-- Mar 31, 2024 (Makoto Kamada) -- # ----------------8<----------------8<----------------8<---------------- # Information # Phin10ex.txt is now available. # The difference between Phin10.txt and Phin10ex.txt is the addition of number expression to information of factors with numbers omitted. # There are only five operators used in that number expression: addition, subtraction, multiplication, division, and exponentiation. # Phin10ex.txt allows you to get the exact value of factors with numbers omitted without having to be aware of cyclotomic polynomial or Aurifeuillean factorization. # For example, # Phin10.txt # 1300L 1301 p237_7763644894_1161115590 # Phin10ex.txt # 1300L 1301 p237_7763644894_1161115590_((10^65+1)*((10^130+10^65)*(10^65-10^33+3)-10^33+2)-1)/128805479070810449200301 # ----------------8<----------------8<----------------8<---------------- -- Mar 29, 2024 (Kurt Beschorner) -- n=713: c632(2522748643......) = 31070861795268450321139284436817844468068239 * c588(8119339142......) # ECM B1=11e7, sigma=4800378595879534 n=13175: c9591(3881903730......) = 422686483673200816801 * c9570(9183884227......) # P-1 B1=56e6 n=13187: c13151(2450408500......) = 2072300747670825285092510827 * c13124(1182457953......) # P-1 B1=35e6 -- Mar 24, 2024 (-) -- # via factordb.com n=695: c545(6173612174......) = 8397548714483238063663389786354175256018831 * c502(7351683669......) n=3019: c3003(2190194150......) = 3139259690159845335135979206644089969 * c2966(6976785505......) n=3023: c2959(2308713813......) = 107018760919046918330490860941009 * c2927(2157298209......) n=3097: c2883(5891256187......) = 57179667256536688029715193166703488359641 * c2843(1030306133......) -- Mar 24, 2024 (Alfred Reich) -- # via Kurt Beschorner n=8914: c4456(9090909090......) = 1680862037183886151986766096284943 * c4423(5408480226......) -- Mar 22, 2024 (Kurt Beschorner) -- n=655: c502(3917622251......) = 2603347672124284040229582413722681735668626862241 * c454(1504840207......) # ECM B1=11e7, sigma=0:3963412036452067 n=13108: c6246(7320780653......) = 44331551068710498173013783881 * c6218(1651370294......) # P-1 B1=94e6 n=13131: c8736(8725710109......) = 276600609054191780298991 * c8713(3154624329......) # P-1 B1=60e6 -- Mar 18, 2024 (Alfred Eichhorn) -- # via Kurt Beschorner n=73019: c73019(1111111111......) = 1323020047051919660237 * c72997(8398293839......) # ECM B1=5e4, sigma=1341369107631264 # 213205 of 300000 Phi_n(10) factorizations were cracked. # 20032 of 25997 R_prime factorizations were cracked. -- Mar 17, 2024 (NFS@Home) -- # via Sam Wagstaff n=1420L: c231(7090462991......) = 247950328172294050136754481538951409190364075674960071233394038784474817867352415168199452660754962688866321901 * p121(2859630412......) # SNFS # 1263 of 300000 Phi_n(10) factorizations were finished. # ----------------8<----------------8<----------------8<---------------- # Largest known factors that appear after the previous one # 1 n=604: 188981422179250214477885038956646476812007525220846625175628245017547495717341304519447280552146559165713534073382085460954497219653965265520569 (NFS@Home / Mar 16, 2017) # 2 n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009) # 3 n=816: 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881 (Yousuke Koide / Apr 5, 2020) # 4 n=1420L: 247950328172294050136754481538951409190364075674960071233394038784474817867352415168199452660754962688866321901 (NFS@Home / Mar 17, 2024) # 5 n=1420M: 150068993718936038588227244574366404285884513639444374982663085901463237698274075317154251769989823397761 (NFS@Home / Mar 13, 2024) # 6 n=1540M: 647799461893729229242068652342456021003805852058736425973158141325454469108253161834095467738437014341 (NFS@Home / Sep 18, 2013) # 7 n=1740M: 38500497070688096027556817882565728990416892548263819672284096593431517949011701136219584563960572421 (Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner / Jun 27, 2021) # 8 n=2340L: 54416219768345058780693800256182138078138198676424989328564702046179663087831396313663972761 (Bo Chen, Wenjie Fang, Maksym Voznyy and Kurt Beschorner / Feb 15, 2016) # 9 n=2700M: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201 (Bo Chen, Maksym Voznyy, Wenjie Fang, Alfred Eichhorn and Kurt Beschorner / May 7, 2017) # 10 n=2940M: 1044845694645532615440579579338650347038975456315052342814839763722781 (George Bradshaw / Feb 19, 2023) # 11 n=5900M: 593243597135622945022444401922545308692618865123732027101 (pi / Sep 17, 2018) # 12 n=13980M: 21166873440679239162423181074773929272724025103001 (Kurt Beschorner / Jul 14, 2011) # 13 n=103748: 1941549624124837091592820526305327246593529 (Makoto Kamada / Jun 18, 2018) # 14 n=112666: 356334694333381082120764457775238849699 (Makoto Kamada / Oct 17, 2018) # 15 n=120833: 79670409416595961896605938971188364397 (Maksym Voznyy / Nov 27, 2015) # 16 n=135070: 9855589830288396166509564150666175361 (Makoto Kamada / Dec 6, 2017) # 17 n=253620L: 1221015147166230558535777472152845661 (Alfred Reich / Oct 23, 2023) # 18 n=268140L: 60348364918187687874129722715181 (Alfred Reich / Oct 23, 2023) # 19 n=283706: 526153303629299051259344033783 (Alfred Reich / Oct 23, 2023) # 20 n=295980M: 98690902056965040529354491601 (Alfred Reich / Oct 23, 2023) # 21 n=298740L: 66173162995033300571567659861 (Alfred Reich / Oct 23, 2023) # 22 n=299420L: 33569847171752615806052144021 (Alfred Reich / Oct 23, 2023) # 23 n=299996: 38693214591429090355181 (Alfred Reich / Oct 23, 2023) # 24 n=299999: 246755644878443 (Makoto Kamada / Oct 23, 2021) # 25 n=300000: 47847600001 (Makoto Kamada / Feb 15, 2019) # ----------------8<----------------8<----------------8<---------------- -- Mar 13, 2024 (NFS@Home) -- # via Sam Wagstaff n=1420M: c212(1748241862......) = 150068993718936038588227244574366404285884513639444374982663085901463237698274075317154251769989823397761 * p108(1164958742......) # GNFS # ----------------8<----------------8<----------------8<---------------- # Largest known factors that appear after the previous one # 1 n=604: 188981422179250214477885038956646476812007525220846625175628245017547495717341304519447280552146559165713534073382085460954497219653965265520569 (NFS@Home / Mar 16, 2017) # 2 n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009) # 3 n=816: 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881 (Yousuke Koide / Apr 5, 2020) # 4 n=1420M: 150068993718936038588227244574366404285884513639444374982663085901463237698274075317154251769989823397761 (NFS@Home / Mar 13, 2024) # 5 n=1540M: 647799461893729229242068652342456021003805852058736425973158141325454469108253161834095467738437014341 (NFS@Home / Sep 18, 2013) # 6 n=1740M: 38500497070688096027556817882565728990416892548263819672284096593431517949011701136219584563960572421 (Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner / Jun 27, 2021) # 7 n=2340L: 54416219768345058780693800256182138078138198676424989328564702046179663087831396313663972761 (Bo Chen, Wenjie Fang, Maksym Voznyy and Kurt Beschorner / Feb 15, 2016) # 8 n=2700M: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201 (Bo Chen, Maksym Voznyy, Wenjie Fang, Alfred Eichhorn and Kurt Beschorner / May 7, 2017) # 9 n=2940M: 1044845694645532615440579579338650347038975456315052342814839763722781 (George Bradshaw / Feb 19, 2023) # 10 n=5900M: 593243597135622945022444401922545308692618865123732027101 (pi / Sep 17, 2018) # 11 n=13980M: 21166873440679239162423181074773929272724025103001 (Kurt Beschorner / Jul 14, 2011) # 12 n=103748: 1941549624124837091592820526305327246593529 (Makoto Kamada / Jun 18, 2018) # 13 n=112666: 356334694333381082120764457775238849699 (Makoto Kamada / Oct 17, 2018) # 14 n=120833: 79670409416595961896605938971188364397 (Maksym Voznyy / Nov 27, 2015) # 15 n=135070: 9855589830288396166509564150666175361 (Makoto Kamada / Dec 6, 2017) # 16 n=253620L: 1221015147166230558535777472152845661 (Alfred Reich / Oct 23, 2023) # 17 n=268140L: 60348364918187687874129722715181 (Alfred Reich / Oct 23, 2023) # 18 n=283706: 526153303629299051259344033783 (Alfred Reich / Oct 23, 2023) # 19 n=295980M: 98690902056965040529354491601 (Alfred Reich / Oct 23, 2023) # 20 n=298740L: 66173162995033300571567659861 (Alfred Reich / Oct 23, 2023) # 21 n=299420L: 33569847171752615806052144021 (Alfred Reich / Oct 23, 2023) # 22 n=299996: 38693214591429090355181 (Alfred Reich / Oct 23, 2023) # 23 n=299999: 246755644878443 (Makoto Kamada / Oct 23, 2021) # 24 n=300000: 47847600001 (Makoto Kamada / Feb 15, 2019) # ----------------8<----------------8<----------------8<---------------- -- Mar 9, 2024 (Makoto Kamada) -- n=146098: c68731(7529141198......) = 431996262649207 * c68717(1742871837......) n=146186: c69216(4252719808......) = 408395912023247 * c69202(1041322815......) n=146276: c64507(2256229670......) = 135347931408821 * c64493(1666984967......) n=146288: c71041(1000000009......) = 421086382544497 * c71026(2374809662......) n=146426: c62749(1099999890......) = 286527270231091 * c62734(3839075733......) n=73224: c24187(6828315659......) = 291215941953841 * c24173(2344760253......) n=146542: c66595(7506329200......) = 686512674799051 * c66581(1093399943......) n=146810: c57408(9091000000......) = 817902637489451 * c57394(1111501489......) n=146926: c67801(1099999999......) = 188831680837463 * c67786(5825293696......) -- Mar 7, 2024 (Alfred Eichhorn) -- # via Kurt Beschorner n=72949: c72949(1111111111......) = 11188142905007361998205693557 * c72920(9931148721......) # ECM B1=5e4, sigma=2465366403184896 n=78787: c78787(1111111111......) = 30646987091435527679 * c78767(3625514990......) # ECM B1=5e4, sigma=4416129323271267 n=79103: c79103(1111111111......) = 3282162411477160845528807707 * c79075(3385302041......) # ECM B1=5e4, sigma=3031437210351021 # 213200 of 300000 Phi_n(10) factorizations were cracked. # 20031 of 25997 R_prime factorizations were cracked. -- Mar 6, 2024 (Makoto Kamada) -- n=147026: c64800(9090909091......) = 849389007431383 * c64786(1070288055......) n=147134: c67897(1099999999......) = 841497481220059 * c67882(1307193455......) n=147382: c72385(1099999999......) = 236720396757743 * c72370(4646832360......) n=147590: c59023(4312332895......) = 195908463906731 * c59009(2201197850......) n=147608: c73800(9999000099......) = 746047027990937 * c73786(1340264048......) n=147648: c49130(4981178709......) = 105298890305473 * c49116(4730513963......) n=147692: c73832(8926565123......) = 863973000052501 * c73818(1033199547......) n=147706: c61767(3247412546......) = 175336090114459 * c61753(1852107312......) n=147788: c73879(2468845449......) = 139801192281749 * c73865(1765968808......) n=147850: c59114(2818198957......) = 224430305126051 * c59100(1255712305......) n=147972: c41697(2585649181......) = 101283409779949 * c41683(2552885203......) -- Mar 5, 2024 (Alfred Reich) -- # via Kurt Beschorner n=16438: c8218(9090909090......) = 8011505186691120932663584183 * c8191(1134731723......) n=31562: c15368(1161722306......) = 35592147487676920463 * c15348(3263984862......) n=31604: c15800(9900990099......) = 2431162452185039922126541 * c15776(4072533322......) n=31682: c12947(3423530829......) = 13058845505765837 * c12931(2621618295......) n=31696: c13528(4213371066......) = 849225733803273972858599153 * c13501(4961426507......) n=31732: c15844(4154251511......) = 12771504608380995375745169 * c15819(3252750274......) n=31788: c10554(6408052166......) = 105480823136736321938422081 * c10528(6075087372......) n=31792: c15884(3145346428......) = 1124862107191521105889 * c15863(2796206226......) n=31794: c9049(3221244661......) = 88267267172719831813 * c9029(3649421540......) n=31800: c8310(5622361200......) = 2327427960927441388068001 * c8286(2415697196......) n=31808: c13441(1000000000......) = 83385115506231195528257 * c13418(1199254799......) n=31816: c15356(3143288179......) = 198354176884174670377 * c15336(1584684642......) n=31822: c13622(6849413392......) = 21223407316494369009703 * c13600(3227292060......) n=31832: c15137(1000099999......) = 3373542187061259737 * c15118(2964539776......) n=31842: c10051(1162044219......) = 121268577044650107133 * c10030(9582401702......) n=31854: c10587(3957814732......) = 92478474903470166967 * c10567(4279714535......) n=31864: c13604(3253039807......) = 517996647217868312873 * c13583(6280040276......) n=31866: c10284(1322613060......) = 37189661286468510889 * c10264(3556399855......) n=31890: c8492(2853498165......) = 1551509199121673731 * c8474(1839175795......) n=31926: c9946(1395149759......) = 332930426175643113828277 * c9922(4190514444......) n=31966: c14514(5735257390......) = 123359708509810153686691 * c14491(4649214447......) n=32130: c6900(7908151074......) = 1101128720508897764041 * c6879(7181858875......) n=32250: c8400(9999999999......) = 103526289664797293205001 * c8377(9659382203......) n=32264: c15529(5912214800......) = 3506122191377189811281 * c15508(1686254636......) n=32354: c13846(2166239787......) = 4806730864780971961801 * c13824(4506680004......) n=32530: c12979(1856687017......) = 70162268702104794108054001 * c12953(2646275629......) n=32600: c12947(5080661553......) = 135544576240587889388401 * c12924(3748332610......) n=32672: c16300(1010699051......) = 13439466818282691185899297 * c16274(7520380569......) n=32702: c16073(1099999999......) = 20917601776236212557397 * c16050(5258729044......) n=32730: c8714(3123989562......) = 796330404308868018721 * c8693(3922981648......) n=32844: c8419(1367443799......) = 690079785060125329306463041 * c8392(1981573478......) n=32944: c15671(2083902550......) = 412860491812863204455537 * c15647(5047473885......) n=33010: c13191(9605356314......) = 416764638677805715091 * c13171(2304743594......) n=33024: c10753(1000000000......) = 364050131659653121 * c10735(2746874435......) n=33054: c9432(9100000909......) = 71589813152701862139157 * x9410(1271130697......) n=33054: x9410(1271130697......) = 135387308179639106311687 * c9386(9388846814......) n=33066: c9955(4316028911......) = 7387282999728627733 * c9936(5842511938......) n=33070: c13225(1099989000......) = 16257062187566054875451 * c13202(6766222503......) n=33088: c14721(1000000000......) = 34926628299166139009 * c14701(2863144966......) n=33104: c16512(3776274264......) = 8551561512557816621435377 * c16487(4415888558......) n=33118: c15904(6869730819......) = 231101417324066259413 * c15884(2972604365......) n=33154: c14961(1000000000......) = 51802540286077905853 * c14941(1930407262......) n=33192: c11020(5513508910......) = 745340157524833631072553889 * c10993(7397305585......) n=33218: c15603(2978581322......) = 9920977165696226539241 * c15581(3002306398......) n=33268: c16626(1322724376......) = 484235742067818657125466001 * c16599(2731571137......) n=33274: c16368(1722176918......) = 6113122020582917 * c16352(2817180668......) n=33280: c12275(1377578946......) = 145579549664727792641 * c12254(9462722955......) n=33282: c10837(1000000000......) = 88824651074901323677 * c10817(1125813597......) n=196634: c98316(9090909090......) = 17096212042074765825002047 * c98291(5317499027......) n=197074: c97861(1099999999......) = 289351276331986049 * c97843(3801607561......) # 213193 of 300000 Phi_n(10) factorizations were cracked. -- Mar 1, 2024 (Makoto Kamada) -- n=148010: c54720(9999999999......) = 245018285711051 * c54706(4081328040......) n=148124: c70129(1009999999......) = 219498280391941 * c70114(4601402790......) n=148222: c72065(3373318297......) = 447624382907971 * c72050(7536046797......) n=148246: c63514(8032818320......) = 178276849691011 * c63500(4505811233......) n=148478: c63348(4934884056......) = 191275689959531 * c63334(2579984972......) n=148814: c72341(8779224530......) = 870188937442339 * c72327(1008887168......) n=148874: c65993(7930447501......) = 195048914222339 * c65979(4065876261......)