# Recent changes of Phin10.txt / Phin10ex.txt # # note # -- date (name) -- # n=... details -- Apr 14, 2024 (Kurt Beschorner) -- n=659: c620(4267053373......) = 149909896971539560984652057797566890100299359259837 * p570(2846412051......) # ECM B1=11e7, sigma=0:4226535905387705 n=13251: c7553(1020556209......) = 12296428612923146794052172531037 * c7521(8299614806......) # P-1 B1=160e6 n=100098: c32439(1651391149......) = 17325552919871634468049 * c32416(9531535053......) # P-1 B1=35e6 n=100105: c80070(3271635196......) = 144493170813628346471 * c80050(2264214411......) # P-1 B1=17e6 # 1265 of 300000 Phi_n(10) factorizations were finished. -- Apr 14, 2024 (Gouik) -- # via yoyo@home n=651: c353(3942538136......) = 18761726160436368465384904039916752385257524435903404839 * p298(2101372817......) # ECM B1=1694085181-2900000000 # 1264 of 300000 Phi_n(10) factorizations were finished. -- Apr 7, 2024 (Kurt Beschorner) -- n=12771: c7490(3265530166......) = 314224898531750364984013 * x7467(1039233422......) # P-1 B1=160e6 n=12771: x7467(1039233422......) = 238824929913673638997582363 * c7440(4351444477......) # P-1 B1=160e6 n=13158: c3973(6498919750......) = 68581509075838066581670099156849 * c3941(9476198231......) # P-1 B1=140e6 n=100079: c77947(4996028157......) = 6068994380637463834185467 * c77922(8232052699......) # P-1 B1=10e6 n=100363: c100338(3342416394......) = 1016391456544433853547 * c100317(3288512878......) # P-1 B1=15e6 n=100379: c100370(2271994863......) = 66388841093949454147 * c100350(3422254141......) # P-1 B1=15e6 n=100417: c100389(1606817930......) = 286825064305738012150961 * c100365(5602083398......) # P-1 B1=15e6 n=100459: c100428(1850977056......) = 22782665966376356329 * c100408(8124497191......) # P-1 B1=15e6 n=100517: c100517(1111111111......) = 17361707890852059740855929 * c100491(6399780010......) # P-1 B1=16e6 n=100519: c100519(1111111111......) = 101147426853941494945049 * c100496(1098506551......) # P-1 B1=16e6 n=100559: c100506(1770694992......) = 95610786074378976307 * c100486(1851982464......) # P-1 B1=16e6 n=100591: c100591(1111111111......) = 1291405529277231477460435169 * c100563(8603889993......) # P-1 B1=16e6 n=100669: c100656(2048201370......) = 2806386502390207284249241483 * c100628(7298358116......) # P-1 B1=16e6 n=100811: c100799(4439811269......) = 281860909823518349338601 * c100776(1575178080......) # P-1 B1=16e6 n=100817: c100069(2554375103......) = 507962247211408289 * c100051(5028671160......) # P-1 B1=16e6 n=147977: c147963(5771101824......) = 114084230812902508795841 * c147940(5058632366......) # P-1 B1=8.8e6 # 213213 of 300000 Phi_n(10) factorizations were cracked. # 20039 of 25997 R_prime factorizations were cracked. -- Apr 1, 2024 (Alfred Eichhorn) -- # via Kurt Beschorner n=79337: c79337(1111111111......) = 9145312312862925909640977721 * c79309(1214951521......) # ECM B1=5e4, sigma=7464158329682606 n=79427: c79427(1111111111......) = 1284283667245483471417172921 * c79399(8651601974......) # ECM B1=5e4, sigma=5590089294394130 # 213210 of 300000 Phi_n(10) factorizations were cracked. # 20036 of 25997 R_prime factorizations were cracked. -- Apr 1, 2024 (Kurt Beschorner) -- n=14549: c14549(1111111111......) = 4005021584963302209471746401 * c14521(2774294938......) # P-1 B1=14e7 n=14747: c14747(1111111111......) = 252632181388341912925629401 * c14720(4398137660......) # P-1 B1=14e7 n=147799: c147784(2810812403......) = 24724127378034035880566249 * c147759(1136870216......) # P-1 B1=8.8e6 -- 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) # 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