Factorizations of repunit numbers of the form (10n-1)/9 (111111...)

Related links:



ECM EFFORTS
with Rn:      323 < n < 2000 (Sep 21, 2017) with Rn:     1999 < n < 3000 (Aug 03, 2017)
with Rn:     2999 < n < 4000 (Aug 03, 2017) with Rn:     3999 < n < 5000 (Aug 03, 2017)
with Rn:     4999 < n < 6000 (Sep 16, 2017) with Rn:     5999 < n < 7000 (Aug 03, 2017)
with Rn:     6999 < n < 8000 (Aug 18, 2017) with Rn:     7999 < n < 9000 (Sep 02, 2017)
with Rn:     8999 < n <10000 (Sep 09, 2017) with Rn:     9999 < n <11000 (Sep 17, 2017)
with Rn:   10999 < n <12000 (in preparation)  




Efforts by   yoyo@home:    ecm-curves
B1 = 43e6/6400 curves/
numbers < 1001 digits
883
working
887
working
889
working
893
working
899
working
B1 = 11e7/13500 curves/
numbers < 601 digits
1185
working
1186
working
1192
working
1197
working
2500M
working
B1 = 26e7/32000 curves/
numbers < 410 digits
407
working
1136
working
1142
working
1160
working
2380M
working
B1 = 85e7/52000 curves/
numbers < 225 digits
477
working
515
working
1420L
working
2420L
working
2460L
working



News
-  Last update:  Sep 21, 2017/2nd    

   the table was extented by the efforts from n = 10000 to n = 10999


   Bo Chen/Maksym Voznyy/Wenjie Fang/Alfred Eichhorn/Kurt Beschorner 
   May 07, 2017   n =2700M: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201; GNFS                       


-  Alfred Eichhorn, Bo Chen, Wenjie Fang, Danilo Nitsche, Kurt Beschorner 
   Sep 21, 2017   R1030/c199/GNFS: norm 1.587617e-019 alpha -6.405212 e 4.818e-015 rroots 3
                  515M unique relations and 571M unique ideals are collected
                  currently progress ~ 71%:    
                  

-  Found by Serge Batalov 
   May 20, 2017   n = 1664: 33705988330014732169259712855760222337             
                            P38: P-1: 2^7 * 7 * 13 * 109 * 158129 * 167887236965173647153941887  
                                 P+1: 2 * 3 * 41 * 163 * 301686997457 * 2786299274392871622433  
   May 20, 2017   n = 1800: 1216057084775405433757097429262954022602494154001;     B1=13544018; sigma = 1:453572236
                            P49: P-1: 2^4 * 3^2 * 5^3 * 9041 * 496029657073809329 * 15064590982733602929277  
                                 P+1: 2 * 59 * 103 * 179 * 137831 * 7079177207 * 828224509093 * 691677948817987 


-  Found by Alfred Eichhorn 
   Jul 11, 2017   n =67369: 98597788467374587 * 1126912812......c67352;            B1=11e3

   Jul 19, 2017   n =18917: 23804677265339797421816437 * 4667616782......c18891;   B1=5e4;  sigma = 3449289100892796519 
                            P26: P-1: 2^2 * 3 * 18917 * 104864571837235455859 
                                 P+1: 2 * 7 * 23 * 1601 * 3592493 * 12853433756903  
   
   Jul 19, 2017   n =67579: 81376586347554751637 * 2533975418......c67543;         B1=11e3; sigma = 10368654149114041945
                            P20: P-1: 2^2 * 67579 * 226463 * 1329322817  
                                 P+1: 2 * 3 * 7 * 11 * 2539 * 1544317 * 44921923  

   Jul 19, 2017   n =67589: 1427490294222230833547 * 7783668411......c67567;       B1=11e3; sigma = 14405740484299038573
                            P22: P-1: 2 * 7 * 31 * 67589 * 48663956314921  
                                 P+1: 2^2 * 3 * 179 * 1481 * 5026289 * 89276339  

   Jul 19, 2017   n =67589: 193970010166543534511963 * 4012820541......c67544;     B1=11e3; sigma = 18257096447838522086
                            P24: P-1: 2 * 11 * 23 * 43 * 14831 * 67589 * 8893427321  
                                 P+1: 2^2 * 3 * 19886213 * 812832866362169  
   
   Jul 19, 2017   n =67631: 12288780393345628792003 * 9041671146......c67608;      B1=11e3; sigma = 16252894969633873995
                            P23: P-1: 2 * 3^3 * 31 * 43 * 67631 * 2524288943081      
                                 P+1: 2^2 * 7 * 11 * 107449 * 739699 * 501996463 

   Jul 27, 2017   n =67783: 4697195943330820726079 * 2365477456......c67761;       B1=11e3; sigma = 2796044459679236971
                            P22: P-1: 2 * 29 * 67783 * 1194785373234877
                                 P+1: 2^6 * 3 * 5 * 733 * 6675187504733431

   Aug 05, 2017   n =19273: 16654668878053598037177599 * 6671469239......c19247;   B1=5e4;  sigma = 3770627784463675785 
                            P26: P-1: 2 * 11 * 31 * 19273 * 46073011 * 27501457513   
                                 P+1: 2^8 * 3^2 * 5^2 * 19 * 337 * 9643819 * 4682534293   

   Aug 17, 2017   n =68749: 999467309588805587 * 1111703304.....c68731;            B1=11e3; sigma = 12948517208099190898

   Aug 17, 2017   n =68993: 7918664704980905173 * 1403154638......c68974;          B1=11e3; sigma = 13347592554612910246

   Aug 24, 2017   n =19489: 4603739457788488002649 * 2413496943......c19467;       B1=5e4;  sigma = 13929637873820805088 
                            P22: P-1: 2^3 * 3 * 13 * 137 * 167 * 19489 * 33092497859  
                                 P+1: 2 * 5^2 * 7 * 13153541307967108579 

   Aug 24, 2017   n =69197: 91670990556046511 * 1212064039......c69180;            B1=11e3  

   Sep 03, 2017   n =69473: 74630488606594604603 * 1488816610......c69453;         B1=11e3; sigma = 15187732668636801744
                            P20: P-1: 2 * 17 * 101 * 69473 * 312823910761
                                 P+1: 2^2 * 3^2 * 739 * 2805235626469501
   
   Sep 11, 2017   n =70099: 2364446426172744837272201 * 4699244181......c70074;    B1=11e3; sigma = 15853464816084341637
                            P25: P-1: 2^3 * 5^2 * 19 * 70099 * 8876342654384081  
                                 P+1: 2 * 3^2 * 7^2 * 23 * 311 * 505187 * 741857517151 

   Sep 14, 2017   n =70249: 105346641434581408021761763 * 1065019315......c70206;  B1=11e3; sigma = 0:5984394627659000491
                            P27: P-1: 2 * 3^2 * 7 * 20593 * 70249 * 206911 * 2793230681
                                 P+1: 2^2 * 281 * 2526763 * 37092821906760547

   Sep 21, 2017   n =70537: 4256914902230650485467 * 2610132306......c70515;       B1=11e3; sigma = 809093756098030474
                            P22: P-1: 2 * 70537 * 3162847 * 9540470747 
                                 P+1: 2^2 * 3 * 17 * 109 * 232751 * 822520531663     
                                 
              
-  Found by  Yousuke Koide  
   Jun 16, 2017   n =  878: 2515873088287897454782011891518911571754342290096763019; B1= 12e7; sigma = 2:168411160075480502  
                            P55: P-1: 2 * 3^2 * 439 * 23269 * 13682768673045146064245165921233113568903662511  
                                 P+1: 2^2 * 5 * 11 * 13 * 19 * 37 * 848995024585270451041 * 1473880341547228807928977559 
   congratulations

   Aug 01, 2017   n =  976: 1333621378380781329750868926173511152429445865079521; B1= 12e7; sigma = 2:17156338585742940671  
                            P52: P-1: 2^5 * 3^2 * 5 * 61 * 149873 * 101301720397463942798137769864149153298111 
                                 P+1: 2 * 77977 * 2211557 * 3866676983397728874053445954723111344549 
   congratulations


-  Found by  Maksym Voznyy 
   May 10, 2017   n = 9901: 267769000737328369377044347;              B1= 25e4; sigma = 8516264195145008
                             P27: P-1: 2 * 3 * 9901 * 4507440338304689246491  
                                  P+1: 2^2 * 17 * 109 * 2377 * 3943 * 5171597 * 7453225347
                            
-  Found by YOYO@home 
   YOYO@home/NeuralMiner
   Jun 31, 2017   n =  833: 3432940252618824434327096124443716640606301456841302413201; B1= 11e7; sigma = 0:16155500098072674487
                            P58: P-1: 2^4 * 5^2 * 7^3 * 17 * 521 * 275498216479061 * 59211525303890317 * 173181081919710959
                                 P+1: 2 * 3 * 333449 * 68014583167 * 69362518858143827 * 363712878130325812612087


-  Found by Kurt Beschorner  
   Mar 02, 2017   n = 5709: 5428244957579115469193605941733;      B1=1e6; sigma = 2137748794  
                            P31: P-1: 2^2 * 3 * 7 * 11 * 13 * 173 * 4621 * 10781 * 52432793481122207 
                                 P+1: 2 * 29 * 266501591 * 351181506841691604553  

-  Correction
   false:   n = 239: 479 *  142847911 *  383155477843726029783939406113226468701730728790004161 (NFS@Home) *  128780300340244872385688233345188210841783983757299260103530718169486826135819357 (NFS@Home) *  3290967632......P94
false: n = 241: 125997820213 * 6864117620760368762783548070444378476387203247067308861991 (NFS@Home) * 1284723718......P172
correct: n = 239: 479 * 142847911 * 383155477843726029783939406113226468701730728790004161 (NFSNET) * 128780300340244872385688233345188210841783983757299260103530718169486826135819357 (NFSNET) * 3290967632......P94
correct: n = 241: 125997820213 * 6864117620760368762783548070444378476387203247067308861991 (NFSNET) * 1284723718......P172
Find out by Bo Chen

Factorizations
Repunits: R1        - R2500 (Sep 12, 2017) Repunits:  R2501 - R5000   (Aug 03, 2017)
Repunits: R5001   - R7500 (Aug 03, 2017) Repunits: R7501 -  R10000 (Aug 18, 2017)
Repunits: R10001 - R12500 (Aug 03, 2017) Repunits: R12540LM - R14980LM (Aug 03, 2017)


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