-- Aug 31, 2017 (Makoto Kamada) -- n=111550: c42213(6313005611......) = 2310051976469609201 * c42195(2732841371......) n=111592: c48379(2986764353......) = 28842615650694270863257 * c48357(1035538659......) n=111610: c44641(1099989000......) = 17591080119788051 * c44624(6253106646......) # P-1 B1=1e6 # 139423 of 200000 Phi_n(10) factorizations were cracked. -- Aug 30, 2017 (Makoto Kamada) -- n=111290: c42954(3889878485......) = 7557452389162891 * c42938(5147076402......) n=111398: c46630(4483383309......) = 247172093761699 * c46616(1813871154......) n=111412: c45408(9900990099......) = 7075320165275881 * 2514504439328974541 * c45374(5565191621......) n=111430: c40445(1526242671......) = 99301528667274121 * c40428(1536978022......) n=111454: c45144(9090910000......) = 1030998125332678567 * c45126(8817581503......) n=111496: c43195(8967954384......) = 665618968221325889 * c43178(1347310520......) n=111518: c48949(1044280749......) = 582527677017529 * c48934(1792671474......) # P-1 B1=1e6 # 139422 of 200000 Phi_n(10) factorizations were cracked. -- Aug 29, 2017 (Makoto Kamada) -- n=110968: c46069(2371999926......) = 31949714913381409 * 269291737791876102161 * c46032(2756923116......) n=110998: c49879(2302623068......) = 48592161564321721 * c49862(4738671823......) n=111010: c41728(9091000000......) = 536170732277011571 * c41711(1695542007......) n=111070: c42773(2021106218......) = 11332702493647242401 * c42754(1783428286......) n=111080: c44409(5557666949......) = 567139347326449483421681 * c44385(9799473401......) n=111146: c44725(3361013161......) = 42085628306671769 * c44708(7986130411......) n=111166: c48575(5077402487......) = 7069924097119865521 * c48556(7181693067......) n=111170: c44454(3805637243......) = 201581518499441 * c44440(1887889957......) # P-1 B1=1e6 # 139420 of 200000 Phi_n(10) factorizations were cracked. -- Aug 28, 2017 (Makoto Kamada) -- n=110732: c49636(2218034822......) = 38608411540078941961 * c49616(5744952288......) n=110750: c44195(3009772732......) = 3597961068453775705261596063442001 * c44161(8365217618......) n=110864: c49905(1478255743......) = 10197931485712108943377 * c49883(1449564301......) n=110870: c44345(1099989000......) = 44172884715451 * c44331(2490190548......) n=110890: c40896(9091000000......) = 3247632595693849091 * c40878(2799269847......) n=110920: c42688(9999000099......) = 8057008138192241 * c42673(1241031401......) n=110930: c44362(5832975839......) = 2515031120511731750208851 * c44338(2319245989......) # P-1 B1=1e6 # 139419 of 200000 Phi_n(10) factorizations were cracked. -- Aug 27, 2017 (Makoto Kamada) -- n=110410: c43186(9889017265......) = 1028786185800811 * c43171(9612315369......) n=110474: c43627(2742993093......) = 1307020251183739 * c43612(2098661509......) n=110560: c44161(1000000000......) = 450991125310936961 * c44143(2217338532......) # P-1 B1=1e6 # 139416 of 200000 Phi_n(10) factorizations were cracked. -- Aug 26, 2017 (Makoto Kamada) -- n=110096: c47137(1000000009......) = 17385711524273 * c47123(5751849779......) n=110126: c49920(9090909090......) = 305690852047336722451 * c49900(2973889807......) n=110152: c47032(8621428645......) = 2444402843167657 * c47017(3527008107......) n=110162: c47952(9090909090......) = 2955112666834303 * c47937(3076332484......) n=110170: c42048(2677866665......) = 4463573029077296862166921 * c42023(5999379080......) n=110210: c43248(9091000000......) = 1407478998020897771 * c43230(6459066183......) n=110278: c47257(1099999890......) = 18494512885593589978624583 * c47231(5947709446......) n=110374: c48118(7507438699......) = 1960398740619089 * c48103(3829546787......) # P-1 B1=1e6 # 139415 of 200000 Phi_n(10) factorizations were cracked. -- Aug 25, 2017 (Makoto Kamada) -- n=109984: c47034(2755220937......) = 8677385460600027430181272001 * c47006(3175174076......) n=110044: c47990(1139908928......) = 53634555475762669 * c47973(2125325581......) n=110050: c41987(1022679635......) = 515086749716251 * c41972(1985451259......) # P-1 B1=1e6 -- Aug 24, 2017 (Alfred Eichhorn) -- # via Kurt Beschorner n=19489: c19489(1111111111......) = 4603739457788488002649 * c19467(2413496943......) # ECM B1=5e4, sigma=13929637873820805088 n=69197: c69197(1111111111......) = 91670990556046511 * c69180(1212064039......) # ECM B1=11e3 # 139410 of 200000 Phi_n(10) factorizations were cracked. # 13834 of 17984 R_prime factorizations were cracked. -- Aug 24, 2017 (Makoto Kamada) -- n=109730: c43866(1828891344......) = 10698851994491 * c43853(1709427651......) n=109750: c43793(1752234067......) = 90091727065001 * c43779(1944944474......) n=109774: c47022(3443755032......) = 701804826386623 * c47007(4906998218......) n=109810: c43056(9091000000......) = 38937870152294081 * c43040(2334745060......) n=109816: c44928(9999000099......) = 28213673813753 * c44915(3544026264......) n=109840: c43896(2192714731......) = 10439719737334561 * c43880(2100357850......) n=109846: c49898(1623930932......) = 2529845582475636009047 * c49876(6419091124......) n=109912: c49877(4381666004......) = 4482162198882597719336617 * c49852(9775786349......) # P-1 B1=1e6 # 139408 of 200000 Phi_n(10) factorizations were cracked. -- Aug 23, 2017 (Makoto Kamada) -- n=109510: c42677(1020285194......) = 20945976593761703732881 * c42654(4871031864......) n=109630: c41458(9946087809......) = 15003044678443752018135121 * c41433(6629379584......) n=109634: c45592(9813081030......) = 115525215770567 * c45578(8494319586......) n=109648: c42235(1302868773......) = 174238045589271981442049 * c42211(7477521739......) # P-1 B1=1e6 -- Aug 22, 2017 (Makoto Kamada) -- n=109310: c41088(9091000000......) = 937980222251523203826611 * c41064(9692102012......) n=109318: c49672(2330874861......) = 1582264830549899 * c49657(1473125621......) n=109382: c43200(9090910000......) = 13812606354718699529 * c43181(6581603621......) n=109384: c49281(1000000000......) = 9871437902182473445753 * c49259(1013023644......) n=109388: c49254(1262520965......) = 4896987432021516941 * c49235(2578158477......) n=109395: c46060(2880693712......) = 299178762665481271 * c46042(9628670454......) n=109396: c46873(1009999999......) = 39685396393730603489 * c46853(2545016786......) n=109490: c43793(1099989000......) = 540090161969172525545048171 * c43766(2036676609......) # P-1 B1=1e6 # 139406 of 200000 Phi_n(10) factorizations were cracked. -- Aug 21, 2017 (Makoto Kamada) -- n=109018: c43046(1930539472......) = 1035510807658609209929 * c43025(1864335416......) n=109070: c40224(9091000000......) = 1311862462820022256001 * c40203(6929842310......) n=109088: c46635(3257180794......) = 5715188749811521 * c46619(5699165744......) n=109102: c46738(1757560024......) = 590263074335074099 * c46720(2977587623......) n=109150: c41760(9999900000......) = 4119657025153817572651 * c41739(2427362263......) n=109160: c43649(1000099999......) = 39488068917601 * c43635(2532663732......) n=109172: c46705(1000000000......) = 5298818983566627686329 * c46683(1887212986......) n=109208: c46080(9999000099......) = 1009368996473687257 * c46062(9906189049......) n=109256: c46801(1000099999......) = 4179041012686022919521 * c46779(2393132771......) # P-1 B1=1e6 # 139401 of 200000 Phi_n(10) factorizations were cracked. -- Aug 20, 2017 (Makoto Kamada) -- n=108830: c43522(2887829541......) = 25789744164841 * c43509(1119758894......) n=108856: c49441(1000099999......) = 1502800093203849353 * c49422(6654910420......) n=108910: c43545(6623688198......) = 21647853202278282841 * c43526(3059743678......) n=108944: c49441(1000000009......) = 83829105907361 * c49427(1192903108......) # P-1 B1=1e6 # 139395 of 200000 Phi_n(10) factorizations were cracked. -- Aug 19, 2017 (Makoto Kamada) -- n=108560: c40832(9999999900......) = 200287761795361 * c40818(4992816241......) n=108584: c46348(5873855971......) = 105076299931077319601 * c46328(5590086418......) n=108590: c43418(8497258401......) = 1004546405486302051094497411 * c43391(8458801260......) n=108592: c49267(4479735652......) = 622914354382575137873 * c49246(7191575569......) n=108675: c47483(4694795378......) = 192671361525639151 * c47466(2436685629......) n=108698: c48576(9090909090......) = 2645193894345524597 * c48558(3436764734......) n=108758: c48558(1171939403......) = 15718250167517 * c48544(7455915199......) # P-1 B1=1e6 # 139393 of 200000 Phi_n(10) factorizations were cracked. -- Aug 18, 2017 (Makoto Kamada) -- n=108370: c43345(1099989000......) = 109290423689281 * 48418623411492601 * c43314(2078709470......) n=108374: c46420(4305886234......) = 4704323862689960251 * c46401(9153039544......) n=108376: c47497(1638606255......) = 1171062812837055307009 * c47476(1399247108......) n=108416: c42226(1330687659......) = 21089073573960544769 * c42206(6309844075......) # P-1 B1=1e6 # 139391 of 200000 Phi_n(10) factorizations were cracked. -- Aug 17, 2017 (Alfred Eichhorn) -- # via Kurt Beschorner n=68749: c68749(1111111111......) = 999467309588805587 * c68731(1111703304......) # ECM B1=11e3, sigma=12948517208099190898 n=68993: c68993(1111111111......) = 7918664704980905173 * c68974(1403154638......) # ECM B1=11e3, sigma=13347592554612910246 # 139390 of 200000 Phi_n(10) factorizations were cracked. # 13832 of 17984 R_prime factorizations were cracked. -- Aug 17, 2017 (Makoto Kamada) -- n=108164: c46318(6166903989......) = 1079208387505949 * c46303(5714284711......) n=108206: c45235(2800486108......) = 27472399807007 * 876302060600726519761 * c45201(1163276598......) n=108280: c43290(9236230849......) = 1521282972183761 * c43275(6071343082......) n=108320: c43259(1538648543......) = 56270499514241 * c43245(2734378682......) # P-1 B1=1e6 -- Aug 16, 2017 (Makoto Kamada) -- n=107978: c49812(1546592597......) = 111762030054013 * c49798(1383826507......) n=108004: c47469(1090434299......) = 233154273303641 * c47454(4676878892......) n=108136: c46308(5414275277......) = 37431883020964236096505279753 * c46280(1446434120......) # P-1 B1=1e6 -- Aug 15, 2017 (Makoto Kamada) -- n=107734: c47560(9090909091......) = 1889167304712997 * c47545(4812124933......) n=107786: c46176(3613804001......) = 439153711964912939 * c46158(8229018457......) n=107810: c43110(1931266063......) = 3003380357852851 * c43094(6430307964......) n=107818: c49680(9090909090......) = 79091284478672310899 * c49661(1149419831......) n=107828: c46192(2694697719......) = 4039755923317766098395956905829 * c46161(6670446856......) n=107840: c42985(4820739788......) = 275419482435079681 * c42968(1750326355......) n=107842: c46213(1099999890......) = 4886911200874249 * c46197(2250910329......) n=107882: c47796(1972483680......) = 2898827850396104399281 * 272726942811635314021703 * c47751(2494956335......) n=107926: c42614(1300766221......) = 66234683307157 * 6524869806213289517533 * c42578(3009829787......) # P-1 B1=1e6 # 139388 of 200000 Phi_n(10) factorizations were cracked. -- Aug 14, 2017 (Makoto Kamada) -- n=107492: c41760(9900990099......) = 7509786285745129 * c41745(1318411699......) n=107530: c42993(5711045388......) = 3043509420611531 * c42978(1876467130......) n=107558: c48860(2168506533......) = 2059031414518321 * c48845(1053168260......) n=107560: c42996(6020020534......) = 761095269680881 * c42981(7909680658......) n=107576: c42994(9818445748......) = 22207413630531193 * c42978(4421246846......) n=107625: c48000(9999999999......) = 76392530786882020309632432001 * c47972(1309028500......) n=107650: c43024(1168986408......) = 10466254791714451 * c43008(1116909946......) n=107692: c46630(9108216650......) = 59713794140509930344769 * c46608(1525311995......) n=107702: c45865(1000000000......) = 628620319998973 * c45850(1590785356......) n=107710: c43081(1099989000......) = 23022887125561 * c43067(4777806511......) n=107716: c46124(1489087534......) = 23714787704807792321 * c46104(6279151865......) # P-1 B1=1e6 # 139385 of 200000 Phi_n(10) factorizations were cracked. -- Aug 13, 2017 (Makoto Kamada) -- n=107270: c40310(1215428128......) = 199552821223830881 * c40292(6090758930......) n=107272: c45749(2020743632......) = 104675002979637179409673 * c45726(1930493025......) n=107302: c49504(9161250916......) = 466295291999967223 * c49487(1964688701......) n=107350: c40311(1576634658......) = 38669145684476260801 * c40291(4077242025......) n=107354: c49489(1123630387......) = 62636386872223607 * c49472(1793894002......) n=107366: c46009(1099999890......) = 10354071770010011 * c45993(1062383876......) n=107404: c48801(1009999999......) = 110002329078176282441 * c48780(9181623775......) n=107408: c45687(1590959237......) = 1001454529506257 * c45672(1588648501......) n=107415: c43188(4518573524......) = 919946130698792486521 * c43167(4911780564......) n=107458: c49579(1462363418......) = 1343480828777188947379 * c49558(1088488489......) # P-1 B1=1e6 # 139381 of 200000 Phi_n(10) factorizations were cracked. -- Aug 12, 2017 (Makoto Kamada) -- n=107080: c42817(1000099999......) = 703137811908641 * c42802(1422338527......) n=107205: c48960(9009100000......) = 1131696590935658444229961 * c48936(7960702606......) n=107206: c48615(3109269041......) = 23485109358848567 * c48599(1323932111......) n=107228: c48700(2486145542......) = 9619067107932215341 * c48681(2584601515......) # P-1 B1=1e6 # 139379 of 200000 Phi_n(10) factorizations were cracked. -- Aug 11, 2017 (Makoto Kamada) -- n=106870: c42732(2378046352......) = 1850029709582722691 * c42714(1285409818......) n=106918: c45769(1050370480......) = 10982195993469289 * c45752(9564302810......) n=107002: c45835(7149109549......) = 47737550758773492779 * c45816(1497586163......) # P-1 B1=1e6 -- Aug 10, 2017 (Makoto Kamada) -- n=106744: c48481(1000099999......) = 103001776533569 * c48466(9709541268......) n=106832: c48481(1000000009......) = 3291170002283320433 * c48462(3038433169......) # P-1 B1=1e6 # 139377 of 200000 Phi_n(10) factorizations were cracked. -- Aug 9, 2017 (Makoto Kamada) -- n=106582: c43560(9090910000......) = 20714335974613 * c43547(4388704523......) n=106624: c42999(5735187118......) = 1158884819723009 * c42984(4948884497......) n=106628: c47512(9622325530......) = 30584723867706634469 * c47493(3146121433......) n=106630: c42649(1099989000......) = 1713599626399571 * c42633(6419171568......) # P-1 B1=1e6 # 139375 of 200000 Phi_n(10) factorizations were cracked. -- Aug 8, 2017 (Makoto Kamada) -- n=106444: c46439(1577331909......) = 51134385358369 * c46425(3084679513......) n=106454: c48000(9090909090......) = 8368329926169090844964369 * c47976(1086346878......) n=106456: c45601(1000099999......) = 1892090311999727897 * c45582(5285688498......) n=106546: c46480(9090909091......) = 3856295386531303 * c46465(2357420316......) n=106575: c47012(1668584527......) = 1155706765899059883601 * c46991(1443778453......) # P-1 B1=1e6 # 139373 of 200000 Phi_n(10) factorizations were cracked. -- Aug 7, 2017 (Makoto Kamada) -- n=106366: c49066(8905937367......) = 521603269925594533 * c49049(1707415938......) n=106372: c43651(2398716643......) = 6717158338392533081 * c43632(3571028882......) n=106390: c42553(1099989000......) = 283464235064401 * c42538(3880521293......) # P-1 B1=1e6 # 139370 of 200000 Phi_n(10) factorizations were cracked. -- Aug 6, 2017 (Makoto Kamada) -- n=106082: c48711(5917075146......) = 18738811652143703 * c48695(3157657623......) n=106114: c49896(4353832612......) = 36770580276365523058317877 * c49871(1184053278......) n=106132: c48650(5251094352......) = 22452625085048818921 * c48631(2338744058......) n=106155: c48373(2633808765......) = 236888967590374935151 * c48353(1111832599......) n=106160: c42433(1000000009......) = 117783818989362198058846166081 * c42403(8490130635......) n=106270: c42499(3450285592......) = 387009046251521 * c42484(8915258250......) n=106280: c42453(2160854405......) = 14665635866561 * c42440(1473413376......) n=106288: c41466(3136132258......) = 11978639888911697 * c41450(2618103797......) # P-1 B1=1e6 # 139369 of 200000 Phi_n(10) factorizations were cracked. -- Aug 5, 2017 (Alfred Eichhorn) -- # via Kurt Beschorner n=19273: c19273(1111111111......) = 16654668878053598037177599 * c19247(6671469239......) # ECM B1=5e4, sigma=3770627784463675785 # 139368 of 200000 Phi_n(10) factorizations were cracked. # 13830 of 17984 R_prime factorizations were cracked. -- Aug 5, 2017 (Makoto Kamada) -- n=106000: c41589(1143979817......) = 69759105871219576001 * c41569(1639900344......) n=106012: c49847(8950792300......) = 100435367198906671601 * c49827(8911992408......) n=106030: c40480(9091000000......) = 241540392466601 * c40466(3763759720......) n=106054: c48937(1099999999......) = 177901002088499 * c48922(6183214187......) # P-1 B1=1e6 # 139367 of 200000 Phi_n(10) factorizations were cracked. -- Aug 4, 2017 (Makoto Kamada) -- n=105808: c49652(1586351115......) = 1298951628212363201 * c49634(1221254957......) n=105826: c45332(6996967875......) = 181285677647909888721571 * c45309(3859636329......) n=105830: c40015(7104551077......) = 5349196536886250482171 * c39994(1328152934......) n=105880: c42315(2015068977......) = 5662456973968817173841 * c42293(3558647751......) n=105898: c48840(1886919029......) = 27324912656876771 * c48823(6905489702......) n=105920: c42241(1000000000......) = 1000442225395841 * c42225(9995579700......) n=105938: c42497(3999780572......) = 339018163196856336481 * c42477(1179813062......) n=105944: c46080(9999000099......) = 14331769101948989792473 * c46058(6976807977......) n=105945: c48353(8476708542......) = 630588752149231 * c48339(1344253051......) # P-1 B1=1e6 # 139365 of 200000 Phi_n(10) factorizations were cracked. -- Aug 1, 2017 (Yousuke Koide) -- n=976: c404(1110976586......) = 1333621378380781329750868926173511152429445865079521 * p352(8330524721......) # ECM B1=120000000, sigma=2:17156338585742940671 # 1134 of 200000 Phi_n(10) factorizations were finished. -- Aug 3, 2017 (Makoto Kamada) -- n=105532: c45186(5988627862......) = 122967907280432161811886569 * c45160(4870073822......) n=105578: c47970(1526343685......) = 20866350501802367 * c47953(7314856926......) n=105602: c42761(4178957693......) = 4254009111206093 * c42745(9823574855......) n=105610: c41279(4252839048......) = 254971864859728546283704331 * c41253(1667964051......) n=105616: c42227(1343488835......) = 16191080291793457 * c42210(8297709674......) n=105622: c47989(1795094111......) = 456946944043801556929 * p47968(3928451945......) # ----------------8<----------------8<----------------8<---------------- # makoto@betelgeuse /cygdrive/c/factorize/Phin10 # $ ./pfgw64 -tc -q"11*(10^52811+1)/(10^11+1)/(10^4801+1)/280008516159268031617409411710601" # PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6] # # Primality testing 11*(10^52811+1)/(10^11+1)/(10^4801+1)/280008516159268031617409411710601 [N-1/N+1, Brillhart-Lehmer-Selfridge] # Running N-1 test using base 2 # Running N+1 test using discriminant 7, base 2+sqrt(7) # Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.11% proof) # 11*(10^52811+1)/(10^11+1)/(10^4801+1)/280008516159268031617409411710601 is Fermat and Lucas PRP! (235.2401s+0.0039s) # ----------------8<----------------8<----------------8<---------------- n=105680: c42227(1061029126......) = 278256925520963769102241 * c42203(3813127470......) n=105688: c47987(4260650934......) = 108128387390057 * c47973(3940362968......) n=105706: c49729(1099999999......) = 14927962969531078771 * c49709(7368721387......) n=105716: c45792(9900990099......) = 16084717211379277954523161 * c45767(6155526372......) # P-1 B1=1e6 # 1133 of 200000 Phi_n(10) factorizations were finished. # 139363 of 200000 Phi_n(10) factorizations were cracked. -- Aug 2, 2017 (Ray Chandler) -- n=106820L: p18129(9626709636......) is definitely prime. # Certification is available at: http://stdkmd.com/nrr/cert/Phi/#CERT_PHI_106820L_10 # See also http://stdkmd.com/nrr/repunit/prpfactors.htm -- Aug 2, 2017 (Makoto Kamada) -- n=105386: c48028(3437991518......) = 27560661379969 * c48015(1247427074......) n=105440: c42103(1019397519......) = 9306349313712641 * c42087(1095378526......) n=105512: c47514(6769706106......) = 80753244233993 * c47500(8383200168......) n=105518: c45204(6233423114......) = 2022881130382211354921 * c45183(3081457936......) # P-1 B1=1e6 -- Aug 1, 2017 (Makoto Kamada) -- n=105238: c45066(6737219435......) = 51116292811823 * c45053(1318018006......) n=105274: c48562(1090469420......) = 127019087896238697251 * c48541(8585083064......) n=105292: c47826(6793624929......) = 61339199600009 * c47813(1107550306......) n=105298: c46648(1812999985......) = 204659682150019 * c46633(8858608427......) n=105315: c44545(1109988789......) = 39785716857291511 * c44528(2789917781......) n=105332: c49537(1009999999......) = 2350341307075267229 * c49518(4297248220......) # P-1 B1=1e6 # 139361 of 200000 Phi_n(10) factorizations were cracked.