025218265267 * c29968(3203471733......)

December 4, 20102010 年 12 月 4 日 (Makoto Kamada)

n=14825: c11825(3752720304......) = 8952463923751 * p11812(4191829575......)

# Phi_14825(10) is the 1009th factorized number of the form Phi_n(10) (n<=100000, L and M are combined).

```Primality testing 4191829575...... [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N+1 test using discriminant 23, base 6+sqrt(23)
Calling N+1 BLS with factored part 0.11% and helper 0.07% (0.40% proof)
4191829575...... is Fermat and Lucas PRP! (55.1480s+0.0696s)
```

n=29675: c23704(5071169220......) = 8483654467801 * c23691(5977576337......)

n=89027: c88200(9000000000......) = 8324986525763 * c88188(1081082830......)

n=89041: c89019(2530821870......) = 6430551704921 * c89006(3935621679......)

n=44535: c23739(1384663143......) = 6061978522231 * c23726(2284176920......)

n=89082: c25181(3122412938......) = 7767760566259 * c25168(4019708011......)

n=89121: c58321(1109999999......) = 6638348975563 * c58308(1672102512......)

n=89144: c40463(7888350913......) = 8296387201433 * c40450(9508175934......)

n=89182: c40320(9090909090......) = 5125721715973 * c40308(1773586159......)

n=89191: c87978(2102229554......) = 6947202759919 * c87965(3026008635......)

n=89192: c44585(8366153633......) = 5791107231601 * c44573(1444655279......)

n=89197: c88540(9000000000......) = 5925287849917 * c88528(1518913549......)

n=89238: c29239(4200365928......) = 6748337831449 * c29226(6224297053......)

n=89271: c46645(2611572176......) = 8022877611841 * c46632(3255156444......)

n=89327: c76524(9999999000......) = 5503385374957 * c76512(1817063192......)

n=29799: c15109(2446087320......) = 6032378503999 * c15096(4054930106......)

n=89422: c44705(1694380232......) = 5694042246917 * c44692(2975707166......)

n=29809: c27499(7547992653......) = 8238847268809 * c27486(9161466898......)

n=89464: c43681(1000099999......) = 6192901968457 * c43668(1614913339......)

December 3, 20102010 年 12 月 3 日 (Makoto Kamada)

n=43768: c21872(5940056672......) = 9859691327921 * c21859(6024586850......)

n=87544: c42213(3387018617......) = 8872166727577 * c42200(3817577737......)

n=43773: c29166(2059460774......) = 6092011061947 * x29153(3380592637......)

n=43773: x29153(3380592637......) = 9006432022129 * c29140(3753531508......)

n=87576: c28151(5428896274......) = 9017253206641 * c28138(6020565409......)

n=87578: c43788(9090909090......) = 8247355743167 * c43776(1102281673......)

n=87586: c43792(9090909090......) = 9714270815609 * c43779(9358303122......)

n=87615: c41752(6477622389......) = 5494116561121 * c41740(1179010732......)

n=87746: c43161(3545629049......) = 7342262374721 * c43148(4829068845......)

n=21983: c19009(1111111111......) = 7099042294241 * c18996(1565156347......)

n=87966: c29161(1000000000......) = 7136051743441 * c29148(1401335130......)

n=88084: c41041(1000000000......) = 6669051922441 * c41028(1499463509......)

n=44077: c40060(9000000000......) = 5097920519803 * c40048(1765425719......)

n=88225: c70560(9999900000......) = 5528959114801 * c70548(1808640612......)

n=44113: c42660(9000000000......) = 5993950658923 * c42648(1501513861......)

n=88245: c44928(9990000009......) = 7682648351311 * c44916(1300332847......)

n=22063: c22047(1283514716......) = 5285733870289 * c22034(2428262087......)

n=88269: c58844(9009009009......) = 7915888185199 * c58832(1138091999......)

n=88330: c31675(2830287472......) = 9043202522531 * c31662(3129740227......)

n=44189: c44182(2565766562......) = 7160061654631 * c44169(3583441995......)

n=22113: c11649(4186993289......) = 7809147040969 * c11636(5361652517......)

n=88520: c35393(1000099999......) = 5223435075601 * c35380(1914640433......)

n=88557: c50593(1109999889......) = 8690224515169 * c50580(1277297136......)

n=44281: c44269(2620165491......) = 8955708351763 * c44256(2925693187......)

n=88576: c44032(9999999999......) = 5809265640449 * c44020(1721387972......)

n=44289: c23323(1025289447......) = 7265380944403 * c23310(1411198470......)

n=88667: c88656(2164043119......) = 9090140485333 * c88643(2380648707......)

n=88674: c29550(2294924791......) = 6500222209237 * c29537(3530532831......)

n=44347: c43554(5073621060......) = 9369498014711 * c43541(5415040434......)

n=44351: c44332(8202694248......) = 6348583446889 * c44320(1292051103......)

n=88706: c41720(3570548234......) = 7990214949089 * c41707(4468651040......)

n=88748: c40321(1009999999......) = 5839099667941 * c40308(1729718719......)

n=88757: c79543(2660469764......) = 6143609008129 * c79530(4330467256......)

n=44383: c44376(4636037019......) = 5834913442199 * c44363(7945339832......)

n=88830: c19867(2814356598......) = 5338844315281 * c19854(5271471562......)

n=88832: c44279(1947512172......) = 6405963424513 * c44266(3040154997......)

n=88844: c35856(9900990099......) = 5718565065529 * c35844(1731376662......)

n=88852: c43768(5755553078......) = 7179945307841 * c43755(8016151700......)

n=22219: c20890(9644245225......) = 5916139368721 * c20878(1630158558......)

December 2, 20102010 年 12 月 2 日 (Kurt Beschorner)

n=7939: c7383(1173803315......) = 514038994239177010993362881 * c7356(2283490802......)

n=7993: c7970(1191800577......) = 202435511780664467 * x7952(5887309823......)

n=7993: x7952(5887309823......) = 66657858989359944649591 * c7929(8832131593......)

n=9305: c7440(9000090000......) = 2346791818574058433441 * c7419(3835061094......)

n=11097: c7339(2503172771......) = 108825358573200914130413773 * x7313(2300174154......)

n=11097: x7313(2300174154......) = 8104144973507901774407392921 * c7285(2838268765......)

December 2, 20102010 年 12 月 2 日 (Serge Batalov)

n=30166: c15082(9090909090......) = 10135451323343 * c15069(8969417148......)

# ECM B1=500, sigma=858020702

n=39941: c36300(9000000000......) = 241032917514797 * c36286(3733929827......)

# ECM B1=5000, sigma=2655087195

n=30043: c27720(9000000000......) = 5667297219533 * c27708(1588058584......)

# ECM B1=5000, sigma=40019972

n=31365: c15360(9990000009......) = 666573798855871 * c15346(1498708774......)

# ECM B1=500, sigma=3202956509

n=49377: c32401(1109999999......) = 25921352836321 * c32387(4282183908......)

# ECM B1=500, sigma=4001545373

n=31982: c15990(9090909090......) = 43930689255527 * c15977(2069375474......)

# ECM B1=500, sigma=1542492450

n=32127: c21416(9009009009......) = 63440191862557 * c21403(1420079092......)

# ECM B1=500, sigma=2309772505

n=49743: c33156(9990000009......) = 27787100884471 * c33143(3595193342......)

# ECM B1=500, sigma=372569594

n=33670: c10369(1099988890......) = 4017509753531 * c10356(2737986856......)

# ECM B1=500, sigma=3113224142

n=33312: c11073(1000000000......) = 6732375187201 * c11060(1485359879......)

# ECM B1=500, sigma=3963580375

n=33920: c13313(1000000000......) = 7961756332801 * c13300(1256004276......)

# ECM B1=500, sigma=2510212920

n=30291: c19273(1109999999......) = 92446145152729 * c19259(1200699064......)

# ECM B1=5000, sigma=1659245888

n=40081: c39664(9000000000......) = 17583856790917 * c39651(5118331039......)

# ECM B1=5000, sigma=3011402888

n=30166: c15069(8969417148......) = 860126700740130447142009 * c15046(1042801850......)

# ECM B1=5000, sigma=2887152568

n=40075: c27361(1000010000......) = 8679943596646351 * c27345(1152092739......)

# ECM B1=5000, sigma=2343922139

n=40980L: c5456(3913542626......) = 527710018372549805041 * c5435(7416085521......)

# ECM B1=5000, sigma=2420626944

n=30375: c16200(9999999999......) = 55682278402473001 * c16184(1795903523......)

n=30429: c16633(1000000000......) = 140962822913053 * c16618(7094069055......)

n=30447: c19009(1001000999......) = 35713071346717 * c18995(2802898104......)

n=30675: c16321(1000010000......) = 24282714357751 * c16307(4118196941......)

n=30715: c24568(9000090000......) = 1577507914966700881 * c24550(5705258221......)

n=30719: c26497(1111111111......) = 645942177644412923 * c26479(1720140206......)

n=30749: c30336(9000000000......) = 454114508864719 * c30322(1981878980......)

n=30799: c29160(9000000000......) = 38049709203721 * c29147(2365326881......)

n=30891: c17641(1109999889......) = 26153959738243 * c17627(4244098790......)

n=40213: c40213(1111111111......) = 20174383749314689 * c40196(5507534331......)

n=40247: c39840(9000000000......) = 23436797006279 * c39827(3840115181......)

n=40263: c26840(9009009009......) = 362835199583917 * c26826(2482947911......)

n=40285: c27601(1111099888......) = 48076286036223061471 * c27581(2311118392......)

n=40347: c26892(9990000009......) = 36561005766991 * c26879(2732419363......)

n=40397: c33265(1111110999......) = 508761747360721 * c33250(2183951536......)

n=40512: c13441(1000000000......) = 25964689899649 * c13427(3851384337......)

n=40523: c34692(9999999000......) = 2925511069577797 * c34677(3418205832......)

December 2, 20102010 年 12 月 2 日 (Makoto Kamada)

n=86337: c56153(3331641775......) = 5205554383933 * c56140(6400167070......)

n=43219: c39267(1370694053......) = 6634823995031 * c39254(2065908687......)

n=86446: c43198(3396947728......) = 6060650048357 * c43185(5604923071......)

n=86449: c75592(2774782614......) = 6906931205879 * c75579(4017388522......)

n=86454: c28801(1000000000......) = 6326279663131 * c28788(1580707863......)

n=86459: c83626(3644027901......) = 6854689817533 * c83613(5316109115......)

n=86478: c23506(7629006757......) = 5537463242557 * c23494(1377707882......)

n=86479: c81369(2588843425......) = 9420071336917 * c81356(2748220616......)

n=86535: c46081(1000000001......) = 5746927806001 * c46068(1740060141......)

n=86552: c41761(1000099999......) = 5197709333249 * c41748(1924116828......)

n=43294: c21634(7127451732......) = 8683816918373 * c21621(8207740673......)

n=43337: c35991(1437977634......) = 7769446785773 * c35978(1850810842......)

n=86691: c50393(1186311926......) = 6886752285403 * c50380(1722599968......)

n=86692: c43344(9900990099......) = 6635660987941 * c43332(1492087995......)

n=86819: c81688(3865173157......) = 7131198058921 * c81675(5420089479......)

n=86920: c33280(9999000099......) = 5143428765281 * c33268(1944033942......)

n=43503: c27265(1109999999......) = 6619013381203 * c27252(1676987091......)

n=43526: c18640(1685153597......) = 5662006586321 * c18627(2976248034......)

n=43535: c34811(3006959857......) = 5727113882041 * c34798(5250392989......)

n=29037: c19334(2575571256......) = 8638198546321 * c19321(2981606919......)

n=43557: c29030(1988774881......) = 6938064991483 * c29017(2866469085......)

n=87135: c44928(9009099100......) = 9029790465151 * c44915(9977085442......)

n=87278: c40801(1000000000......) = 6442880637493 * c40788(1552100770......)

n=29097: c18691(5473639041......) = 9853854660757 * c18678(5554820149......)

n=87389: c84521(3460515293......) = 8107125943507 * x84508(4268485918......)

n=87389: x84508(4268485918......) = 8662441965677 * c84495(4927578084......)

December 1, 20102010 年 12 月 1 日 (Makoto Kamada)

n=21293: c20983(3522270533......) = 8020236114757 * c20970(4391729225......)

n=85205: c68151(1474436910......) = 7092378142951 * c68138(2078903410......)

n=85226: c41569(8188800254......) = 7270484579219 * c41557(1126307354......)

n=85233: c56803(2101325788......) = 9161330884159 * c56790(2293690529......)

n=85239: c43195(2932921157......) = 6228853904197 * c43182(4708604828......)

n=21311: c20978(3734545265......) = 6821066240917 * c20965(5475016857......)

n=21319: c21310(3777239467......) = 6116810640769 * c21297(6175178028......)

n=85280: c30720(9999999999......) = 9001065898241 * c30708(1110979534......)

n=85321: c83173(6375053465......) = 8164406590871 * c83160(7808348830......)

n=42671: c42000(9000000000......) = 5932443817973 * c41988(1517081370......)

n=85370: c34125(1000729094......) = 7975313548681 * c34112(1254783386......)

n=85383: c55537(1001000999......) = 7418256051961 * c55524(1349375099......)

n=21365: c17077(3067954654......) = 7619139809761 * c17064(4026641761......)

n=42755: c32129(1111099999......) = 8341545050711 * c32116(1332007431......)

n=42807: c26992(7920078897......) = 8486181251881 * c26979(9332912723......)

n=85615: c68470(2529664488......) = 9616292724391 * c68457(2630602625......)

n=42831: c28548(9990000009......) = 8482604681413 * c28536(1177704300......)

n=42851: c42187(3500488123......) = 5924650478363 * c42174(5908345372......)

n=42936: c14278(1786490019......) = 9214346315569 * c14265(1938813626......)

n=85892: c42337(1009999999......) = 9695134140149 * c42324(1041759696......)

n=85910: c30800(9999999999......) = 6047639862331 * c30788(1653537615......)

# The ratio of factored part of 6*10^85910-7+1 was raised from 1.52% to 1.53%.

n=86073: c52939(6447977600......) = 9786773123557 * c52926(6588461302......)

n=86089: c77617(1111111111......) = 5734891049761 * c77604(1937458098......)

n=43049: c43027(1424851091......) = 7665342306533 * c43014(1858822522......)

n=86113: c86107(2150486300......) = 6560550939037 * c86094(3277905042......)

n=17223: c11467(1389319894......) = 9931501204711 * c11454(1398902206......)

n=86167: c85524(5046213259......) = 8648122864559 * c85511(5835038815......)

n=86200: c34393(5420994133......) = 6373145797201 * c34380(8505994223......)

n=86205: c39344(1806329802......) = 8881249263391 * c39331(2033869053......)

n=86264: c41921(1000099999......) = 6258444746129 * c41908(1598000846......)

n=14381: c14098(2431011402......) = 6665862108319 * c14085(3646957232......)

n=86315: c67658(2292154229......) = 5626089210871 * c67645(4074151943......)

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