-- Nov 30, 2016 (Makoto Kamada) -- n=112272: c37409(1000000009......) = 6592319055344920321 * c37390(1516916887......) n=112284: c37401(2024059325......) = 36995428322821 * c37387(5471106613......) n=112296: c37425(1000099999......) = 9651540399554857 * c37409(1036207650......) n=112326: c36855(9924560914......) = 83631517023973 * c36842(1186701051......) n=112386: c37440(1748625908......) = 769198431725570659 * c37422(2273309247......) n=112416: c37433(1626239623......) = 920113336972513 * c37418(1767434030......) n=112494: c37489(4719096781......) = 9999741010296727 * c37473(4719219003......) n=112524: c37497(1081428175......) = 89959327138034581 * c37480(1202130128......) n=112536: c37433(4726619645......) = 176080178399532886065817 * c37410(2684356461......) # P-1 B1=1e6 # 139062 of 200000 Phi_n(10) factorizations were cracked. -- Nov 29, 2016 (Makoto Kamada) -- n=111798: c37253(3024881170......) = 15175361542659247 * c37237(1993284418......) n=111822: c37253(4096158642......) = 1390828141099590733 * 36512663766319884103 * c37215(8066029036......) n=111858: c36720(9100000000......) = 25597020386993929 * c36704(3555101282......) n=111894: c35066(9036321045......) = 75096591600549972289 * c35047(1203293099......) n=111912: c37269(6370113092......) = 2093227850150814299658217 * c37245(3043201002......) n=111948: c35275(8844205843......) = 2847623234642209 * c35260(3105820227......) n=111978: c37303(3593823563......) = 55475890483752504361 * c37283(6478171927......) n=112026: c37341(1098901098......) = 143769773283943 * c37326(7643477998......) n=112104: c37153(1000000000......) = 871193493592810487497 * c37132(1147850629......) n=112158: c35632(1552767935......) = 3897117444210247 * c35616(3984401183......) n=112188: c37386(1500455841......) = 64326069373613809 * c37369(2332578154......) n=112218: c36637(2203367709......) = 155653319848841668597 * c36617(1415561011......) # P-1 B1=1e6 # 139060 of 200000 Phi_n(10) factorizations were cracked. -- Nov 28, 2016 (Makoto Kamada) -- n=111438: c35985(2786728306......) = 9118915346419852152997 * c35963(3055986595......) n=111504: c35190(1340493168......) = 569387836050531027667153 * c35166(2354270822......) n=111534: c35829(7573556566......) = 63629922357439296551383 * c35807(1190250794......) n=111558: c37169(1299910481......) = 2006867210148058099 * c37150(6477311877......) n=111582: c37189(1000999998......) = 2637796899440971 * c37173(3794833480......) n=111642: c35539(2838665590......) = 3046922915338725211 * c35520(9316499530......) n=111702: c37233(1098901098......) = 29422434947735779321 * c37213(3734908755......) n=111714: c36270(3099321892......) = 64866196197091 * 92209320981361 * c36242(5181713879......) n=111732: c37241(1009998990......) = 15192698811649 * c37227(6647923469......) # P-1 B1=1e6 # 139057 of 200000 Phi_n(10) factorizations were cracked. -- Nov 27, 2016 (Makoto Kamada) -- n=111084: c37025(1009998990......) = 3512596668403833361261 * c37003(2875362830......) n=111186: c35280(9999999990......) = 350675777166409 * c35266(2851636936......) n=111192: c35840(9999000100......) = 739348194372289 * c35826(1352407455......) n=111204: c37036(1807855327......) = 81717700399176781 * c37019(2212317916......) n=111396: c37121(1850355839......) = 109788301180141 * c37107(1685385254......) # P-1 B1=1e6 # 139054 of 200000 Phi_n(10) factorizations were cracked. -- Nov 26, 2016 (Makoto Kamada) -- n=110556: c35409(2942205248......) = 143324561909992069 * c35392(2052826961......) n=110562: c36853(1098901098......) = 17467752133962853 * c36836(6291027548......) n=110574: c36835(4023251510......) = 145037685232305839595961 * c36812(2773935273......) n=110598: c36846(6489366544......) = 13353541478751841 * c36830(4859659555......) n=110600: c37411(2128399850......) = 59628574957156257351601 * c37388(3569429341......) n=110622: c36307(8226137421......) = 1128146236416895291 * c36289(7291729703......) n=110630: c38005(1614163336......) = 261428615170451 * c37990(6174394244......) n=110634: c36871(1986548642......) = 1739081825527394527753103659 * c36844(1142297396......) n=110676: c35194(8945924187......) = 2654706460270849 * c35179(3369835543......) n=110724: c36905(1009998990......) = 3567676138674289 * c36889(2830971620......) n=110778: c35856(9100000000......) = 254540714357023 * c35842(3575066575......) n=110898: c35979(1957710433......) = 81715113560503 * c35965(2395775210......) n=110950: c37910(9508164000......) = 30885653437801 * 62801669799876001 * c37880(4901947762......) # P-1 B1=1e6 # 139051 of 200000 Phi_n(10) factorizations were cracked. -- Nov 25, 2016 (Makoto Kamada) -- n=110268: c36715(9068731919......) = 6739941186804781 * c36700(1345520927......) n=110320: c37620(4051571066......) = 893287216950241 * c37605(4535574884......) n=110388: c36767(1859790440......) = 96825228733596589 * c36750(1920770510......) n=110406: c36787(3872542604......) = 4301091484103779 * c36771(9003627610......) n=110412: c36793(1000000999......) = 3301597334966729401 * c36774(3028839978......) # P-1 B1=1e6 # 139048 of 200000 Phi_n(10) factorizations were cracked. -- Nov 24, 2016 (Makoto Kamada) -- n=109716: c35511(1913530100......) = 276301850494103557799821 * c35487(6925505916......) n=109734: c36561(5290285313......) = 36072970173789517 * c36545(1466551073......) n=109908: c35259(3624684050......) = 2978018107376869 * c35244(1217146410......) n=109938: c36000(9100000000......) = 508718112784225087 * c35983(1788809906......) n=109944: c36577(1000000000......) = 3899320613598457 * c36561(2564549312......) n=110028: c35776(9901000000......) = 1027780272230149 * c35761(9633382024......) n=110034: c36673(1000999998......) = 1690294080427903 * c36657(5922046409......) n=110046: c36664(1515829490......) = 20239858907140819 * c36647(7489328346......) n=110064: c36663(4702946838......) = 18062441910706561 * c36647(2603715965......) n=110142: c35275(1511684141......) = 493619237531804611 * c35257(3062449812......) # P-1 B1=1e6 # 139047 of 200000 Phi_n(10) factorizations were cracked. -- Nov 23, 2016 (Makoto Kamada) -- n=109302: c36428(1005371397......) = 12739366384947463 * c36411(7891847737......) n=109308: c36426(2566648403......) = 56471059356674101 * c36409(4545068629......) n=109404: c36424(8385718849......) = 17126237603793061 * c36408(4896416272......) n=109482: c35832(7349132228......) = 1936702717870984660889569 * c35808(3794662010......) n=109506: c36477(1637162088......) = 1748248338926809 * c36461(9364585408......) n=109524: c36496(2659854008......) = 41094796391876465101 * c36476(6472483724......) n=109542: c36490(1104899200......) = 35841352915360579 * c36473(3082749701......) n=109584: c36481(1000000000......) = 8117119545461281 * c36465(1231964115......) n=109602: c36510(6453029802......) = 135197418409957 * c36496(4773042176......) # P-1 B1=1e6 # 139043 of 200000 Phi_n(10) factorizations were cracked. -- Nov 22, 2016 (Makoto Kamada) -- n=109146: c36362(1508303612......) = 49200577302166706885179 * 153466940564034351089023 * c36316(1997577957......) n=109188: c36289(1000000000......) = 256156907619053908734229 * c36265(3903857246......) n=109194: c36370(3501692230......) = 51015491672656167828830689 * c36344(6863978207......) n=109248: c36324(1055992230......) = 18606838922568961 * c36307(5675290867......) # P-1 B1=1e6 # 139042 of 200000 Phi_n(10) factorizations were cracked. -- Nov 22, 2016 (Alfred Eichhorn) -- # via Kurt Beschorner n=86381: c86381(1111111111......) = 221330036551319831 * c86363(5020155096......) # ECM B1=2e3 # 139041 of 200000 Phi_n(10) factorizations were cracked. # 13798 of 17984 R_prime factorizations were cracked. -- Nov 22, 2016 (Makoto Kamada) -- n=108978: c35360(9100000000......) = 663851947526992087459 * c35340(1370787573......) # P-1 B1=1e6 # 139040 of 200000 Phi_n(10) factorizations were cracked. -- Nov 22, 2016 (Ray Chandler) -- n=64410: p16115(1233544571......) is definitely prime. # Certification is available at: http://stdkmd.com/nrr/cert/Phi/#CERT_PHI_64410_10 # See also http://stdkmd.com/nrr/repunit/prpfactors.htm -- Nov 21, 2016 (Makoto Kamada) -- n=108792: c36203(1246335096......) = 14040335628557353 * c36186(8876818402......) n=108920: c37242(2868790520......) = 96094715330245217041 * c37222(2985378030......) # P-1 B1=1e6 -- Nov 20, 2016 (Makoto Kamada) -- n=108456: c36120(1712475435......) = 7146085494670185913 * c36101(2396382517......) n=108492: c36161(1009998990......) = 230830281735721 * 200230462259612749 * c36129(2185234295......) n=108588: c36158(5402454415......) = 10651627943132095669 * c36139(5071951859......) n=108594: c36168(1284822261......) = 7097652884818979317 * c36149(1810207236......) n=108648: c36123(2515327909......) = 4561635536222689 * c36107(5514092236......) n=108710: c37248(9091000909......) = 25529640663451 * c37235(3560959211......) # P-1 B1=1e6 # 139039 of 200000 Phi_n(10) factorizations were cracked. -- Nov 19, 2016 (Makoto Kamada) -- n=107988: c35979(3724377417......) = 2184182301394500769 * c35961(1705158683......) n=107994: c35034(2106598027......) = 40678694499929281 * c35017(5178627419......) n=108012: c35995(1870157241......) = 45150518856673507709401 * c35972(4142050388......) n=108096: c35953(8823760773......) = 1858468681504847495617 * c35932(4747866273......) n=108204: c35280(9901000000......) = 54468813253574382721 * c35261(1817737418......) n=108246: c36076(1015179264......) = 67045729416268783 * c36059(1514159475......) # P-1 B1=1e6 # 139037 of 200000 Phi_n(10) factorizations were cracked. -- Nov 18, 2016 (Makoto Kamada) -- n=107470: c38995(2634294091......) = 1544846650416082453001 * c38974(1705213971......) n=107496: c35800(9228840914......) = 35550186838129 * c35787(2596003491......) n=107556: c35843(3130139523......) = 92456055913798073881 * c35823(3385542994......) n=107574: c35847(9207953727......) = 2564311627345651 * c35832(3590809178......) n=107598: c35239(1179079178......) = 11389370316133 * 11096726727336619 * c35209(9329285102......) n=107658: c35881(1000999998......) = 464248449070129 * c35866(2156173059......) n=107770: c39727(4974354589......) = 27785736722975444201 * c39708(1790254704......) n=107808: c35886(3020685742......) = 9422626583457697 * c35870(3205778894......) n=107826: c35935(5095691221......) = 25162285474816545493 * c35916(2025130517......) n=107868: c35200(9901000000......) = 23038682234686792272421 * c35178(4297554825......) n=107928: c35938(2276341533......) = 38006671524313033 * 1363156220359222791841 * c35900(4393715733......) # P-1 B1=1e6 # 139036 of 200000 Phi_n(10) factorizations were cracked. -- Nov 17, 2016 (Makoto Kamada) -- n=107022: c35662(9382303135......) = 30720024573331 * c35649(3054132692......) n=107106: c35692(6099845195......) = 965328875915647 * c35677(6318929587......) n=107154: c35713(1000999998......) = 498165909425480048491 * c35692(2009370733......) n=107198: c38871(6423401841......) = 19083596601825757 * c38855(3365928328......) n=107232: c35713(1000000000......) = 32110957630242914881 * c35693(3114201736......) n=107286: c35761(1098901098......) = 94852303509742372152619 * c35738(1158539179......) n=107292: c35761(1009998990......) = 91778080152218208901 * c35741(1100479535......) n=107360: c38393(2531102119......) = 2339839593877276481 * c38375(1081741725......) n=107440: c39936(9999999900......) = 66388183285240321 * c39920(1506292144......) n=107450: c36720(9999900000......) = 29840032294721450163251 * c36698(3351169295......) # P-1 B1=1e6 # 139034 of 200000 Phi_n(10) factorizations were cracked. -- Nov 16, 2016 (Alfred Eichhorn) -- # via Kurt Beschorner n=31567: c31567(1111111111......) = 271696556465943213043 * c31546(4089529604......) # ECM B1=5e4, sigma=1:187854045 # 139028 of 200000 Phi_n(10) factorizations were cracked. # 13797 of 17984 R_prime factorizations were cracked. -- Nov 16, 2016 (Makoto Kamada) -- n=106542: c35489(9480776739......) = 7171436926122013 * c35474(1322019120......) n=106584: c35521(1000099999......) = 8527640677605924529 * c35502(1172774554......) n=106600: c38388(9286142528......) = 114076737236801 * c38374(8140259577......) n=106614: c35514(2615292664......) = 25366438809349327 * c35498(1031005055......) n=106632: c35508(2035821785......) = 170686004907169 * c35494(1192729179......) n=106716: c35562(1631786505......) = 4386669281707261 * c35546(3719875835......) n=106842: c35600(6289613262......) = 9986000071588765849 * c35581(6298431020......) n=106866: c35605(1000000000......) = 11494261126308529 * c35588(8699993762......) n=106914: c35057(1033570599......) = 1940698100234716171 * c35038(5325767049......) n=106956: c35633(2184497254......) = 212479921729261 * c35619(1028095848......) # P-1 B1=1e6 # 139027 of 200000 Phi_n(10) factorizations were cracked. -- Nov 15, 2016 (Makoto Kamada) -- n=105950: c38856(1049338397......) = 281564393071651 * c38841(3726814980......) n=105972: c35321(1009998990......) = 99450914955901 * c35307(1015575362......) n=106146: c35351(3251410677......) = 6345122499782567299 * c35332(5124267778......) n=106254: c35398(6049868028......) = 562075467856549166413 * c35378(1076344436......) n=106308: c35388(1021052867......) = 1740163355715529 * c35372(5867569065......) n=106332: c35414(5160804920......) = 25405065332021209 * 65234892673458779452501 * c35375(3113989720......) n=106480: c38714(7826189717......) = 4351937853892247288567041 * c38690(1798322949......) # P-1 B1=1e6 # 139025 of 200000 Phi_n(10) factorizations were cracked. -- Nov 14, 2016 (Makoto Kamada) -- n=105582: c35178(5500988721......) = 42272561611856772487 * c35159(1301314259......) n=105594: c35197(1098901098......) = 121854225315625651 * c35179(9018161627......) n=105696: c35137(1000000000......) = 6723053611960558753 * c35118(1487419345......) n=105762: c35245(1396548464......) = 514910983675568209 * c35227(2712213390......) n=105804: c35257(1000000999......) = 90310326460376928999126375889 * c35228(1107294192......) n=105828: c35249(1568615928......) = 50581408736553080329 * c35229(3101170899......) n=105888: c35265(1000000000......) = 3574435613361234049 * c35246(2797644462......) # P-1 B1=1e6 # 139024 of 200000 Phi_n(10) factorizations were cracked. -- Nov 13, 2016 (Makoto Kamada) -- n=103930: c39300(3691423207......) = 29048552375735891 * c39284(1270776994......) n=104006: c38001(7383671580......) = 1432591558217009 * c37986(5154066096......) n=104090: c35646(1390018154......) = 3540576667344498110633081 * c35621(3925965415......) n=104104: c37440(9999999999......) = 2595327671728793 * c37425(3853078017......) n=104120: c39168(9999000099......) = 288000685572401 * 126021669452185908481 * c39134(2754976017......) n=104510: c35790(9529296899......) = 6145629757394891 * p35775(1550581026......) # ----------------8<----------------8<----------------8<---------------- # makoto@betelgeuse /cygdrive/c/factorize/Phin10 # $ ./pfgw64 -tc -q"90910009091*(10^1493+1)*(10^52255+1)/(10^35+1)/(10^7465+1)/(10^10451+1)/5862964109357781734610136635096521" # PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11] # # Primality testing 90910009091*(10^1493+1)*(10^52255+1)/(10^35+1)/(10^7465+1)/(10^10451+1)/5862964109357781734610136635096521 [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% (0.09% proof) # 90910009091*(10^1493+1)*(10^52255+1)/(10^35+1)/(10^7465+1)/(10^10451+1)/5862964109357781734610136635096521 is Fermat and Lucas PRP! (104.0329s+0.0074s) # ----------------8<----------------8<----------------8<---------------- n=105028: c39586(9896780024......) = 11566398180569 * c39573(8556492583......) n=105170: c38784(9091000000......) = 3131627237795291 * c38769(2902963638......) n=105174: c35034(2812243806......) = 3016515946595197500757 * c35012(9322820949......) n=105230: c39552(9091000000......) = 1466982284072175971 * c39534(6197075519......) n=105234: c35068(2870382894......) = 16435267049405773 * c35052(1746477794......) # P-1 B1=1e6 # 1127 of 200000 Phi_n(10) factorizations were finished. # 139020 of 200000 Phi_n(10) factorizations were cracked. # See also http://stdkmd.com/nrr/repunit/prpfactors.htm -- Nov 12, 2016 (Alfred Eichhorn) -- # via Kurt Beschorner n=80657: c80635(6269769367......) = 290433298476811653481 * c80615(2158763957......) # ECM B1=2e3, sigma=0:10596707231362242639 -- Nov 12, 2016 (Makoto Kamada) -- n=102350: c38714(1221287100......) = 791451560858283001 * c38696(1543097721......) n=102490: c39744(9091000000......) = 1438826092750695168361 * c39723(6318345243......) n=102520: c37120(9999000099......) = 851942080646801 * c37106(1173671347......) n=102550: c35035(3250403867......) = 1217475719093201 * c35020(2669789480......) n=102790: c38880(9091000000......) = 1769782893796451 * c38865(5136788264......) n=102850: c35193(2331630023......) = 317458236323801 * c35178(7344682721......) n=102950: c39185(1915911476......) = 566887853753610435386051 * c39161(3379701052......) n=103270: c39387(1272446857......) = 367000984227343721 * c39369(3467148352......) n=103510: c37600(9091000000......) = 23225037229312931 * c37584(3914310194......) n=103610: c38193(2220223029......) = 5079138446799246961 * c38174(4371259127......) # P-1 B1=1e6 # 139016 of 200000 Phi_n(10) factorizations were cracked. -- Nov 11, 2016 (Makoto Kamada) -- n=101332: c38640(9999999999......) = 345179824130901767701 * c38620(2897040701......) n=101480: c38976(9999000099......) = 316964316348063530703661155244612481 * c38941(3154613811......) n=101840: c37993(2710073839......) = 104994715437433441 * c37976(2581152611......) n=101890: c38891(8922279691......) = 153963328564774321 * c38874(5795068068......) n=102170: c38382(1517943633......) = 3700101039937321780917811 * c38357(4102438331......) n=102256: c39360(9999999900......) = 97280753512207514637476088001 * c39332(1027952553......) n=102310: c37718(7167999918......) = 49405952319218198731 * c37699(1450837314......) # P-1 B1=1e6 # 139012 of 200000 Phi_n(10) factorizations were cracked. -- Nov 10, 2016 (Makoto Kamada) -- n=100016: c39736(2041323016......) = 1238142240167057 * c39721(1648698308......) n=100160: c39921(2973374630......) = 7764464840482201341692015032321 * c39890(3829464994......) n=100190: c38959(4439425706......) = 950265107753201 * c38944(4671775981......) n=100282: c36252(5018508151......) = 972102175791022277 * c36234(5162531548......) n=100360: c36864(9999000099......) = 6745955126888641 * c36849(1482221555......) n=100510: c36432(9999999999......) = 32862472209687721 * c36416(3042984695......) n=100880: c36837(3424125006......) = 9619704584998561 * c36821(3559490810......) n=101230: c39520(9091000000......) = 7802829902594309801 * c39502(1165090116......) # P-1 B1=1e6 # 139009 of 200000 Phi_n(10) factorizations were cracked. -- Nov 7, 2016 ([P3D] Crashtest) -- # via yoyo@home n=1213: c1213(1111111111......) = 14539506681835624339134436400997541040884253 * c1169(7642013827......) # ECM B1=11000000, sigma=166611344 # 139006 of 200000 Phi_n(10) factorizations were cracked. # 13796 of 17984 R_prime factorizations were cracked. -- Nov 7, 2016 (Mumps [MM]) -- # via yoyo@home n=1167: c639(2054671040......) = 613485710812313000516466620592830345835145382211665323 * c585(3349175057......) # ECM B1=110000000, sigma=2673943130 -- Nov 6, 2016 (Alfred Eichhorn) -- # via Kurt Beschorner n=55889: c55889(1111111111......) = 22725551385595799107 * c55869(4889259196......) # ECM B1=11e3, sigma=12720872794617635669 n=77867: c77867(1111111111......) = 12146261490914239566523 * c77844(9147762148......) # ECM B1=2e3, sigma=9656516878805326347 # 139005 of 200000 Phi_n(10) factorizations were cracked. # 13795 of 17984 R_prime factorizations were cracked. -- Nov 5, 2016 (WhiteFire) -- # via yoyo@home n=1173: c693(3372467419......) = 51127988434642542343102991812662340182552388237 * c646(6596127723......) # ECM B1=43000000, sigma=1917067894 -- Nov 2, 2016 (Alfred Eichhorn) -- # via Kurt Beschorner n=55399: c55379(4797623652......) = 2288856241024717845347 * c55358(2096079066......) # ECM B1=11e3, sigma=2794405507697790298