News and updates, October 2004

Factorizations

News and updates, October 2004	2007-04-11(Wed) 19:57

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News and updates, October 2004

Oct 31, 2004 (4th): 99...997 (n≤150) was completed.
Oct 31, 2004 (3rd): By Greg Childers / GGNFS
10¹⁴⁸-3 = (9)₁₄₇7_<148> = 13 · 59 · 8902981 · 2092098327453367265488153_<25> · C114
C114 = P49 · P66
P49 = 1313437274082906131865018524905745892254428247173_<49>
P66 = 532939316067522452437009431855311310168767228534802154162283932019_<66>
Oct 31, 2004 (2nd): By Tyler Cadigan / PPSIQS
(43·10¹²⁸-7)/9 = 4(7)₁₂₈_<129> = 3² · 154937 · 738616566413580841092563_<24> · C99
C99 = P40 · P60
P40 = 1954973229374376044259837704014211718857_<40>
P60 = 237283989262243286151858068264136304653121566371862021029459_<60>
Oct 31, 2004: By Sander Hoogendoorn / GGNFS
(2·10¹³⁰+61)/9 = (2)₁₂₉9_<130> = 3 · 1013 · 1297927 · 4119130853_<10> · 82383989539_<11> · C100
C100 = P44 · P57
P44 = 12893334001210030724132713775348201750269021_<44>
P57 = 128763531207327046074262161561454733351447087377845111599_<57>
Oct 30, 2004 (4th): By Shusuke Kubota / GMP-ECM 5.0c
(10¹⁷⁷+17)/9 = (1)₁₇₆3_<177> = 79 · 199 · 337 · C170
C170 = P31 · C140
P31 = 1892299672990464278460298053559_<31>
C140 = [11083004451549544720109865787472537752249266606417007670255378526710604506596194032710063538973026910205000830114341184301551035751303036791_<140>]
Oct 30, 2004 (3rd): By Makoto Kamada / GMP-ECM 5.0.3
(10¹⁸⁰-7)/3 = (3)₁₇₉1_<180> = C180
C180 = P32 · P148
P32 = 49177191501454157350182747447299_<32>
P148 = 6778210043236746233828300268523246840277702850524567595358247821792960480246500354171003532043608637885168961086829129013098596280247355631530720369_<148>
Oct 30, 2004 (2nd): GGNFS 0.60.9-unstable was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)
Oct 30, 2004: By Sander Hoogendoorn / GMP-ECM
(10¹⁵⁴+17)/9 = (1)₁₅₃3_<154> = 3 · 7 · 4175881 · 117171638757881_<15> · 4829596115648201347913864129_<28> · C104
C104 = P30 · P74
P30 = 788762691872479934761930966381_<30>
P74 = 28386405587527475548491315882496594361400361139034948208375826137519369177_<74>
Oct 29, 2004 (2nd): The condition of 188...881 was extended to n≤200.
We have not factored following numbers yet. These numbers passed GMP-ECM (B1=77970+alpha) 100 times.
(17·10¹⁵²-71)/9, (17·10¹⁵³-71)/9, (17·10¹⁵⁵-71)/9, (17·10¹⁵⁷-71)/9, (17·10¹⁵⁸-71)/9, (17·10¹⁶¹-71)/9, (17·10¹⁶²-71)/9, (17·10¹⁶⁴-71)/9, (17·10¹⁶⁵-71)/9, (17·10¹⁶⁶-71)/9, (17·10¹⁷⁴-71)/9, (17·10¹⁷⁹-71)/9, (17·10¹⁸⁰-71)/9, (17·10¹⁸¹-71)/9, (17·10¹⁸²-71)/9, (17·10¹⁸³-71)/9, (17·10¹⁸⁴-71)/9, (17·10¹⁸⁵-71)/9, (17·10¹⁸⁶-71)/9, (17·10¹⁸⁷-71)/9, (17·10¹⁸⁸-71)/9, (17·10¹⁸⁹-71)/9, (17·10¹⁹¹-71)/9, (17·10¹⁹²-71)/9, (17·10¹⁹³-71)/9, (17·10¹⁹⁵-71)/9, (17·10¹⁹⁷-71)/9, (17·10¹⁹⁸-71)/9, (17·10¹⁹⁹-71)/9, (17·10²⁰⁰-71)/9, (30/200)
The condition of 211...11 was extended to n≤200.
We have not factored following numbers yet. These numbers passed GMP-ECM (B1=78950+alpha) 100 times.
(19·10¹⁵²-1)/9, (19·10¹⁵⁵-1)/9, (19·10¹⁵⁶-1)/9, (19·10¹⁵⁷-1)/9, (19·10¹⁵⁸-1)/9, (19·10¹⁶⁰-1)/9, (19·10¹⁶¹-1)/9, (19·10¹⁶⁴-1)/9, (19·10¹⁶⁵-1)/9, (19·10¹⁶⁶-1)/9, (19·10¹⁶⁷-1)/9, (19·10¹⁶⁹-1)/9, (19·10¹⁷⁰-1)/9, (19·10¹⁷⁶-1)/9, (19·10¹⁷⁸-1)/9, (19·10¹⁷⁹-1)/9, (19·10¹⁸³-1)/9, (19·10¹⁸⁴-1)/9, (19·10¹⁸⁵-1)/9, (19·10¹⁸⁷-1)/9, (19·10¹⁸⁸-1)/9, (19·10¹⁸⁹-1)/9, (19·10¹⁹²-1)/9, (19·10¹⁹³-1)/9, (19·10¹⁹⁴-1)/9, (19·10¹⁹⁵-1)/9, (19·10¹⁹⁶-1)/9, (19·10¹⁹⁷-1)/9, (19·10¹⁹⁹-1)/9, (19·10²⁰⁰-1)/9, (30/200)
Oct 29, 2004: By Philippe Strohl / newpgen, pfgw, primo 2.2.0 beta 5
(28·10⁵⁵⁴-1)/9 = 3(1)₅₅₄_<555>, (28·10⁵⁸⁰-1)/9 = 3(1)₅₈₀_<581> and (28·10¹³¹⁰-1)/9 = 3(1)₁₃₁₀_<1311> are definitely prime.
(28·10⁸⁵³⁷-1)/9 = 3(1)₈₅₃₇_<8538> is a strong-tested near-repdigit prp for bases 2, 3, 5, 7, 11, 13, 101.
Oct 28, 2004: By Tyler Cadigan / PPSIQS
(73·10¹³⁴-1)/9 = 8(1)₁₃₄_<135> = 13881683 · 269001190545339915526867145161_<30> · C99
C99 = P47 · P53
P47 = 18432819128434097282510480246554333039481218741_<47>
P53 = 11783987259061293732004233277125153540987549016928417_<53>
Oct 27, 2004 (3rd): By Makoto Kamada / GMP-ECM 5.0.3
(2·10¹⁸⁷-11)/9 = (2)₁₈₆1_<187> = 19 · 4649532960488279_<16> · C170
C170 = P26 · C144
P26 = 66702983608994124414569333_<26>
C144 = [377119764747833718003946378619475660102486646646917939582436513454949109037981126041578149847338179007647070268403253033533084661810688970509237_<144>]
(2·10¹⁹⁸-11)/9 = (2)₁₉₇1_<198> = C198
C198 = P28 · P171
P28 = 1544037026288694228448962803_<28>
P171 = 143922858350336298007015876592048703111776471944979409246319942874278590726370537456210410833733045044256670966248552842007007774259251774964473490039868315319739946574207_<171>
(2·10¹⁹⁹-11)/9 = (2)₁₉₈1_<199> = C199
C199 = P22 · C177
P22 = 6963796279053002235013_<22>
C177 = [319110745514861526794711378703572343995428106001193557079701797757226211580497488909530035973009966646124859139500542679842644131385590979909709371867619340587830262001201479017_<177>]
(2·10²⁰⁰-11)/9 = (2)₁₉₉1_<200> = 3 · 7 · C199
C199 = P26 · C173
P26 = 14001880603763633983098127_<26>
C173 = [75575637883715360494127604153948330408332570614645220164868186345149960834182522442943792947391780510225177833932663779244341727897146410091059638069084001256139164641000663_<173>]
(2·10¹⁸⁷+43)/9 = (2)₁₈₆7_<187> = 7 · 239 · 2089 · 2719 · 3599899 · C170
C170 = P31 · C140
P31 = 1454013060523477510672955511551_<31>
C140 = [44677130729451804862805296406299145317435763417023166693374258901454414212791155339352971120916809652830021667465704793500230882435827163161_<140>]
(2·10²⁰⁰+43)/9 = (2)₁₉₉7_<200> = 3² · 31 · 359 · 17737 · C191
C191 = P26 · C165
P26 = 38777212649318798402557141_<26>
C165 = [322576020641972706302877554164604660713708913064209859124760804918641746437488561431324513986094863871011370553215853295417573007065639808150520269489150069649253071_<165>]
Oct 27, 2004 (2nd): By Greg Childers / GGNFS
10¹⁴⁷-3 = (9)₁₄₆7_<147> = 87257 · 2581475893243546379399562049_<28> · C115
C115 = P34 · P35 · P47
P34 = 2978486598601309977385667600190257_<34>
P35 = 76939696440259536071166115723477303_<35>
P47 = 19372493773537840831076728862163526175658084499_<47>
Oct 27, 2004: By Shusuke Kubota / GMP-ECM 5.0c
(10¹⁵⁵+17)/9 = (1)₁₅₄3_<155> = 166099 · C149
C149 = P27 · P123
P27 = 273317524842305270518823897_<27>
P123 = 244750165230574200547682049835258201594816962750328193064042361804148517538105347084808386128960345614953858844611763145771_<123>
(10¹⁶⁰+17)/9 = (1)₁₅₉3_<160> = 3³ · 7 · 23² · 53 · 107881 · C148
C148 = P27 · C121
P27 = 301787558315959860024628403_<27>
C121 = [6440474276189063029469896370990258701549175964742824120735650981327705765751244667703443710331099759156990377210821915787_<121>]
Oct 26, 2004 (2nd): By Greg Childers / GGNFS
(2·10¹⁴⁸+7)/9 = (2)₁₄₇3_<148> = 3⁴ · 13 · 19 · 101567257305949471_<18> · C127
C127 = P48 · P79
P48 = 141303761410777573245254533260661267574419385131_<48>
P79 = 7739235575743774151398238877945382293130861185697207152777976673706588113101589_<79>
(2·10¹⁴⁹+7)/9 = (2)₁₄₈3_<149> = 8821 · C145
C145 = P43 · P103
P43 = 1840443781568006396865580669535155839494213_<43>
P103 = 1368822414508331612887738891689191177896334116203834760359254573437015084565780181118874791758026980951_<103>
10¹⁴⁶-3 = (9)₁₄₅7_<146> = 786435493 · 33687902299127_<14> · 739507611188227323791_<21> · C103
C103 = P51 · P53
P51 = 147774458556369431910404840981974982225732968722011_<51>
P53 = 34539886053501171347512504592110662553160109081260627_<53>
Oct 26, 2004: By Sander Hoogendoorn / GGNFS-0.60.6-unstable
(8·10¹²²-53)/9 = (8)₁₂₁3_<122> = 4657 · 15971 · 9148829 · 297320813 · C99
C99 = P34 · P65
P34 = 4827809083534124843321592349710763_<34>
P65 = 91005621608334442248646511271192948866304220688718076292235913339_<65>
(10¹²⁶+53)/9 = (1)₁₂₅7_<126> = 3 · 4969 · 17471 · C117
C117 = P30 · P88
P30 = 425870593031226135936543563393_<30>
P88 = 1001778768087818674719079587739198460979731073535208269904425228780987895998402881908777_<88>
10¹⁴¹-3 = (9)₁₄₀7_<141> = 757 · 21395260840097_<14> · 1998567824579494876129_<22> · C104
C104 = P47 · P58
P47 = 12839483153589083628646788780690801027737944337_<47>
P58 = 2406135617024184285708011017528134490384412631178837377241_<58>
Oct 25, 2004: By Tyler Cadigan / PPSIQS
(52·10¹³⁴-7)/9 = 5(7)₁₃₄_<135> = 113 · 21401 · 97117666918073_<14> · 2950265320624201_<16> · C99
C99 = P34 · P65
P34 = 9827130435253045429747763011768723_<34>
P65 = 84852040039259635923938051822061659838632591751201421054543493651_<65>
Oct 24, 2004 (5th): By Wataru Sakai / GMP-ECM
(10¹⁸⁰+17)/9 = (1)₁₇₉3_<180> = 6949 · 135862068644287_<15> · 21633659135200744087543_<23> · C139
C139 = P23 · C116
P23 = 57990409560719099220689_<23>
C116 = [93810358881996442890482228144067883749540447348259571159075789651402467670223973413339539712829879169409153603718813_<116>]
Oct 24, 2004 (4th): By Sander Hoogendoorn / GGNFS-0.60.6-unstable
(8·10¹¹⁸-53)/9 = (8)₁₁₇3_<118> = 3 · 7 · 19 · 228233 · 241565141 · C102
C102 = P45 · P57
P45 = 578704942589176822629197761530448010148528217_<45>
P57 = 698239940722979733212883687994620092969422992590640558217_<57>
Oct 24, 2004 (3rd): By Shusuke Kubota / GMP-ECM 5.0c
(10¹⁵⁶+17)/9 = (1)₁₅₅3_<156> = 17477 · 2390473 · 37402307 · 1264206703_<10> · 47444143291487343389_<20> · 48680022488359635652849_<23> · C86
C86 = P28 · P58
P28 = 3167489193406668807814739101_<28>
P58 = 7688502524564656969822416010021474832000147918615571810313_<58>
Oct 24, 2004 (2nd): The condition of 166...661 was extended to n≤200.
We have not factored following numbers yet. These numbers passed GMP-ECM (B1=76900+alpha) 100 times.
(5·10¹⁵⁵-17)/3, (5·10¹⁵⁶-17)/3, (5·10¹⁵⁷-17)/3, (5·10¹⁵⁸-17)/3, (5·10¹⁵⁹-17)/3, (5·10¹⁶⁰-17)/3, (5·10¹⁶²-17)/3, (5·10¹⁶³-17)/3, (5·10¹⁶⁴-17)/3, (5·10¹⁶⁵-17)/3, (5·10¹⁶⁶-17)/3, (5·10¹⁶⁷-17)/3, (5·10¹⁷¹-17)/3, (5·10¹⁷²-17)/3, (5·10¹⁷⁴-17)/3, (5·10¹⁷⁵-17)/3, (5·10¹⁷⁶-17)/3, (5·10¹⁷⁷-17)/3, (5·10¹⁷⁸-17)/3, (5·10¹⁷⁹-17)/3, (5·10¹⁸⁰-17)/3, (5·10¹⁸¹-17)/3, (5·10¹⁸³-17)/3, (5·10¹⁸⁴-17)/3, (5·10¹⁸⁵-17)/3, (5·10¹⁸⁶-17)/3, (5·10¹⁸⁷-17)/3, (5·10¹⁸⁹-17)/3, (5·10¹⁹⁰-17)/3, (5·10¹⁹²-17)/3, (5·10¹⁹⁴-17)/3, (5·10¹⁹⁵-17)/3, (5·10¹⁹⁶-17)/3, (5·10¹⁹⁷-17)/3, (5·10¹⁹⁸-17)/3, (5·10¹⁹⁹-17)/3, (5·10²⁰⁰-17)/3, (37/200)
Oct 24, 2004: By Sander Hoogendoorn / GGNFS-0.60.6-unstable
(22·10¹²⁵-1)/3 = 7(3)₁₂₅_<126> = 1303 · C123
C123 = P62 · P62
P62 = 13076611503468354728659845656356098066371387730347509283020637_<62>
P62 = 43038962041908707110557819970297770102457906275634967258060303_<62>
Oct 23, 2004 (2nd): By Wataru Sakai / GMP-ECM
2·10¹⁵⁹-1 = 1(9)₁₅₉_<160> = 31 · 269 · 1069 · 624521 · 972779112004724071_<18> · C129
C129 = P30 · P100
P30 = 198218330943890143039085853511_<30>
P100 = 1863087356568022561958848459430622336906208220440978054782168211919375375101660488520582074357218689_<100>
Oct 23, 2004: By Tyler Cadigan / PPSIQS
(88·10¹³⁰-7)/9 = 9(7)₁₃₀_<131> = 2267 · 287735621603_<12> · 1724181776773381577_<19> · C98
C98 = P39 · P60
P39 = 480171920602619344674066954688017245953_<39>
P60 = 181056950467383564559423822136384214704873049423423083461817_<60>
Oct 22, 2004 (2nd): GGNFS 0.60.6-unstable was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)
Oct 22, 2004: The condition of 11...113 was extended to n≤200.
We have not factored following numbers yet. These numbers passed GMP-ECM (B1=74360+alpha) 100 times.
(10¹⁵¹+17)/9, (10¹⁵²+17)/9, (10¹⁵³+17)/9, (10¹⁵⁴+17)/9, (10¹⁵⁵+17)/9, (10¹⁵⁶+17)/9, (10¹⁵⁷+17)/9, (10¹⁵⁹+17)/9, (10¹⁶⁰+17)/9, (10¹⁶²+17)/9, (10¹⁶⁵+17)/9, (10¹⁶⁹+17)/9, (10¹⁷⁰+17)/9, (10¹⁷²+17)/9, (10¹⁷³+17)/9, (10¹⁷⁴+17)/9, (10¹⁷⁶+17)/9, (10¹⁷⁷+17)/9, (10¹⁷⁸+17)/9, (10¹⁷⁹+17)/9, (10¹⁸⁰+17)/9, (10¹⁸¹+17)/9, (10¹⁸³+17)/9, (10¹⁸⁴+17)/9, (10¹⁸⁵+17)/9, (10¹⁸⁷+17)/9, (10¹⁸⁸+17)/9, (10¹⁸⁹+17)/9, (10¹⁹²+17)/9, (10¹⁹³+17)/9, (10¹⁹⁵+17)/9, (10¹⁹⁸+17)/9, (10¹⁹⁹+17)/9, (33/200)
Oct 20, 2004 (4th): The condition of 33...331 was extended to n≤200.
We have not factored following numbers yet. These numbers passed GMP-ECM (B1=54860+alpha) 100 times.
n= (10¹⁵²-7)/3, (10¹⁵⁴-7)/3, (10¹⁵⁹-7)/3, (10¹⁶¹-7)/3, (10¹⁶³-7)/3, (10¹⁶⁶-7)/3, (10¹⁶⁷-7)/3, (10¹⁶⁸-7)/3, (10¹⁶⁹-7)/3, (10¹⁷⁰-7)/3, (10¹⁷²-7)/3, (10¹⁷⁴-7)/3, (10¹⁷⁵-7)/3, (10¹⁸⁰-7)/3, (10¹⁸²-7)/3, (10¹⁸³-7)/3, (10¹⁸⁵-7)/3, (10¹⁸⁷-7)/3, (10¹⁸⁹-7)/3, (10¹⁹⁰-7)/3, (10¹⁹¹-7)/3, (10¹⁹³-7)/3, (10¹⁹⁵-7)/3, (10¹⁹⁶-7)/3, (10¹⁹⁸-7)/3, (10¹⁹⁹-7)/3, (10²⁰⁰-7)/3, (27/200)
Oct 20, 2004 (3rd): The condition of 833...33 was extended to n≤200.
We have not factored following numbers yet. These numbers passed GMP-ECM (B1=68230+alpha) 100 times.
n= (25·10¹⁵¹-1)/3, (25·10¹⁵³-1)/3, (25·10¹⁵⁵-1)/3, (25·10¹⁵⁹-1)/3, (25·10¹⁶¹-1)/3, (25·10¹⁶³-1)/3, (25·10¹⁶⁵-1)/3, (25·10¹⁶⁹-1)/3, (25·10¹⁷¹-1)/3, (25·10¹⁷⁹-1)/3, (25·10¹⁸¹-1)/3, (25·10¹⁸³-1)/3, (25·10¹⁸⁵-1)/3, (25·10¹⁸⁹-1)/3, (25·10¹⁹³-1)/3, (25·10¹⁹⁵-1)/3, (25·10¹⁹⁷-1)/3, (17/200)
Oct 20, 2004 (2nd): By Tyler Cadigan / PPSIQS
(73·10¹⁴²-1)/9 = 8(1)₁₄₂_<143> = 3 · 89 · 110879 · 316896856426336397_<18> · 128431369081220952707_<21> · C98
C98 = P47 · P52
P47 = 29112024575477100392322967162534860141551931511_<47>
P52 = 2312375378201714336124580223199023275409487476004683_<52>
Oct 20, 2004: By Sander Hoogendoorn / GGNFS-0.60.3-unstable, GGNFS-0.54.5b
(7·10¹¹⁹+11)/9 = (7)₁₁₈9_<119> = 13 · 79 · C116
C116 = P47 · P70
P47 = 21200188520689563589776797426334823576191297367_<47>
P70 = 3572278947023668975795230555579869684684367732959994202489268058449431_<70>
Oct 19, 2004 (3rd): 211...11 (n≤150) was completed.
Oct 19, 2004 (2nd): By Greg Childers / GGNFS
(7·10¹¹⁷+11)/9 = (7)₁₁₆9_<117> = 65843 · C113
C113 = P32 · P81
P32 = 17618579928725054681087090473267_<32>
P81 = 670463313689757794025465783085063598471823980469840546178141528091016173914592059_<81>
(19·10¹⁴¹-1)/9 = 2(1)₁₄₁_<142> = 808001147 · 14451177179_<11> · C123
C123 = P61 · P62
P61 = 1967526606641874254902868696224753606009599388741835659032403_<61>
P62 = 91891485965508071388404658746315616009850224878544027799539749_<62>
(19·10¹⁴⁶-1)/9 = 2(1)₁₄₆_<147> = 192366985120423_<15> · C133
C133 = P38 · P45 · P51
P38 = 29365301023666568488392630000453630649_<38>
P45 = 355187872431500922702175275160737857693544593_<45>
P51 = 105217497198344900059826621607642715596457417792601_<51>
(2·10¹⁴⁴+7)/9 = (2)₁₄₃3_<144> = 53611 · 117563 · 60387159023969_<14> · C120
C120 = P38 · P82
P38 = 88692373338546605226340701414858466691_<38>
P82 = 6583124119103824473232830829207215208475424966357525746284822636946549026969966109_<82>
Oct 19, 2004: By Wataru Sakai / GMP-ECM, PPSIQS
2·10¹⁷⁸-1 = 1(9)₁₇₈_<179> = 7 · 19697 · 49871 · 2168131776887_<13> · 21546540858697_<14> · 34452787495073_<14> · 702699414074538345359_<21> · C109
C109 = P26 · P41 · P43
P26 = 11232286032052640081577527_<26>
P41 = 67824241037706050027234164121994583646719_<41>
P43 = 3375775122619098833564433321864778716021439_<43>
Oct 18, 2004: GGNFS 0.60.3-unstable was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)
Oct 17, 2004 (2nd): By Makoto Kamada / PFGW
(10⁵³⁷¹⁸-7)/3 is near-repdigit PRP! (53718 digits)

PFGW Version 20031222.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] ...snip... Primality testing (10^53718-7)/3 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 191 Calling Brillhart-Lehmer-Selfridge with factored part 0.00% (10^53718-7)/3 is PRP! (369.0068s+0.0255s)
Note:
N = (10⁵³⁷¹⁸-7)/3 = 33...331_<53718> = PRP53718
N-1 = 2·3·5·(10⁵³⁷¹⁷-1)/9 = 2·3·5·11...11_<53717> = 2·3·5·C53717
N+1 = 2²·(5²·10⁵³⁷¹⁶-1)/3 = 2²·833...33_<53717> = 2²·(5·10²⁶⁸⁵⁸+1)/3·(5·10²⁶⁸⁵⁸-1) = 2²·166...667_<26859>·499...99_<26859> = 2²·23·307·C26855·C26859
Oct 17, 2004: By Tyler Cadigan / PPSIQS
(55·10¹³⁴-1)/9 = 6(1)₁₃₄_<135> = 13 · 36767 · 660263837 · 61946758732347766777697_<23> · C98
C98 = P46 · P52
P46 = 8755150783849633265491267457055286984814318113_<46>
P52 = 3570416687946609499815611721841848091904442919247713_<52>
Oct 16, 2004 (2nd): By Wataru Sakai / GMP-ECM
2·10¹⁸¹-1 = 1(9)₁₈₁_<182> = 19 · 71 · 7349 · 808897818779368181_<18> · C157
C157 = P27 · C130
P27 = 797129087967153857493783971_<27>
C130 = [3128725609853561538026773920634567520995491992088880828324972714133336327873248318256123375586149260625874239143237635528827613049_<130>]
2·10¹⁹³-1 = 1(9)₁₉₃_<194> = 61 · 3011 · 3019 · 2630399 · 1921011481_<10> · C169
C169 = P28 · C142
P28 = 5467489597378404813936108409_<28>
C142 = [1305529637784949287620571177887970771289520181235731640907698902880282231900498703097479220981210951629363692688397047212888405051383997623781_<142>]
Oct 16, 2004: GGNFS 0.60.2-unstable was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)
Oct 15, 2004 (2nd): GGNFS 0.60.1-unstable was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)
Oct 15, 2004: By Tyler Cadigan / PPSIQS
(43·10¹⁴²-7)/9 = 4(7)₁₄₂_<143> = 73 · 5029713022533431_<16> · 7982206761553087772094608069_<28> · C98
C98 = P47 · P52
P47 = 13161811572942026780272299603740292163817712761_<47>
P52 = 1238571941870914213650789099380420961210434567724331_<52>
Oct 14, 2004 (3rd): GGNFS 0.60-unstable was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)
Oct 14, 2004 (2nd): By Greg Childers / GGNFS
(19·10¹³⁷-1)/9 = 2(1)₁₃₇_<138> = 433 · 1153 · 11393 · 368897952710839480161169_<24> · C105
C105 = P49 · P56
P49 = 6537808630984692512469327874650028071620851099861_<49>
P56 = 15389245976913122179432504758319730080753497050831216747_<56>
(19·10¹³⁸-1)/9 = 2(1)₁₃₈_<139> = 232782754247700067_<18> · C121
C121 = P35 · P36 · P51
P35 = 83845459775834452015372760685094399_<35>
P36 = 519453467494562654362155883937185937_<36>
P51 = 208225584050293597284203129689776748924665335039491_<51>
(19·10¹⁴⁰-1)/9 = 2(1)₁₄₀_<141> = 222326827 · C132
C132 = P45 · P88
P45 = 394108304678831242112558499262511688888855913_<45>
P88 = 2409370758501444138484329720023565745017813043666268787378494727668172943572169242450061_<88>
Oct 14, 2004: By Wataru Sakai / GMP-ECM
(88·10¹³⁷-7)/9 = 9(7)₁₃₇_<138> = 61 · 151381 · 57788731821397588871_<20> · C112
C112 = P33 · P79
P33 = 423159888810652517177897177983787_<33>
P79 = 4330033931355453127427368400603870758421240640236447768211277207463100054506261_<79>
Oct 13, 2004: By Tyler Cadigan / PPSIQS
(2·10¹⁵²+43)/9 = (2)₁₅₁7_<152> = 3 · 239 · 5009 · 449657941 · 2049787717937_<13> · 197698919201521_<15> · 3382715237604481_<16> · C95
C95 = P36 · P59
P36 = 123507170992907914494904032797740999_<36>
P59 = 81276358251977578443368209020381440283647979206625391847573_<59>
Oct 12, 2004 (3rd): 33...337 (n≤150) was completed.
Oct 12, 2004 (2nd): By Greg Childers / GGNFS
(10¹⁴⁷+11)/3 = (3)₁₄₆7_<147> = 1162937 · C141
C141 = P57 · P85
P57 = 122298277433855682221983303461516529262928308651913502673_<57>
P85 = 2343701062831766762630355127557560272330817932239700191200456367244305886653028541137_<85>
(10¹⁴⁹+11)/3 = (3)₁₄₈7_<149> = 17 · 29² · 37 · 378223 · 5825627 · 32925367 · 756636899 · C115
C115 = P48 · P67
P48 = 195198074094872806630540943368285016578324654027_<48>
P67 = 5880954575013582298632130756027502940541749324006917590815713873903_<67>
(10¹⁵⁰+11)/3 = (3)₁₄₉7_<150> = 2130699499_<10> · 8218293359_<10> · 740149080574399_<15> · C116
C116 = P41 · P76
P41 = 15627473558923467190534668668177581868687_<41>
P76 = 1645761600727067557000325053584468951705606827951606549532721342029062419189_<76>
5·10¹⁴¹-1 = 4(9)₁₄₁_<142> = 863 · 864112969 · C130
C130 = P35 · P96
P35 = 33102413419941380298625729200482713_<35>
P96 = 202548498000084611654776402535431487378132205253772216085513563043908316903499360835198098115009_<96>
5·10¹⁴²-1 = 4(9)₁₄₂_<143> = 19 · 33738391 · 69976289 · 727879169 · C118
C118 = P44 · P75
P44 = 14451133963291796815528100748696733275771551_<44>
P75 = 105969262443706424717542949006868182672629853917824633425083022550272421341_<75>
5·10¹⁴⁹-1 = 4(9)₁₄₉_<150> = 439 · 6361 · 9892593989592316723951_<22> · C122
C122 = P47 · P76
P47 = 12991330986777786451229660905897078106018495159_<47>
P76 = 1393208949869384358841491740657456164913361005125028453793652095448657424009_<76>
Oct 12, 2004: By Tyler Cadigan / PPSIQS
(2·10¹⁵⁸+43)/9 = (2)₁₅₇7_<158> = 3 · 3911 · 12757 · 682183455257780153_<18> · 18569608690644895717_<20> · 500852893304150454113762519_<27> · C87
C87 = P39 · P48
P39 = 171656453521669967343858143055323881547_<39>
P48 = 136318752457961309113115770941045842568542636819_<48>
Oct 11, 2004 (4th): By Tyler Cadigan / PPSIQS
(37·10¹³⁹-1)/9 = 4(1)₁₃₉_<140> = 17170064291_<11> · 53006618019086698414143574579147_<32> · C98
C98 = P41 · P58
P41 = 18911677647762284989893684069553245761137_<41>
P58 = 2388510423164987611147342476383446855248011165523062280439_<58>
Oct 11, 2004 (3rd): Factor tables of 244...441, 244...443, 244...447 and 244...449 are available.
Oct 11, 2004 (2nd): The condition of 22...227 was extended to n≤200.
We have not factored following numbers yet. These numbers passed GMP-ECM (B1=51570+alpha) 100 times.
n= (2·10¹⁵¹+43)/9, (2·10¹⁵²+43)/9, (2·10¹⁵³+43)/9, (2·10¹⁵⁵+43)/9, (2·10¹⁵⁷+43)/9, (2·10¹⁵⁸+43)/9, (2·10¹⁵⁹+43)/9, (2·10¹⁶²+43)/9, (2·10¹⁶³+43)/9, (2·10¹⁶⁴+43)/9, (2·10¹⁶⁶+43)/9, (2·10¹⁶⁷+43)/9, (2·10¹⁶⁸+43)/9, (2·10¹⁷⁰+43)/9, (2·10¹⁷¹+43)/9, (2·10¹⁷²+43)/9, (2·10¹⁷⁴+43)/9, (2·10¹⁷⁶+43)/9, (2·10¹⁷⁷+43)/9, (2·10¹⁷⁹+43)/9, (2·10¹⁸⁰+43)/9, (2·10¹⁸³+43)/9, (2·10¹⁸⁴+43)/9, (2·10¹⁸⁵+43)/9, (2·10¹⁸⁶+43)/9, (2·10¹⁸⁷+43)/9, (2·10¹⁸⁹+43)/9, (2·10¹⁹⁰+43)/9, (2·10¹⁹²+43)/9, (2·10¹⁹⁴+43)/9, (2·10¹⁹⁶+43)/9, (2·10¹⁹⁷+43)/9, (2·10¹⁹⁹+43)/9, (2·10²⁰⁰+43)/9, (34/200)
Oct 11, 2004: By Wataru Sakai / GMP-ECM
2·10¹⁵¹-1 = 1(9)₁₅₁_<152> = 401 · 15791 · 320609 · C139
C139 = P29 · P111
P29 = 13051070336175283765241555981_<29>
P111 = 754838685673403250817815467686560425964416958861401194449084381071630229722100857179323372193549672196641809541_<111>
2·10¹⁶²-1 = 1(9)₁₆₂_<163> = 127 · 5273 · 450446783 · 424040923727_<12> · 6946941874684115687_<19> · C118
C118 = P29 · P89
P29 = 44150768863179970138761108743_<29>
P89 = 50978294951850258538993701135036765568108019089176244471733547982180755616368273282307049_<89>
Oct 10, 2004: By Tyler Cadigan / PPSIQS
(34·10¹³³-7)/9 = 3(7)₁₃₃_<134> = 37² · 60343 · 1557629594509_<13> · 8382888599399617_<16> · C98
C98 = P37 · P62
P37 = 1868838626555299774986718212188695121_<37>
P62 = 18740292929201735880696313935601292593395711295563291441836987_<62>
Oct 9, 2004: By Wataru Sakai / GMP-ECM
2·10¹⁷¹-1 = 1(9)₁₇₁_<172> = 6569 · 568471 · 1534359796328829895031_<22> · C141
C141 = P25 · C116
P25 = 5602144536868763044479389_<25>
C116 = [62307582226426941282730497418239251189478704230641873240737131725763565707384336402366220505143817417223703576438339_<116>]
Oct 8, 2004 (2nd): 722...227 (n≤150) and 33...331 (n≤150) were completed.
Oct 8, 2004: By Greg Childers / GGNFS
(65·10¹⁴⁸+43)/9 = 7(2)₁₄₇7_<149> = 30319 · 1303787 · C139
C139 = P40 · P49 · P50
P40 = 6924695532357538392015942113619235446521_<40>
P49 = 7709243533890924197434092113655130735615595589973_<49>
P50 = 34224481685633447311809947418522210620362025399123_<50>
(10¹³⁹+11)/3 = (3)₁₃₈7_<139> = 7 · 165449 · 1932922237_<10> · C124
C124 = P46 · P79
P46 = 1447597086558252872609466688690209993094429259_<46>
P79 = 1028618843428473398923491637224670996938221974613555125780688474782548389050873_<79>
(10¹⁴⁹-7)/3 = (3)₁₄₈1_<149> = 97 · 1658927 · 11332213 · 35664040793_<11> · C123
C123 = P43 · P80
P43 = 5617135602839255500916665079545771553298613_<43>
P80 = 91247200780038965312128628153119391614786243061577711245686454708892750851633197_<80>
(10¹⁵⁰-7)/3 = (3)₁₄₉1_<150> = 2696167 · 156780139 · 84715134434546281_<17> · C118
C118 = P46 · P73
P46 = 6604930489864216126722326114502720837851717003_<46>
P73 = 1409326621098177761765122201344192612588820084693889200289238400674958709_<73>
Oct 7, 2004: By Tyler Cadigan / PPSIQS
(79·10¹¹⁸-7)/9 = 8(7)₁₁₈_<119> = 3 · 47 · 4024277 · 34089915659071_<14> · C97
C97 = P45 · P52
P45 = 883144159821027373966672839952504573443041011_<45>
P52 = 5138307307076065050635534448422224366101312899311781_<52>
Oct 6, 2004 (2nd): 188...881 (n≤150) was completed.
Oct 6, 2004: By Greg Childers / GGNFS
(17·10¹⁴⁷-71)/9 = 1(8)₁₄₆1_<148> = 3² · 11 · 19 · 79 · 107 · 2781801353422423656539918239_<28> · C113
C113 = P47 · P67
P47 = 25676953116135086178490153800162757142685512269_<47>
P67 = 1663171924588523777382227652703467418748719317652827597186987650887_<67>
(17·10¹⁵⁰-71)/9 = 1(8)₁₄₉1_<151> = 3 · C150
C150 = P75 · P76
P75 = 105402820794387104653536298689177070169650261803766637528304966641861624359_<75>
P76 = 5973555782324552106124283562382297323088488515591965666516908145969488005453_<76>
(65·10¹⁴²+43)/9 = 7(2)₁₄₁7_<143> = 89 · 193 · 198638087 · 2247087431_<10> · C121
C121 = P43 · P78
P43 = 9742597873074661129511930834554049809707829_<43>
P78 = 966865935733139211288991786743936943283865345411378831384056867611197604830127_<78>
(65·10¹⁴⁴+43)/9 = 7(2)₁₄₃7_<145> = 3 · 251 · 7331 · C139
C139 = P65 · P74
P65 = 48022449417411814334223229597104761154016667704312594421848222541_<65>
P74 = 27243841422266516181382717463539825882527519190626776820706713205388886629_<74>
(10¹⁴⁴-7)/3 = (3)₁₄₃1_<144> = 479 · 3257 · 127403 · 1672219 · 6038359 · C120
C120 = P58 · P62
P58 = 1902529719932711787220600137563189019784143649015519831397_<58>
P62 = 87297596280136341089385935585276804436752469640445637040911007_<62>
(10¹⁴⁵-7)/3 = (3)₁₄₄1_<145> = 1303 · 2091183973_<10> · C133
C133 = P39 · P94
P39 = 378880904950944761348832993283679200643_<39>
P94 = 3228786805238941383170279259073448703600543986249677725106177919641344030607291283713411374443_<94>
Oct 5, 2004 (5th): By Tyler Cadigan / PPSIQS
(2·10¹⁵⁴-11)/9 = (2)₁₅₃1_<154> = 4679929 · 62151671 · 474111779 · 10123931833_<11> · 21340649531177_<14> · 124377581827049_<15> · C93
C93 = P29 · P31 · P35
P29 = 11155972892775276123423372961_<29>
P31 = 2679162778111367510973787621601_<31>
P35 = 20063613869583775177852334220694889_<35>
Oct 5, 2004 (4th): Factor Table Search is available.
Examples:
Search prime numbers.
Search composite numbers which consist of 100 digits or less.
Search factors which was discovered by GGNFS.
Search factors which was found by Makoto Kamada.
Oct 5, 2004 (3rd): By Wataru Sakai / GMP-ECM
10¹⁶¹-9 = (9)₁₆₀1_<161> = 37871278906453241_<17> · C145
C145 = P29 · P117
P29 = 21025652136804630508221938561_<29>
P117 = 125585804992968912808788945390634517801861766554822671111449018351172498773938268560062296220409535778931448185975791_<117>
10¹⁹⁵-9 = (9)₁₉₄1_<195> = 1289 · 283435121 · 190918276279_<12> · 1608873192799_<13> · 387312818354664563_<18> · 1079504646683992390751_<22> · C122
C122 = P27 · P95
P27 = 296827436308088224012637591_<27>
P95 = 71801525491886233491994351008708055401003967702537009426787904436648333892829264331597536123173_<95>
Oct 5, 2004 (2nd): By Tyler Cadigan / PPSIQS
(34·10¹³⁷-7)/9 = 3(7)₁₃₇_<138> = 50406390252637_<14> · 34685456789003348824526610617033_<32> · C93
C93 = P46 · P48
P46 = 1547872150201415036131766313731406384544218071_<46>
P48 = 139594499354033237182438517098215139294193516747_<48>
Oct 5, 2004: The condition of 199...99 was extended to n≤200.
We have not factored following numbers yet. These numbers passed GMP-ECM (B1=50250+alpha) 100 times.
2·10¹⁵¹-1, 2·10¹⁵³-1, 2·10¹⁵⁴-1, 2·10¹⁵⁵-1, 2·10¹⁵⁶-1, 2·10¹⁵⁷-1, 2·10¹⁵⁸-1, 2·10¹⁵⁹-1, 2·10¹⁶⁰-1, 2·10¹⁶²-1, 2·10¹⁶⁵-1, 2·10¹⁶⁷-1, 2·10¹⁶⁸-1, 2·10¹⁶⁹-1, 2·10¹⁷⁰-1, 2·10¹⁷¹-1, 2·10¹⁷⁴-1, 2·10¹⁷⁵-1, 2·10¹⁷⁶-1, 2·10¹⁷⁸-1, 2·10¹⁷⁹-1, 2·10¹⁸⁰-1, 2·10¹⁸¹-1, 2·10¹⁸³-1, 2·10¹⁸⁶-1, 2·10¹⁸⁹-1, 2·10¹⁹⁰-1, 2·10¹⁹¹-1, 2·10¹⁹²-1, 2·10¹⁹³-1, 2·10¹⁹⁵-1, 2·10¹⁹⁶-1, 2·10¹⁹⁷-1, 2·10¹⁹⁹-1, 2·10²⁰⁰-1, (35/200)
The condition of 22...221 was extended to n≤200.
We have not factored following numbers yet. These numbers passed GMP-ECM (B1=50910+alpha) 100 times.
(2·10¹⁵⁴-11)/9, (2·10¹⁵⁷-11)/9, (2·10¹⁵⁸-11)/9, (2·10¹⁶²-11)/9, (2·10¹⁶³-11)/9, (2·10¹⁶⁴-11)/9, (2·10¹⁶⁵-11)/9, (2·10¹⁶⁷-11)/9, (2·10¹⁶⁸-11)/9, (2·10¹⁷⁰-11)/9, (2·10¹⁷¹-11)/9, (2·10¹⁷³-11)/9, (2·10¹⁷⁴-11)/9, (2·10¹⁷⁵-11)/9, (2·10¹⁷⁶-11)/9, (2·10¹⁷⁹-11)/9, (2·10¹⁸⁰-11)/9, (2·10¹⁸²-11)/9, (2·10¹⁸³-11)/9, (2·10¹⁸⁴-11)/9, (2·10¹⁸⁵-11)/9, (2·10¹⁸⁶-11)/9, (2·10¹⁸⁷-11)/9, (2·10¹⁸⁸-11)/9, (2·10¹⁸⁹-11)/9, (2·10¹⁹¹-11)/9, (2·10¹⁹²-11)/9, (2·10¹⁹³-11)/9, (2·10¹⁹⁶-11)/9, (2·10¹⁹⁸-11)/9, (2·10¹⁹⁹-11)/9, (2·10²⁰⁰-11)/9, (32/200)
Oct 4, 2004 (2nd): By Patrick De Geest
(4·10⁴²²⁶²-7)/3 = 133...331_<42263> is PRP. This is the largest known PRP in Plateau and Depression numbers.
See also Plateau and Depression Primes (Patrick De Geest).
Oct 4, 2004: By Tyler Cadigan / PPSIQS
(22·10¹³⁷-1)/3 = 7(3)₁₃₇_<138> = 17 · 73 · 173 · 6671719 · 10568333 · 60742673 · 202488391993093_<15> · C97
C97 = P33 · P64
P33 = 512311765871649016717149445233953_<33>
P64 = 7687956991006814118171485855493171149932213428300967303883804759_<64>
Oct 2, 2004 (4th): By Tyler Cadigan / PPSIQS
(4·10¹³³-13)/9 = (4)₁₃₂3_<133> = 3² · 881 · 88443650427428754868785226431323_<32> · C97
C97 = P47 · P50
P47 = 68594005391360380024254797250897286959710951501_<47>
P50 = 92394525921162910215679849872435259743072248714029_<50>
Oct 2, 2004 (3rd): 88...887 (n≤150) was completed.
Oct 2, 2004 (2nd): By Greg Childers / GGNFS
(13·10¹⁴¹-31)/9 = 1(4)₁₄₀1_<142> = 11 · 619 · 898348572287549_<15> · C123
C123 = P58 · P65
P58 = 3435189413553562745845330774313551979056266719647909175383_<58>
P65 = 68741964319513004279674267230306341436095887451228338365581020147_<65>
(13·10¹⁴⁵-31)/9 = 1(4)₁₄₄1_<146> = 11² · C144
C144 = P40 · P48 · P56
P40 = 3215091692475905492834991049431234800323_<40>
P48 = 869531799058872659572202283364390718753855862811_<48>
P56 = 42700861821644302938568173372339627573281339908570890257_<56>
(17·10¹⁴⁰-71)/9 = 1(8)₁₃₉1_<141> = 197 · 47255407 · 103652035862097857_<18> · C114
C114 = P49 · P65
P49 = 4666166461726179380801129928968110270436020676303_<49>
P65 = 41951801327579378159478866821820484800548073276834673164905690109_<65>
(8·10¹⁴⁴-17)/9 = (8)₁₄₃7_<144> = 599 · 241135754907107_<15> · C127
C127 = P41 · P86
P41 = 75874025239004842373359386572738631090619_<41>
P86 = 81108415893382466766494696285229496838195542104199630796025605211394157625582860602961_<86>
(8·10¹⁴⁸-17)/9 = (8)₁₄₇7_<148> = 61 · 2963 · 4327 · 2220971 · 49257293 · 252105043583_<12> · C114
C114 = P42 · P73
P42 = 107068210544832033178144510647295264556809_<42>
P73 = 3848961691473928008685333750034076914162492347136794688130393671496560287_<73>
Oct 2, 2004: Factor table of 233...339 is available.
Oct 1, 2004: Factor tables of 211...113, 211...117 and 211...119 are available.

More: September

Factorizations