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News and updates, September 2004

Sep 30, 2004 (3rd)

388...883 (n≤150) was completed.

Sep 30, 2004 (2nd)

By Greg Childers / GGNFS
(35·10¹⁴³-53)/9 = 3(8)₁₄₂3_<144> = 11 · 3400813033692143362347940975577_<31> · C113
C113 = P47 · P66
P47 = 39822446802521162148555054998307315520708034161_<47>
P66 = 261049071330740757048830626374673546304849204595034145153972051249_<66>
(35·10¹⁴⁶-53)/9 = 3(8)₁₄₅3_<147> = 71 · 5981 · 113359 · C136
C136 = P61 · P76
P61 = 1480268819384325264781085684978331400775146249333139098019773_<61>
P76 = 5457538228209977795726029602237625811827880296502011865351753095329546180419_<76>

Sep 30, 2004

By Wataru Sakai / GMP-ECM
9·10¹⁵⁹-1 = 8(9)_159<160> = 151 · 2081 · 37756997 · C147
C147 = P37 · P111
P37 = 2749349496945658330354039617246556963_<37>
P111 = 275909138843910536233458866490589939907450080666251250831272212920006003585355634397268342209549828865520254039_<111>

Sep 29, 2004

By Tyler Cadigan / PPSIQS
(37·10¹²⁵-1)/9 = 4(1)_125<126> = 3 · 23 · 71 · 307 · 150587 · 149254163 · 27005742979_<11> · C96
C96 = P41 · P55
P41 = 67420974835632498533086420758075874107517_<41>
P55 = 6679566951980833263633468017337747460136592113701042969_<55>

Sep 28, 2004 (5th)

By Julien Peter Benney
(7·10⁷⁷⁸⁴+11)/9 is PRP.

Sep 28, 2004 (4th)

22...221 (n≤150) was completed.

Sep 28, 2004 (3rd)

By Greg Childers / GGNFS
(2·10¹⁴⁶-11)/9 = (2)₁₄₅1_<146> = 3 · 7 · C145
C145 = P61 · P84
P61 = 1629005499570503911522997110980887938657079503413966178632607_<61>
P84 = 649599438725074052277587080056907926964379332648616521940920933450301174280530982343_<84>
(2·10¹⁵⁰-11)/9 = (2)₁₄₉1_<150> = 279912173263_<12> · 458976686907073_<15> · C124
C124 = P58 · P66
P58 = 2834188426788549952231733673773047461459519075813368357123_<58>
P66 = 610304192083969965409076522824019775128554583673057741177067810273_<66>
(35·10¹⁴⁰-53)/9 = 3(8)₁₃₉3_<141> = 359 · 577 · 170623768786145750823691763_<27> · C110
C110 = P38 · P72
P38 = 24728406160615287305877860914676618707_<38>
P72 = 444958612515831389347540610612885488167438846639007749453827719018700141_<72>
(8·10¹³⁹-17)/9 = (8)₁₃₈7_<139> = 7 · 1170563 · 9195458197_<10> · 11506362253_<11> · C113
C113 = P42 · P71
P42 = 541853661698287032693368052012284236209641_<42>
P71 = 18921746304900975852505751265110395654913726325261378404329220798970547_<71>

Sep 28, 2004 (2nd)

By Tyler Cadigan / PPSIQS
(8·10¹²⁵-53)/9 = (8)₁₂₄3_<125> = 83 · 383 · 619 · 40140051714723693674509_<23> · C96
C96 = P34 · P62
P34 = 1617387764872172982324268516123627_<34>
P62 = 69580553803633007114920480486810142828978681396742673009816691_<62>

Sep 28, 2004

By Wataru Sakai / GMP-ECM
9·10¹⁶³-1 = 8(9)_163<164> = 9311 · 9923 · 1563631 · 2134098490901084289819240413_<28> · C123
C123 = P35 · P88
P35 = 60061438682395359593398744400877001_<35>
P88 = 4860251353176521897528790975585779837716210646651067100277891814302127723420307300678561_<88>
(88·10¹²²-7)/9 = 9(7)_122<123> = 157 · 1409 · 438427477 · 94161267251_<11> · C99
C99 = P32 · P67
P32 = 45940653614093461774921904253449_<32>
P67 = 2330570733202423767193315194625818946554610929797213770469865501523_<67>

Sep 27, 2004 (5th)

Factor tables of 200...003 and 200...009 are available.

Sep 27, 2004 (4th)

922...229 (n≤150) was completed.

Sep 27, 2004 (3rd)

By Greg Childers / GGNFS
(83·10¹⁴¹+61)/9 = 9(2)₁₄₀9_<142> = 11 · 4337 · 1872939015628631473_<19> · C120
C120 = P53 · P67
P53 = 54272364006449135417917424191715164257876553537322123_<53>
P67 = 1901739818949460046819138208375310564699275416725059067732453145693_<67>
(83·10¹⁴⁶+61)/9 = 9(2)₁₄₅9_<147> = 157 · 48216364239555767_<17> · C129
C129 = P37 · P92
P37 = 6737715143530254530717600356878452627_<37>
P92 = 18081265583937853293018450560900085680497487595808160549311853998971936416529132034859354933_<92>
(2·10¹⁴³-11)/9 = (2)₁₄₂1_<143> = 3 · C142
C142 = P37 · P106
P37 = 1639704346744230467897817374963936809_<37>
P106 = 4517526237041105422717248364841109362832890589334397951090334806082732090436300786518717858790161469411223_<106>

Sep 27, 2004 (2nd)

The condition of 99...991 was extended to n≤200.
We have not factored following numbers yet. Run GMP-ECM (B1≥50000) first.
10^153-9, 10^159-9, 10^161-9, 10^163-9, 10^165-9, 10^169-9, 10^171-9, 10^173-9, 10^175-9, 10^177-9, 10^179-9, 10^181-9, 10^183-9, 10^185-9, 10^187-9, 10^189-9, 10^191-9, 10^193-9, 10^195-9, (19/200)

Sep 27, 2004

By Makoto Kamada / GGNFS-0.54.4-k1
10¹⁵⁷-9 = (9)₁₅₆1_<157> = C157
C157 = P76 · P82
P76 = 1182138400863175552253848266595264231758705488091359346888751281045582124679_<76>
P82 = 8459246390015065347380115262012913546306699962332583936149204215042988678809171729_<82>

99991_157.polyname: 99991_157 n: 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 m: 10000000000000000000000000000000 deg: 5 c5: 100 c4: 0 c3: 0 c2: 0 c1: 0 c0: -9 skew: 1 rlim: 2000000 alim: 2000000 lpbr: 25 lpba: 25 mfbr: 42 mfba: 42 rlambda: 1.70 alambda: 1.70 qintsize: 1000000

factLat.sh (extractive)FORCECC=0 LATSIEVER=$GGNFS_BIN_PATH/gnfs-lasieve4I12e

ggnfs.log[09/19 11:32:24] GGNFS-0.54.4-k1 : makefb [09/19 11:32:26] name: 99991_157 [09/19 11:32:26] n=9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 (157 digits) [09/19 11:32:26] c0: -9 [09/19 11:32:26] c1: 0 [09/19 11:32:26] c2: 0 [09/19 11:32:26] c3: 0 [09/19 11:32:26] c4: 0 [09/19 11:32:26] c5: 100 [09/19 11:32:26] RFBsize: 148933 (upto 1999993) [09/19 11:32:26] AFBsize: 149080 (upto 1999993) [09/19 11:32:26] maxNumLargeRatPrimes: 2 [09/19 11:32:26] maxLargeRatPrime: 33554432 [09/19 11:32:26] maxNumLargeAlgPrimes: 2 [09/19 11:32:26] maxLargeAlgPrime: 33554432 LatSieveTime: 26799 [09/19 18:59:06] GGNFS-0.54.4-k1 : getdeps [09/19 19:00:25] RelProcTime: 79.3 [09/19 19:00:32] largePrimes: 438530 , relations: 279690 LatSieveTime: 26705 [09/20 02:25:40] GGNFS-0.54.4-k1 : getdeps [09/20 02:26:56] RelProcTime: 76.0 [09/20 02:27:10] largePrimes: 750129 , relations: 509971 LatSieveTime: 26013 [09/20 09:40:44] GGNFS-0.54.4-k1 : getdeps [09/20 09:41:59] RelProcTime: 74.1 [09/20 09:42:16] largePrimes: 994998 , relations: 712281 LatSieveTime: 25660 [09/20 16:49:58] GGNFS-0.54.4-k1 : getdeps [09/20 16:51:13] RelProcTime: 74.3 [09/20 16:51:33] largePrimes: 1194658 , relations: 892019 LatSieveTime: 25995 [09/21 00:04:51] GGNFS-0.54.4-k1 : getdeps [09/21 00:06:25] RelProcTime: 90.8 [09/21 00:06:51] largePrimes: 1363907 , relations: 1055264 LatSieveTime: 27548 [09/21 07:46:04] GGNFS-0.54.4-k1 : getdeps [09/21 07:47:39] RelProcTime: 94.0 [09/21 07:48:08] largePrimes: 1512560 , relations: 1207969 LatSieveTime: 25525 [09/21 14:53:37] GGNFS-0.54.4-k1 : getdeps [09/21 14:55:17] RelProcTime: 99.2 [09/21 14:55:50] largePrimes: 1644022 , relations: 1351342 LatSieveTime: 25288 [09/21 21:57:22] GGNFS-0.54.4-k1 : getdeps [09/21 21:59:30] RelProcTime: 81.6 [09/21 22:00:06] largePrimes: 1760591 , relations: 1484901 [09/21 22:00:15] rels:1484901, initialFF:0, finalFF:25984 LatSieveTime: 24853 [09/22 04:54:32] GGNFS-0.54.4-k1 : getdeps [09/22 04:55:55] RelProcTime: 82.5 [09/22 04:56:33] largePrimes: 1864303 , relations: 1609977 [09/22 04:56:44] rels:1609977, initialFF:0, finalFF:32134 LatSieveTime: 24720 [09/22 11:48:49] GGNFS-0.54.4-k1 : getdeps [09/22 11:50:33] RelProcTime: 104.1 [09/22 11:51:18] largePrimes: 1961108 , relations: 1730133 [09/22 11:51:33] rels:1730133, initialFF:0, finalFF:39678 LatSieveTime: 25873 [09/22 19:02:52] GGNFS-0.54.4-k1 : getdeps [09/22 19:05:09] RelProcTime: 136.3 [09/22 19:07:03] largePrimes: 2048888 , relations: 1844210 [09/22 19:07:36] rels:1844210, initialFF:0, finalFF:48585 LatSieveTime: 25383 [09/23 02:10:49] GGNFS-0.54.4-k1 : getdeps [09/23 02:12:32] RelProcTime: 102.3 [09/23 02:13:16] largePrimes: 2130995 , relations: 1954569 [09/23 02:13:36] rels:1954569, initialFF:0, finalFF:58985 LatSieveTime: 24136 [09/23 08:55:57] GGNFS-0.54.4-k1 : getdeps [09/23 08:57:17] RelProcTime: 78.8 [09/23 08:58:12] largePrimes: 2207547 , relations: 2060930 [09/23 08:58:35] rels:2060930, initialFF:0, finalFF:71019 LatSieveTime: 24314 [09/23 15:43:55] GGNFS-0.54.4-k1 : getdeps [09/23 15:45:42] RelProcTime: 106.9 [09/23 15:46:43] largePrimes: 2278270 , relations: 2162704 [09/23 15:47:11] rels:2162704, initialFF:0, finalFF:84739 LatSieveTime: 24280 [09/23 22:31:56] GGNFS-0.54.4-k1 : getdeps [09/23 22:33:43] RelProcTime: 106.6 [09/23 22:34:43] largePrimes: 2345282 , relations: 2261228 [09/23 22:35:13] rels:2261228, initialFF:0, finalFF:99435 LatSieveTime: 24308 [09/24 05:20:26] GGNFS-0.54.4-k1 : getdeps [09/24 05:22:00] RelProcTime: 93.3 [09/24 05:23:04] largePrimes: 2408533 , relations: 2357520 [09/24 05:23:37] rels:2357520, initialFF:0, finalFF:116177 LatSieveTime: 24153 [09/24 12:06:16] GGNFS-0.54.4-k1 : getdeps [09/24 12:07:59] RelProcTime: 102.2 [09/24 12:09:07] largePrimes: 2468626 , relations: 2452136 [09/24 12:09:45] rels:2452136, initialFF:0, finalFF:134716 LatSieveTime: 23810 [09/24 18:46:42] GGNFS-0.54.4-k1 : getdeps [09/24 18:48:33] RelProcTime: 110.7 [09/24 18:49:44] largePrimes: 2524992 , relations: 2542706 [09/24 18:50:21] rels:2542706, initialFF:0, finalFF:154269 LatSieveTime: 24129 [09/25 01:32:36] GGNFS-0.54.4-k1 : getdeps [09/25 01:34:33] RelProcTime: 116.0 [09/25 01:36:14] largePrimes: 2578485 , relations: 2631098 [09/25 01:36:55] rels:2631098, initialFF:0, finalFF:175308 LatSieveTime: 23527 [09/25 08:09:09] GGNFS-0.54.4-k1 : getdeps [09/25 08:11:03] RelProcTime: 113.4 [09/25 08:13:16] largePrimes: 2629631 , relations: 2717249 [09/25 08:14:00] rels:2717249, initialFF:0, finalFF:197145 LatSieveTime: 23495 [09/25 14:45:41] GGNFS-0.54.4-k1 : getdeps [09/25 14:47:28] RelProcTime: 106.3 [09/25 14:49:54] largePrimes: 2678637 , relations: 2801727 [09/25 14:50:39] rels:2801727, initialFF:0, finalFF:219471 LatSieveTime: 24037 [09/25 21:31:24] GGNFS-0.54.4-k1 : getdeps [09/25 21:33:11] RelProcTime: 106.8 [09/25 21:35:51] largePrimes: 2725315 , relations: 2883650 [09/25 21:36:44] rels:2883650, initialFF:0, finalFF:243141 LatSieveTime: 23630 [09/26 04:10:40] GGNFS-0.54.4-k1 : getdeps [09/26 04:12:24] RelProcTime: 102.9 [09/26 04:15:05] largePrimes: 2769947 , relations: 2963866 [09/26 04:15:59] rels:2963866, initialFF:0, finalFF:267897 LatSieveTime: 23271 [09/26 10:43:58] GGNFS-0.54.4-k1 : getdeps [09/26 10:45:41] RelProcTime: 102.4 [09/26 10:48:26] largePrimes: 2812856 , relations: 3042946 [09/26 10:49:17] rels:3042946, initialFF:0, finalFF:292804 LatSieveTime: 24280 [09/26 17:34:05] GGNFS-0.54.4-k1 : getdeps [09/26 17:35:54] RelProcTime: 108.1 [09/26 17:38:48] largePrimes: 2854260 , relations: 3120087 [09/26 17:42:15] rels:3120087, initialFF:0, finalFF:318362 [09/26 17:42:15] depinf file written. Run matsolve. [09/26 17:42:23] GGNFS-0.54.4-k1 : matsolve [09/26 17:42:32] Initial matrix is 298077 x 318362 with sparse part having weight 47350711. [09/26 17:42:32] (total weight is 73043806) [09/26 17:48:48] Matrix pruned to 289244 x 289574 with weight 43464120. [09/27 02:24:29] BLanczosTime: 30941.1 [09/27 02:24:30] GGNFS-0.54.4-k1 : sqrt [09/27 02:24:33] bmultiplier=10 [09/27 02:35:46] From dependence 0, sqrt obtained: [09/27 02:35:46] r1=1 [09/27 02:35:46] r2=9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 [09/27 02:35:46] sqrtTime: 675.5 [09/27 02:35:47] GGNFS-0.54.4-k1 : sqrt [09/27 02:35:49] bmultiplier=10 [09/27 02:46:55] From dependence 1, sqrt obtained: [09/27 02:46:55] r1=8459246390015065347380115262012913546306699962332583936149204215042988678809171729 (pp82) [09/27 02:46:55] r2=1182138400863175552253848266595264231758705488091359346888751281045582124679 (pp76) [09/27 02:46:55] (pp=probable prime, c=composite) [09/27 02:46:55] sqrtTime: 667.2

summary.txtNumber: 99991_157 Factor base limits: 2000000/2000000 Large prime bits: / Sieved special-q from 2000000 to 28000000 Relations: 3120087, initialFF:0, finalFF:318362 Initial matrix obtained: 298077 x 318362 with sparse part having weight 47350711. Pruned matrix: 289244 x 289574 with weight 43464120. Total sieving time: 172.70333 hours Total relation processing time: .68025 hours Total matrix solve time: 8.59475 hours Time per square root: .18763 hours Total time: 182.16596 hours

Sep 26, 2004 (2nd)

By Tyler Cadigan / PPSIQS
(7·10¹²³+11)/9 = (7)₁₂₂9_<123> = 41 · 1429 · 29023 · 60942313 · 104687100851_<12> · C95
C95 = P30 · P66
P30 = 383568871677228514534281646481_<30>
P66 = 186913935623500644552720987765239281460148290673971815841649202819_<66>

Sep 26, 2004

Factor tables of 188...883, 188...889, 199...993 and 199...997 are available.

Sep 25, 2004 (2nd)

Factor tables of 166...663, 166...669, 177...773 and 177...779 are available.

Sep 25, 2004

10¹⁴⁹-3 = (9)₁₄₈7_<149> = 19 · 71 · 83 · 37573 · 721606590563161_<15> · 1609561207914191556407872402061_<31> · C95
C95 = P30 · P65
P30 = 420200185405225537573496373857_<30>
P65 = 48704586230979775559414535682143440300694313427376479940972273211_<65>

Sep 24, 2004 (3rd)

GGNFS 0.54.5b was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 24, 2004 (2nd)

Factor tables of 155...553, 155...557 and 155...559 are available.

Sep 24, 2004

By Greg Childers / GGNFS
(4·10¹¹⁹+41)/9 = (4)₁₁₈9_<119> = 3767 · C116
C116 = P37 · P79
P37 = 5468351428162845370288634843373069443_<37>
P79 = 2157572731254216322797535461742378405090055809165408722439987179245836849818829_<79>
(4·10¹²²+41)/9 = (4)₁₂₁9_<122> = 7 · 1190509 · 43648126993_<11> · C105
C105 = P43 · P62
P43 = 1355682374562492274028257535179450122541253_<43>
P62 = 90128718688220038570007654000671430737058414743221536299348487_<62>
(4·10¹²³+41)/9 = (4)₁₂₂9_<123> = 18341 · 2910007 · 6126089 · 51192157 · C98
C98 = P45 · P53
P45 = 788001598394943477222987830954477571791295403_<45>
P53 = 33696640755473013504475945049652716797179319979435933_<53>
(4·10¹²⁵+41)/9 = (4)₁₂₄9_<125> = 17 · 29 · 9844186708663_<13> · C109
C109 = P52 · P58
P52 = 1533404138434748955067339228171983791194792755281563_<52>
P58 = 5972196511516268410199167419596854493297224535950345471897_<58>
(4·10¹²⁶+41)/9 = (4)₁₂₅9_<126> = 47 · 199 · C122
C122 = P28 · P95
P28 = 2893252527708410532977738743_<28>
P95 = 16424048027032334977250468790379564247730051161966791325488984093154339188794529669214911213231_<95>
(4·10¹²⁹+41)/9 = (4)₁₂₈9_<129> = 67 · 109 · 313 · 133967 · 4693228361977_<13> · C105
C105 = P51 · P55
P51 = 232902447970350783340422379838762899844194911860293_<51>
P55 = 1327786570528305761356677665494842809303205078766279093_<55>
(4·10¹³⁰+41)/9 = (4)₁₂₉9_<130> = 3 · 55691 · 85285559 · C117
C117 = P57 · P61
P57 = 107253181340326856748878384566645427907354430330055026519_<57>
P61 = 2908208419864634963145751009015726613842860127576032867907153_<61>

Sep 23, 2004 (2nd)

Factor tables of 144...447 and 144...449 are available.

Sep 23, 2004

By Tyler Cadigan / PPSIQS
(64·10¹⁹⁵-1)/9 = 7(1)_195<196> = 13 · 439 · 645877 · 741787444609_<12> · 20194065442294414119935380483_<29> · 179746009860835570206934469326647488405593736221729237_<54> · C93
C93 = P34 · P60
P34 = 2453911908929535375171255435229813_<34>
P60 = 291983498833927501377447781952357414915912130035189285430307_<60>

Sep 22, 2004

By Tyler Cadigan / PPSIQS
(5·10¹⁴⁷+31)/9 = (5)₁₄₆9_<147> = 13 · 29 · 129119 · 8232703 · 4452154780181895301_<19> · 1479486472724455175482176443_<28> · C87
C87 = P33 · P54
P33 = 595505161404659395002894544770481_<33>
P54 = 353416449589679235783582856189198275165958030520153657_<54>

Sep 21, 2004 (3rd)

By Wataru Sakai / GMP-ECM
9·10¹⁸⁵-1 = 8(9)_185<186> = 51506797 · C179
C179 = P37 · C142
P37 = 6651080365041166203291134547420211961_<37>
C142 = [2627155446018583376056001129947388070101320462055070329967261485572839484407296033679509907414358095104997570766676583504598716504545452477747_<142>]

Sep 21, 2004 (2nd)

Sequence (5·10ⁿ+13)/9 = { 7, 57, 557, 5557, 55557, ... } (n≤150) was completed.

Sep 21, 2004

By Greg Childers / GGNFS
(5·10¹⁴¹+13)/9 = (5)₁₄₀7_<141> = 17 · 4936099597171592587_<19> · C121
C121 = P53 · P69
P53 = 33701761657256276577940756283838594522347463549612481_<53>
P69 = 196445487242682624913904252831967998446323930075923773236971184506143_<69>
(5·10¹⁴²+13)/9 = (5)₁₄₁7_<142> = C142
C142 = P54 · P89
P54 = 120665111524603501081477618600243932272409645287711429_<54>
P89 = 46041109027797012227496452577514434934470047064643607309722643103546554142308843339849633_<89>
(83·10¹³⁹+61)/9 = 9(2)₁₃₈9_<140> = 3 · 11 · 19 · 53 · 563 · 1312667 · C127
C127 = P49 · P79
P49 = 3662336709704897069095805506501482949465860726713_<49>
P79 = 1025347177134503905396383859019448574941117439030030908633069003023552449572883_<79>

Sep 20, 2004

Factor tables of 133...337 and 133...339 are available.

Sep 19, 2004

Factor tables of 122...227 and 122...229 are available.

Sep 18, 2004 (3rd)

Sequence (86·10ⁿ+31)/9 = { 99, 959, 9559, 95559, 955559, ... } (n≤150) was completed.

Sep 18, 2004 (2nd)

By Greg Childers / GGNFS
(86·10¹⁴⁰+31)/9 = 9(5)₁₃₉9_<141> = 7 · 331883 · 1041670471_<10> · C126
C126 = P46 · P80
P46 = 4516102175060756280599235604030246161696107219_<46>
P80 = 87433684958660932996293941748919220401982452540216084709225342140147098500015111_<80>
(86·10¹⁴⁵+31)/9 = 9(5)₁₄₄9_<146> = 3² · 11 · 47 · 263 · 157489 · C135
C135 = P66 · P69
P66 = 748644374794864688961065096979617418385841681617804563480087292231_<66>
P69 = 662279557109722383625027011785700167308449647917293861449905366672259_<69>
(5·10¹³⁹+13)/9 = (5)₁₃₈7_<139> = 7 · 3863 · C135
C135 = P51 · P85
P51 = 119593518641097451644193896912291636728002588053467_<51>
P85 = 1717896927710932976108335587671600737580141438304167747953842334628585908745228760031_<85>

Sep 18, 2004

By Wataru Sakai / GMP-ECM
(34·10¹²⁴-7)/9 = 3(7)_124<125> = 37 · 71 · 9507133 · 37002749319959491_<17> · C98
C98 = P35 · P63
P35 = 54160504315818838339683617139143941_<35>
P63 = 754762079112596521424663770266038984483850910872151629562729337_<63>

Sep 17, 2004 (2nd)

Yahoo! Group for GGNFS users was created.
Yahoo! Groups : ggnfs

Sep 17, 2004

GGNFS 0.54.4 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 16, 2004 (3rd)

GGNFS 0.54.3 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 16, 2004 (2nd)

Sequence (89·10ⁿ+1)/9 = { 99, 989, 9889, 98889, 988889, ... } (n≤150) was completed.

Sep 16, 2004

By Greg Childers / GGNFS
(89·10¹³⁸+1)/9 = 9(8)₁₃₇9_<139> = 31 · 7739203631_<10> · C128
C128 = P45 P45 = 123848493724489026440104908771242383090771607_<45>
P84 = 332811864832857994803825785286396971936555207279064853034369400273436459201384992607_<84>
(89·10¹⁴⁷+1)/9 = 9(8)₁₄₆9_<148> = 11 · 2423 · 14741 · C140
C140 = P39 · P49 · P53
P39 = 160222624630254869280396258996178652003_<39>
P49 = 4972139990969861070890682623316998893525772950021_<49>
P53 = 31594192671194606533148648647345097435701380247405111_<53>

Sep 14, 2004 (3rd)

Sequence (82·10ⁿ+71)/9 = { 99, 919, 9119, 91119, 911119, ... } (n≤150) was completed.

Sep 14, 2004 (2nd)

By Greg Childers / GGNFS
(82·10¹⁴⁶+71)/9 = 9(1)₁₄₅9_<147> = 61 · 569 · 11093 · 16706953 · C132
C132 = P62 · P70
P62 = 15053743424163591157391476013331832737622728051781855562824069_<62>
P70 = 9408891664939924579917892583360464032946180141104136360744149482265091_<70>

Sep 14, 2004

By Wataru Sakai / GMP-ECM, ppmpqs
(5·10¹³⁹+31)/9 = (5)₁₃₈9_<139> = 3 · 13381169 · 488233961499763027_<18> · C114
C114 = P36 · P37 · P41
P36 = 767937389205546486990497899383321239_<36>
P37 = 5067987060927461212198258191296636443_<37>
P41 = 72832109410715101979304172083529747274603_<41>

Sep 13, 2004 (3rd)

Sequence (25·10ⁿ-1)/3 = { 83, 833, 8333, 83333, 833333, ... } (n≤150) was completed.

Sep 13, 2004 (2nd)

By Greg Childers / GGNFS
(82·10¹⁴⁵+71)/9 = 9(1)₁₄₄9_<146> = 3⁴ · 11 · 4409 · 30570937 · C132
C132 = P53 · P80
P53 = 55623864836423887831193780354836900950336852724991831_<53>
P80 = 13639034531999080193140484277331303730420699844795939558191731427804915955621883_<80>
(25·10¹⁴³-1)/3 = 8(3)_143<144> = 151² · 643 · 29129 · 15000224477369_<14> · C120
C120 = P48 · P72
P48 = 850059927425215940194387730228305887793457647027_<48>
P72 = 153031561240574261950447694587661791245925129000655462949369722678775053_<72>

Sep 13, 2004

GGNFS 0.54.2 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 12, 2004

By Makoto Kamada / GGNFS-0.53.3-k2, GGNFS-0.54.1-k1
(4·10¹⁵⁰+41)/9 = (4)₁₄₉9_<150> = C150
C150 = P38 · P113
P38 = 24478169540608218973559824375006284619_<38>
P113 = 18156767960411845144545021647808332832799204299279924680716228196015707338698208678714543612583310171092766533571_<113>

Sep 11, 2004 (3rd)

GGNFS 0.54.1 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 11, 2004 (2nd)

Sequence (13·10ⁿ-1)/3 = { 43, 433, 4333, 43333, 433333, ... } (n≤150) was completed.

Sep 11, 2004

By Greg Childers / GGNFS
(13·10¹⁴³-1)/3 = 4(3)_143<144> = 821 · 7993 · 224134284877_<12> · C126
C126 = P48 · P78
P48 = 496669957831811171429452328504036234709614664907_<48>
P78 = 593188799492163143544655710343277873676156368756362875007640032998963193696199_<78>
(25·10¹⁴¹-1)/3 = 8(3)_141<142> = 13 · 43766441 · C134
C134 = P57 · P77
P57 = 173646134673467043474614594249996799616095097962318053773_<57>
P77 = 84346885144182371325885485048193091944351393978571177194778531824663780319237_<77>

Sep 10, 2004 (5th)

By Wataru Sakai / GMP-ECM
(88·10¹²⁸-7)/9 = 9(7)_128<129> = 4159 · 5657 · 2186341 · C116
C116 = P33 · P83
P33 = 501252067274896148186736882778243_<33>
P83 = 37921978507996725275019959958606512270468583114190168121096926524710791167838513033_<83>

Sep 10, 2004 (4th)

GGNFS 0.54.0 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 10, 2004 (3rd)

By Sander Hoogendoorn / GMP-ECM
9·10¹⁶⁵-1 = 8(9)_165<166> = 1139239 · C160
C160 = P22 · C139
P22 = 3500008777892854273507_<22>
C139 = [2257140180752772341749697563476673520949004624616088331617541248692208685477716800333936267810500726303368685688650280142696027086834845763_<139>]
9·10¹⁸¹-1 = 8(9)_181<182> = 2347 · 18121 · 14881545317_<11> · C165
C165 = P23 · C142
P23 = 18520231788365026399039_<23>
C142 = [7678083141389664656001425818220694158822776458038611028631283111975249628251012772571482748321660481753969878560664066088398797796345069148879_<142>]
9·10¹⁸⁹-1 = 8(9)_189<190> = 67 · 133187 · 2078087862871_<13> · 234621664993637_<15> · C157
C157 = P28 · C129
P28 = 5363095884001110231789672199_<28>
C129 = [385707683405733164444530365933755816046832242345670430607839333744882290009141947111896835408591178894659692587255754972460523547_<129>]
9·10¹⁹⁹-1 = 8(9)_199<200> = 311 · 18816601 · 7199849885356048147_<19> · 6189868364159015753089_<22> · C150
C150 = P19 · C131
P19 = 8780607192536057363_<19>
C131 = [39301718485862350257708325333181729090996815780048171845715841482163767806759091111427975609647926520399156269244884232809787052921_<131>]

Sep 10, 2004 (2nd)

GGNFS 0.53.4 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 10, 2004

By Wataru Sakai / GMP-ECM
9·10¹⁹⁷-1 = 8(9)_197<198> = 31 · 277 · C195
C195 = P23 · C172
P23 = 27450632285963828291729_<23>
C172 = [3818112268196165689479781790439330543302891662224712896124961773277885163454921823655935042268853704582463791302464990137598241649983644542032759069272259846593508442000013_<172>]

Sep 8, 2004 (3rd)

Sequence (4·10ⁿ+23)/9 = { 7, 47, 447, 4447, 44447, ... } (n≤150) was completed.

Sep 8, 2004 (2nd)

By Greg Childers / GGNFS
(4·10¹⁵⁰+23)/9 = (4)₁₄₉7_<150> = 3² · 14797 · 158129 · C140
C140 = P52 · P88
P52 = 2334639100316582423542633998614479963495682843452583_<52>
P88 = 9040033073803432887815150453074684725159462725714073113819607020985016556962672188533077_<88>
(13·10¹³⁷-1)/3 = 4(3)_137<138> = 393253967 · 1142265150635677_<16> · C114
C114 = P49 · P66
P49 = 5827423332237870322314881927068091355028309484501_<49>
P66 = 165540967720274491075300161169534948362158630988747150913146422587_<66>

Sep 8, 2004

By Wataru Sakai / GMP-ECM
(5·10¹³²+31)/9 = (5)₁₃₁9_<132> = 17 · 15009607 · C124
C124 = P35 · P90
P35 = 16735349127842839384417436402568419_<35>
P90 = 130099154892445905531232574715219228257936537877690891576918266610176625381368629581225019_<90>

Sep 7, 2004 (3rd)

By Sander Hoogendoorn
9·10¹⁶³-1 = 8(9)_163<164> = 9311 · 9923 · 1563631 · C150
C150 = P28 · C123
P28 = 2134098490901084289819240413_<28>
C123 = [291913688629840742869263333478236850875137905645395736028272329354747978590525243351837422492661183198777698321810798675561_<123>]
9·10¹⁶⁹-1 = 8(9)_169<170> = 90911 · 303273671083_<12> · C154
C154 = P21 · P153
P21 = 561921476752175312039_<21>
P153 = 5809192057492029790189790649473348809407304780607105559887659626527691939992391503927629486440677147928852285888430859909715432233957_<133>
9·10¹⁸³-1 = 8(9)_183<184> = 9587 · 44803933 · 328987231 · C164
C164 = P25 · P140
P25 = 2440572839378229347582719_<25>
P140 = 26095932910686069765618451295488481733475751249529060617603572778843532932969652780988006968716186630596900105613502368966849560241018262121_<140>
9·10¹⁸⁷-1 = 8(9)_187<188> = 107 · 3091427 · C180
C180 = P21 · C160
P21 = 119847129180121192841_<21>
C160 = [2270241721559984930272736143311910112693495887639753969987718778079115797333387754225729923122144151094026523595963349024633942322055857934743702122096103206951_<160>]

Sep 7, 2004 (2nd)

By Sander Hoogendoorn
(64·10¹⁶⁷-1)/9 = 7(1)_167<168> = 3 · 17430641850992347_<17> · 1507214810701852948504954498877_<31> · C121
C121 = P31 · P91
P31 = 2593393711071875340499604499083_<31>
P91 = 3479038412691528923419866920945000559517759572016377269174396284827135012176337635978462281_<91>
(64·10¹⁷⁷-1)/9 = 7(1)_177<178> = 13 · 43 · 67 · 641 · 304879 · 1430811465791_<13> · 145377867948394877437832769951054564028056043_<45> · C109
C109 = P28 · P30 · P52
P28 = 2486758115223396550967154991_<28>
P30 = 257817544682932484846649464881_<30>
P52 = 7285151607634411586597669155389338444323201940852071_<52>
(64·10¹⁸⁹-1)/9 = 7(1)_189<190> = 13 · 31 · 1307 · 9643 · 16111 · 168927683 · 5434428449_<10> · 710050492681_<12> · 9557531723783932333_<19> · 35846499715122706776413163888590388065147_<41> · C87
C87 = P39 · P49
P39 = 182561575784510959989401173628946017923_<39>
P49 = 2131455913202100114324989458676266259381078561077_<49>

Sep 7, 2004

By Sander Hoogendoorn
(64·10¹⁶⁷-1)/9 = 7(1)_167<168> = 3 · 17430641850992347_<17> · C152
C152 = P31 · C121
P31 = 1507214810701852948504954498877_<31>
C121 = [9022516340051690763495090685189602263225102783722102169688190088102308544830931331235226799541233270412550586475614588323_<121>]
(64·10¹⁹⁵-1)/9 = 7(1)_195<196> = 13 · 439 · 645877 · 741787444609_<12> · 179746009860835570206934469326647488405593736221729237_<54> · C122
C122 = P29 · C93
P29 = 20194065442294414119935380483_<29>
C93 = [716501784999487801171216138669504140498635676344979947291466821869221874333608342721140142591_<93>]

Sep 6, 2004 (3rd)

By Makoto Kamada
R49081+6, R86453+6, R86453+2 and R86453+8 are composite.

As "Factorizations of 11...117" says:
(10^6k+1+53)/9 is divisible by 7.
(10^34k+25+53)/9 is divisible by 4013.

R49081+6 = (10⁴⁹⁰⁸¹-1)/9+6 = (10⁴⁹⁰⁸¹+53)/9 = (10^6·8180+1+53)/9 is divisible by 7.

R86453+6 = (10⁸⁶⁴⁵³-1)/9+6 = (10⁸⁶⁴⁵³+53)/9 = (10^34·2542+25+53)/9 is divisible by 4013.

As "Factorizations of 11...113" says:
(10^18k+17+17)/9 is divisible by 19.

R86453+2 = (10⁸⁶⁴⁵³-1)/9+2 = (10⁸⁶⁴⁵³+17)/9 = (10^18·4802+17+17)/9 is divisible by 19.

R86453+8 little confuses us. In the same way,
(10^52364k+34089+71)/9 is divisible by 104729.

R86453+8 = (10⁸⁶⁴⁵³-1)/9+8 = (10⁸⁶⁴⁵³+71)/9 = (10^{52364·1+34089}+71)/9 is divisible by 104729.

Sep 6, 2004 (2nd)

Sequence (10ⁿ+17)/9 = { 3, 13, 113, 1113, 11113, ... } (n≤150) was completed.

Sep 6, 2004

By Greg Childers / GGNFS
(10¹⁴⁶+17)/9 = (1)₁₄₅3_<146> = 13 · 1231 · C141
C141 = P36 · P52 · P54
P36 = 438093756688394904258681753902386243_<36>
P52 = 5023228213095364349383280538083151469018517484491963_<52>
P54 = 315504902521584066530740748554192812824625874515224819_<54>
(10¹⁴⁸+17)/9 = (1)₁₄₇3_<148> = 3 · 7 · 1051 · C143
C143 = P40 · P104
P40 = 1027191010958335312343169808383374823067_<40>
P104 = 49009951146811381275847466159640285794901276734209720419172068637840787902160249833635533661924144332909_<104>

Sep 5, 2004

Conditions of the sequence (64·10ⁿ-1)/9 = { 71, 711, 7111, 71111, 711111, ... } and 9·10ⁿ-1 = { 89, 899, 8999, 89999, 899999, ... } were extended to n≤200.
We have not factorized following numbers yet. Run GMP-ECM (B1≥250000) first.
(64·10¹⁵¹-1)/9, (64·10¹⁵⁷-1)/9, (64·10¹⁶¹-1)/9, (64·10¹⁶³-1)/9, (64·10¹⁶⁷-1)/9, (64·10¹⁶⁹-1)/9, (64·10¹⁷³-1)/9, (64·10¹⁷⁷-1)/9, (64·10¹⁸¹-1)/9, (64·10¹⁸⁵-1)/9, (64·10¹⁸⁷-1)/9, (64·10¹⁸⁹-1)/9, (64·10¹⁹¹-1)/9, (64·10¹⁹³-1)/9, (64·10¹⁹⁵-1)/9, (64·10¹⁹⁷-1)/9, (64·10¹⁹⁹-1)/9, (17/200)
9·10¹⁵⁵-1, 9·10¹⁵⁹-1, 9·10¹⁶³-1, 9·10¹⁶⁵-1, 9·10¹⁶⁹-1, 9·10¹⁷¹-1, 9·10¹⁷³-1, 9·10¹⁷⁷-1, 9·10¹⁸¹-1, 9·10¹⁸³-1, 9·10¹⁸⁵-1, 9·10¹⁸⁷-1, 9·10¹⁸⁹-1, 9·10¹⁹¹-1, 9·10¹⁹³-1, 9·10¹⁹⁷-1, 9·10¹⁹⁹-1, (17/200)

Sep 4, 2004 (3rd)

Sequence (5·10ⁿ-41)/9 = { 1, 51, 551, 5551, 55551, ... } (n≤150) was completed.

Sep 4, 2004 (2nd)

By Greg Childers / GGNFS 0.53.3
(4·10¹⁴³+23)/9 = (4)₁₄₂7_<143> = 13 · C142
C142 = P51 · P92
P51 = 180844134716075035203997990871394431806442451443269_<51>
P92 = 18904696158218976770356643450736744237863202773063745264948680236412794860271753591597064351_<92>
(5·10¹⁴³-41)/9 = (5)₁₄₂1_<143> = 3³ · 23 · 29 · 216916329106936233353_<21> · C119
C119 = P47 · P72
P47 = 90598328670329288633752170604448516198086340879_<47>
P72 = 156973182953920998467116851061533821887338330176601859281927461141694097_<72>
(5·10¹⁴⁶-41)/9 = (5)₁₄₅1_<146> = 3 · 17 · 47 · C143
C143 = P56 · P88
P56 = 13516118890631063865273661782358529123478184587876781679_<56>
P88 = 1714776241251344387094512862437122338817972507003457126221272519176089410866002866913477_<88>

Sep 4, 2004

By Wataru Sakai / GMP-ECM
(34·10¹³⁶-7)/9 = 3(7)_136<137> = 37 · 7561 · 17627 · 33034501 · 537464580563_<12> · 106397931249683_<15> · C94
C94 = P34 · P60
P34 = 5266615485269965446457200154214233_<34>
P60 = 770006950366641907581458326988091801669850181785441305478499_<60>
(5·10¹³⁴+31)/9 = (5)₁₃₃9_<134> = 293957 · 44997707753_<11> · 83394628547_<11> · C107
C107 = P30 · P78
P30 = 138866219249377123128336908279_<30>
P78 = 362675824798389919823466254642372711644808581986822726155119511526421051854983_<78>

Sep 2, 2004

By Greg Childers / GGNFS 0.53.3
(7·10¹³²-61)/9 = (7)₁₃₁1_<132> = 3⁵ · 78681091949_<11> · C119
C119 = P57 · P62
P57 = 997159532317710164827409930329006977759922101974333857913_<57>
P62 = 40795685327010248173017671377143396808763033998584125184263381_<62>
(7·10¹³³-61)/9 = (7)₁₃₂1_<133> = 56883344330411_<14> · 1157987595398831_<16> · C105
C105 = P39 · P66
P39 = 605590275489498678158994613991181901667_<39>
P66 = 194978896828514501026116372320202578329571184138844238719786421093_<66>
(7·10¹³⁴-61)/9 = (7)₁₃₃1_<134> = 599 · 51599 · C127
C127 = P50 · P77
P50 = 33590633004144418105975015304787218817644473943831_<50>
P77 = 74915077847348830254424937905257609877425606983958772187549932272034696889941_<77>

Sep 1, 2004 (2nd)

By Greg Childers / GGNFS 0.53.3
(7·10¹²⁸-61)/9 = 77...771_<128> = 83 · 5017511 · C120
C120 = P50 · P70
P50 = 41898366721982735345452155476439819713064825086237_<50>
P70 = 4457506767999863893087424223511112803488068968019975028810921032313691_<70>
(7·10¹²⁹-61)/9 = 77...771_<129> = 3 · C129
C129 = P40 · P90
P40 = 2004019751938548505602825576080732027539_<40>
P90 = 129369612753801448206766034833512222723128676656403384621304657427751534950891311922173763_<90>

Sep 1, 2004

By Wataru Sakai / GMP-ECM
(88·10¹²¹-7)/9 = 977...77_<122> = 193 · 18216906809_<11> · C110
C110 = P30 · C80
P30 = 543098398934116820600769928163_<30>
C80 = [51207042619214580326770717794607953096741049490737309279078438743985183013967667_<80>]
(88·10¹³²-7)/9 = 977...77_<133> = 3 · 29 · 1429 · 330749 · 10113404043467_<14> · C110
C110 = P31 · C79
P31 = 5555454819131271767810517200293_<31>
C79 = [4232268025350110505638603754126975557672854401820692974551059282484805493945121_<79>]
By Makoto Kamada / PPSIQS 1.1
(88·10¹³²-7)/9 = 977...77_<133> = 3 · 29 · 1429 · 330749 · 10113404043467_<14> · 5555454819131271767810517200293_<31> · C79
C79 = P36 · P43
P36 = 560996190255377500506099490941179599_<36>
P43 = 7544201010390981992746447100393963449963279_<43>
(88·10¹²¹-7)/9 = 977...77_<122> = 193 · 18216906809_<11> · 543098398934116820600769928163_<30> · C80
C80 = P33 · P47
P33 = 849372735117096335241019546017641_<33>
P47 = 60288069656668539414818301579223067728720316987_<47>