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
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
# 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......)
# via Kurt Beschorner
n=8914: c4456(9090909090......) = 1680862037183886151986766096284943 * c4423(5408480226......)
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
# via Kurt Beschorner
n=73019: c73019(1111111111......) = 1323020047051919660237 * c72997(8398293839......)
# ECM B1=5e4, sigma=1341369107631264
# 213205 of 300000 Φn(10) factorizations were cracked. 300000 個中 213205 個の Φn(10) の素因数が見つかりました。
# 20032 of 25997 Rprime factorizations were cracked. 25997 個中 20032 個の Rprime の素因数が見つかりました。
# via Sam Wagstaff
n=1420L: c231(7090462991......) = 247950328172294050136754481538951409190364075674960071233394038784474817867352415168199452660754962688866321901 * p121(2859630412......)
# SNFS
# 1263 of 300000 Φn(10) factorizations were finished. 300000 個中 1263 個の Φn(10) の素因数分解が終わりました。
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)
# via Sam Wagstaff
n=1420M: c212(1748241862......) = 150068993718936038588227244574366404285884513639444374982663085901463237698274075317154251769989823397761 * p108(1164958742......)
# GNFS
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)
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......)
# 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 Φn(10) factorizations were cracked. 300000 個中 213200 個の Φn(10) の素因数が見つかりました。
# 20031 of 25997 Rprime factorizations were cracked. 25997 個中 20031 個の Rprime の素因数が見つかりました。
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......)
# 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 Φn(10) factorizations were cracked. 300000 個中 213193 個の Φn(10) の素因数が見つかりました。
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......)