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Factorizations
Records2008-08-18(Mon) 23:21

Index

  1. Large numbers factored by SNFS
  2. Large numbers factored by GNFS
  3. Large factors found by NFS
  4. Large factors found by ECM
  5. Nice split
  6. Unprovable near-repdigit PRPs
  7. Unprovable Plateau and Depression PRPs
  8. Quasi-repdigit twin primes

1. Large numbers factored by SNFS

Large numbers which have 170 digits at least and were factored by SNFS.


  digits composite number prime factors from when who
1 205 P100 · P106 (4·10207-1)/3 Jul 19, 2008 Serge Batalov
2 201 P77 · P125 (79·10200-7)/9 Dec 25, 2006 Alexander Mkrtychyan
3 201 P53 · P70 · P79 (22·10200-31)/9 Aug 1, 2008 Serge Batalov
4 200 P84 · P116 6·10200+1 Jul 4, 2008 Serge Batalov
5 197 P67 · P131 6·10196+1 Jul 21, 2008 Wataru Sakai
6 196 P56 · P140 (5·10195+7)/3 May 17, 2008 Sinkiti Sibata
7 195 P76 · P120 5·10194-1 Sep 20, 2007 Sinkiti Sibata
8 193 P57 · P136 (4·10193-31)/9 Aug 12, 2008 Jo Yeong Uk
9 193 P52 · P141 10360+1 Jul 4, 2005 Tomoya Adachi
10 192 P89 · P104 (4·10192-13)/9 Feb 19, 2008 Jo Yeong Uk
11 192 P51 · P141 (2·10192-11)/9 Jan 30, 2007 Wataru Sakai
12 192 P51 · P141 (13·10191+41)/9 Jul 15, 2008 Jo Yeong Uk
13 191 P41 · P150 (14·10190-41)/9 Aug 5, 2007 Sinkiti Sibata
14 191 P83 · P108 (10192+53)/9 May 18, 2008 Wataru Sakai
15 190 P62 · P129 9·10192+1 Aug 18, 2008 Robert Backstrom
16 190 P57 · P65 · P69 7·10191+9 Aug 14, 2008 Robert Backstrom
17 190 P89 · P101 (4·10190-31)/9 Nov 2, 2007 Jo Yeong Uk
18 190 P70 · P120 (55·10190-1)/9 Aug 11, 2008 Robert Backstrom
19 189 P41 · P41 · P109 (67·10189+23)/9 Aug 8, 2008 Wataru Sakai
20 189 P47 · P51 · P93 (31·10189-13)/9 Jul 26, 2008 Wataru Sakai
21 189 P77 · P112 (4·10189-7)/3 Jun 16, 2006 Alexander Mkrtychyan
22 188 P37 · P67 · P86 5·10190-7 Jul 25, 2008 Kenji Ibusuki
23 188 P89 · P100 (4·10188-31)/9 Oct 17, 2007 Jo Yeong Uk
24 187 P59 · P129 8·10186-7 Dec 7, 2007 Jo Yeong Uk
25 187 P77 · P111 (32·10186-23)/9 Jul 7, 2007 Sinkiti Sibata
26 187 P73 · P114 (82·10187-1)/9 Aug 1, 2008 Robert Backstrom
27 186 P61 · P125 (16·10187-7)/9 Aug 6, 2008 Robert Backstrom
28 186 P48 · P59 · P80 (19·10187-1)/9 Aug 7, 2008 Robert Backstrom
29 186 P64 · P122 (8·10186+7)/3 Aug 1, 2008 Robert Backstrom
30 186 P53 · P133 (10186+71)/9 Jun 16, 2006 Alexander Mkrtychyan
31 186 P48 · P138 2·10186-3 Apr 29, 2008 matsui
32 185 P44 · P142 (7·10185-43)/9 May 28, 2005 Greg Childers
33 185 P40 · P43 · P43 · P61 (46·10186-1)/9 Jan 12, 2008 Sinkiti Sibata
34 185 P62 · P124 3·10184-1 Sep 12, 2007 Jo Yeong Uk
35 185 P45 · P66 · P75 (13·10184+23)/9 Mar 28, 2008 Robert Backstrom
36 184 P68 · P117 4·10185+3 Nov 21, 2007 Sinkiti Sibata
37 184 P45 · P139 (88·10186-7)/9 May 31, 2008 Wataru Sakai
38 184 P67 · P117 10184+3 Apr 23, 2008 Robert Backstrom
39 184 P88 · P96 (82·10185-1)/9 Jun 15, 2008 Robert Backstrom
40 184 P42 · P60 · P82 (28·10184+17)/9 Apr 30, 2008 Robert Backstrom
41 183 P59 · P62 · P63 10183-9 Oct 9, 2006 Wataru Sakai
42 183 P82 · P102 (17·10185-53)/9 Jun 3, 2008 Robert Backstrom
43 183 P48 · P48 · P87 (86·10182+31)/9 Sep 25, 2007 Robert Backstrom
44 182 P62 · P121 10182-3 Aug 25, 2007 Jo Yeong Uk
45 182 P48 · P135 8·10181-7 Nov 22, 2007 Jo Yeong Uk
46 182 P50 · P59 · P74 (7·10181-1)/3 Jul 27, 2007 Jo Yeong Uk
47 182 P86 · P96 (11·10181+43)/9 Mar 5, 2008 Jo Yeong Uk
48 182 P47 · P135 5·10182-3 Sep 12, 2007 Robert Backstrom
49 181 P85 · P97 10183+3 Mar 3, 2008 Robert Backstrom
50 181 P81 · P100 (2·10185+1)/3 Aug 5, 2008 matsui
51 181 P84 · P97 (16·10181-61)/9 Sep 9, 2007 Robert Backstrom
52 181 P41 · P140 (2·10184-17)/3 Mar 3, 2008 Robert Backstrom
53 181 P81 · P100 (52·10181-7)/9 Sep 20, 2007 Robert Backstrom
54 180 P76 · P105 7·10182+3 Jun 24, 2008 Sinkiti Sibata
55 180 P74 · P106 7·10179-3 Aug 13, 2007 Jo Yeong Uk
56 180 P86 · P94 4·10180+3 Jun 17, 2007 Sinkiti Sibata
57 180 P45 · P135 4·10179+9 Dec 10, 2007 Sinkiti Sibata
58 180 P63 · P118 6·10183-1 Jul 17, 2008 Wataru Sakai
59 179 P44 · P62 · P74 10179-3 Jan 1, 2006 Kenichiro Yamaguchi
60 179 P71 · P109 (55·10178-1)/9 May 16, 2007 Sinkiti Sibata
61 179 P46 · P62 · P72 10185-9 May 17, 2008 Wataru Sakai
62 179 P68 · P112 (31·10179-13)/9 May 17, 2008 matsui
63 179 P44 · P136 (79·10178-7)/9 Jul 17, 2008 Wataru Sakai
64 179 P76 · P104 (73·10178-1)/9 Jul 15, 2007 Robert Backstrom
65 179 P78 · P101 (8·10178+7)/3 Nov 12, 2007 Jo Yeong Uk
66 179 P88 · P91 (5·10179-17)/3 Jul 9, 2007 Robert Backstrom
67 179 P52 · P58 · P70 (19·10179+17)/9 Jun 20, 2008 Wataru Sakai
68 178 P54 · P55 · P70 3·10180+1 Mar 2, 2008 matsui
69 178 P45 · P133 (23·10178+1)/3 May 27, 2008 Sinkiti Sibata
70 178 P70 · P109 (14·10177+31)/9 May 9, 2008 Jo Yeong Uk
71 177 P38 · P40 · P101 (71·10176-17)/9 Apr 16, 2007 Sinkiti Sibata
72 177 P53 · P124 10179+7 Jun 9, 2007 Alexander Mkrtychyan
73 177 P42 · P136 (4·10177+41)/9 Jun 14, 2007 Jo Yeong Uk
74 177 P65 · P112 (13·10176+41)/9 Mar 24, 2008 Jo Yeong Uk
75 177 P81 · P96 (2·10178+1)/3 Jul 17, 2008 Wataru Sakai
76 176 P43 · P134 (16·10175-1)/3 Dec 15, 2004 Greg Childers
77 176 P80 · P96 (19·10175+71)/9 Jun 18, 2008 Jo Yeong Uk
78 176 P45 · P49 · P83 (14·10179+31)/9 Jul 26, 2008 matsui
79 175 P64 · P112 9·10174+1 Jun 5, 2007 Jo Yeong Uk
80 175 P82 · P94 (23·10174+1)/3 Mar 1, 2007 Tyler Cadigan
81 175 P69 · P106 8·10177-7 Apr 10, 2008 matsui
82 175 P45 · P131 6·10176+7 Jun 24, 2008 matsui
83 175 P38 · P137 (5·10174+1)/3 May 29, 2007 Jo Yeong Uk
84 175 P76 · P99 (25·10179-1)/3 Mar 28, 2008 Tyler Cadigan
85 174 P52 · P122 (4·10187-1)/3 Dec 3, 2007 Jo Yeong Uk
86 174 P76 · P98 (8·10175-71)/9 Jul 6, 2008 Wataru Sakai
87 174 P66 · P108 (7·10174-61)/9 Jul 9, 2007 Robert Backstrom
88 174 P35 · P139 8·10175-3 Mar 22, 2008 matsui
89 174 P66 · P108 (4·10174+23)/9 Jul 9, 2007 Robert Backstrom
90 173 P70 · P104 (22·10173+41)/9 Jul 22, 2008 Sinkiti Sibata
91 173 P46 · P128 (14·10175-41)/9 Jan 29, 2007 Sinkiti Sibata
92 173 P80 · P93 (5·10175+1)/3 Jun 15, 2008 Kenji Ibusuki
93 173 P81 · P93 8·10176+9 Feb 24, 2008 matsui
94 173 P38 · P57 · P79 (19·10173+17)/9 Jun 20, 2008 Robert Backstrom
95 172 P62 · P111 (22·10173-31)/9 Jul 7, 2008 Robert Backstrom
96 172 P68 · P104 (16·10173-1)/3 Jun 21, 2007 Robert Backstrom
97 172 P48 · P125 6·10171+1 Apr 22, 2007 Jo Yeong Uk
98 172 P47 · P51 · P75 4·10175+1 Feb 8, 2008 matsui
99 172 P43 · P130 (2·10172+43)/9 Apr 1, 2007 Robert Backstrom
100 172 P79 · P93 (13·10171+23)/9 Mar 12, 2008 Jo Yeong Uk
101 172 P61 · P111 (10172+53)/9 Dec 15, 2005 Sinkiti Sibata
102 171 P50 · P57 · P65 7·10173+9 Jul 1, 2008 Robert Backstrom
103 171 P80 · P92 (13·10171-1)/3 Jun 7, 2007 Robert Backstrom
104 171 P50 · P56 · P66 2·10170-7 Aug 28, 2007 Jo Yeong Uk
105 171 P67 · P104 (5·10170-11)/3 Apr 14, 2008 Jo Yeong Uk
106 171 P42 · P129 (5·10173-41)/9 Jun 25, 2007 Robert Backstrom
107 171 P41 · P51 · P80 (11·10172+61)/9 Jun 2, 2008 Robert Backstrom
108 170 P64 · P107 8·10169-1 Oct 24, 2005 Makoto Kamada
109 170 P77 · P94 (5·10170+31)/9 Nov 3, 2005 Makoto Kamada
110 170 P45 · P53 · P74 (10175-7)/3 Jul 9, 2008 matsui
111 170 P48 · P122 (11·10169+43)/9 Feb 15, 2008 Jo Yeong Uk

2. Large numbers factored by GNFS

Large numbers which have 120 digits at least and were factored by GNFS.


  digits composite number prime factors from when who
1 144 P70 · P74 (64·10232+53)/9 Aug 13, 2008 Serge Batalov
2 140 P53 · P88 (16·10214-61)/9 Aug 4, 2008 Serge Batalov
3 140 P45 · P95 4·10200+7 Mar 6, 2008 Tyler Cadigan
4 139 P60 · P79 6·10199+1 Jul 10, 2008 Tyler Cadigan
5 138 P49 · P89 (10198+53)/9 Aug 1, 2008 Tyler Cadigan
6 138 P64 · P74 (7·10196-43)/9 May 9, 2008 Wataru Sakai
7 135 P49 · P86 (4·10195-1)/3 Nov 17, 2007 Jo Yeong Uk
8 134 P47 · P88 8·10190-1 May 28, 2008 Jo Yeong Uk
9 131 P60 · P72 (22·10186-31)/9 Jul 29, 2008 Sinkiti Sibata
10 129 P61 · P69 3·10191+1 Jul 3, 2008 matsui
11 127 P39 · P89 8·10187-1 Apr 24, 2008 Jo Yeong Uk
12 126 P50 · P76 (16·10182-7)/9 Apr 22, 2008 Wataru Sakai
13 126 P55 · P71 (5·10185-23)/9 Aug 10, 2008 Serge Batalov
14 124 P59 · P65 (5·10198-11)/3 Aug 4, 2008 Tyler Cadigan
15 124 P62 · P63 8·10197+9 Jun 1, 2008 Tyler Cadigan
16 124 P59 · P65 (5·10190+13)/9 May 30, 2008 Tyler Cadigan
17 123 P59 · P65 3·10179-1 Feb 16, 2008 matsui
18 123 P53 · P71 6·10192+7 May 28, 2008 Tyler Cadigan
19 123 P59 · P64 (16·10190-61)/9 Feb 12, 2008 Tyler Cadigan
20 122 P39 · P41 · P43 (2·10188-17)/3 May 31, 2007 Sinkiti Sibata
21 122 P55 · P67 (85·10185+41)/9 Aug 12, 2008 Serge Batalov
22 122 P45 · P77 (19·10176+53)/9 Aug 13, 2008 Serge Batalov
23 122 P46 · P76 (2·10178+61)/9 Mar 12, 2008 Robert Backstrom
24 122 P61 · P61 (8·10178-53)/9 Aug 12, 2008 Serge Batalov
25 122 P51 · P71 5·10180-7 Jul 11, 2008 Sinkiti Sibata
26 121 P56 · P66 (16·10199-43)/9 Aug 4, 2008 Serge Batalov
27 121 P59 · P62 5·10179-7 Sep 28, 2007 Sinkiti Sibata
28 120 P44 · P77 (71·10182-17)/9 Jan 4, 2007 Alexander Mkrtychyan
29 120 P54 · P67 (2·10197+7)/9 Dec 4, 2006 Tyler Cadigan
30 120 P48 · P73 (4·10179-1)/3 Nov 15, 2006 Tyler Cadigan
31 120 P38 · P83 10187+9 Oct 7, 2006 Tyler Cadigan
32 120 P58 · P63 (22·10189-1)/3 Dec 13, 2006 Tyler Cadigan
33 120 P29 · P43 · P49 10177+9 Aug 11, 2007 Sinkiti Sibata
34 120 P43 · P78 (86·10171+31)/9 Jan 10, 2008 Jo Yeong Uk
35 120 P44 · P76 (5·10172+31)/9 Aug 15, 2008 Jo Yeong Uk
36 120 P57 · P64 (8·10189-71)/9 Dec 21, 2006 Tyler Cadigan
37 120 P59 · P61 9·10184+1 May 23, 2007 Sinkiti Sibata
38 120 P38 · P82 (61·10169-7)/9 Oct 6, 2007 Bryan Koen

3. Large factors found by NFS

Second largest factors which have 70 digits at least and were found by NFS.


  digits prime factor from when who
1 100 (4·10207-1)/3 Jul 19, 2008 Serge Batalov
2 89 (4·10190-31)/9 Nov 2, 2007 Jo Yeong Uk
3 89 (4·10192-13)/9 Feb 19, 2008 Jo Yeong Uk
4 89 (4·10188-31)/9 Oct 17, 2007 Jo Yeong Uk
5 88 (82·10185-1)/9 Jun 15, 2008 Robert Backstrom
6 88 (5·10179-17)/3 Jul 9, 2007 Robert Backstrom
7 86 4·10180+3 Jun 17, 2007 Sinkiti Sibata
8 86 (11·10181+43)/9 Mar 5, 2008 Jo Yeong Uk
9 85 10183+3 Mar 3, 2008 Robert Backstrom
10 84 (16·10181-61)/9 Sep 9, 2007 Robert Backstrom
11 84 6·10200+1 Jul 4, 2008 Serge Batalov
12 83 (10192+53)/9 May 18, 2008 Wataru Sakai
13 82 (17·10185-53)/9 Jun 3, 2008 Robert Backstrom
14 82 (23·10174+1)/3 Mar 1, 2007 Tyler Cadigan
15 81 (37·10167-1)/9 May 14, 2007 Robert Backstrom
16 81 (2·10185+1)/3 Aug 5, 2008 matsui
17 81 (52·10181-7)/9 Sep 20, 2007 Robert Backstrom
18 81 (67·10166+23)/9 Jan 12, 2008 Robert Backstrom
19 81 (2·10178+1)/3 Jul 17, 2008 Wataru Sakai
20 81 8·10176+9 Feb 24, 2008 matsui
21 80 (5·10175+1)/3 Jun 15, 2008 Kenji Ibusuki
22 80 (19·10175+71)/9 Jun 18, 2008 Jo Yeong Uk
23 80 (13·10171-1)/3 Jun 7, 2007 Robert Backstrom
24 79 (8·10164-71)/9 Aug 12, 2007 Robert Backstrom
25 79 5·10164+9 Dec 18, 2007 Jo Yeong Uk
26 79 (13·10171+23)/9 Mar 12, 2008 Jo Yeong Uk
27 79 (5·10165-11)/3 Apr 14, 2008 Robert Backstrom
28 79 8·10170-3 Jun 8, 2008 matsui
29 79 (4·10168+23)/9 Jun 13, 2008 Robert Backstrom
30 79 (4·10164-13)/9 Jun 26, 2007 Robert Backstrom
31 78 (83·10166+61)/9 Jan 17, 2008 Robert Backstrom
32 78 (8·10178+7)/3 Nov 12, 2007 Jo Yeong Uk
33 78 (13·10172+41)/9 Jun 27, 2008 Robert Backstrom
34 78 (19·10171+53)/9 Jun 7, 2008 Robert Backstrom
35 78 10181-9 May 12, 2008 Wataru Sakai
36 77 (17·10156-53)/9 May 5, 2008 Robert Backstrom
37 77 10155+3 Jun 12, 2006 Wojciech Florek
38 77 (88·10165-7)/9 Jul 14, 2006 Sinkiti Sibata
39 77 (17·10165-53)/9 May 10, 2008 Robert Backstrom
40 77 8·10171-7 May 29, 2008 Robert Backstrom
41 77 (4·10189-7)/3 Jun 16, 2006 Alexander Mkrtychyan
42 77 (32·10186-23)/9 Jul 7, 2007 Sinkiti Sibata
43 77 4·10168-3 Jul 2, 2008 Robert Backstrom
44 77 (13·10165-1)/3 Oct 22, 2007 Robert Backstrom
45 77 (5·10162+1)/3 Apr 29, 2007 Robert Backstrom
46 77 4·10162+9 Dec 1, 2007 Robert Backstrom
47 77 5·10157+3 Jul 16, 2007 Robert Backstrom
48 77 (79·10200-7)/9 Dec 25, 2006 Alexander Mkrtychyan
49 77 (5·10170+31)/9 Nov 3, 2005 Makoto Kamada
50 76 7·10182+3 Jun 24, 2008 Sinkiti Sibata
51 76 (8·10175-71)/9 Jul 6, 2008 Wataru Sakai
52 76 (7·10173-61)/9 Jun 22, 2008 Wataru Sakai
53 76 (67·10165+23)/9 Nov 8, 2007 Robert Backstrom
54 76 (25·10179-1)/3 Mar 28, 2008 Tyler Cadigan
55 76 5·10194-1 Sep 20, 2007 Sinkiti Sibata
56 76 (73·10178-1)/9 Jul 15, 2007 Robert Backstrom
57 76 10157-9 Sep 27, 2004 Makoto Kamada
58 76 2·10155+3 May 18, 2007 Robert Backstrom
59 75 (11·10167+43)/9 Feb 7, 2008 Robert Backstrom
60 75 (85·10167+41)/9 Apr 26, 2008 Robert Backstrom
61 75 (7·10161+17)/3 Jun 21, 2008 Robert Backstrom
62 75 8·10158-7 Oct 17, 2007 Robert Backstrom
63 75 9·10154+7 Nov 7, 2007 Robert Backstrom
64 75 (7·10174+11)/9 Jun 20, 2008 Wataru Sakai
65 75 (17·10154+1)/9 May 12, 2008 Robert Backstrom
66 75 (17·10150-71)/9 Oct 6, 2004 Greg Childers
67 74 (61·10167-7)/9 Jun 1, 2008 Wataru Sakai
68 74 7·10179-3 Aug 13, 2007 Jo Yeong Uk
69 74 2·10161+9 Nov 18, 2007 Robert Backstrom
70 74 (14·10158-41)/9 Apr 25, 2007 Robert Backstrom
71 74 8·10160-7 Oct 18, 2007 Robert Backstrom
72 74 (7·10170-1)/3 Jun 12, 2007 Robert Backstrom
73 73 9·10157-7 Oct 31, 2007 Robert Backstrom
74 73 (5·10160-17)/3 Jun 25, 2005 Samuel Chong
75 73 (16·10155-7)/9 Oct 5, 2005 Sinkiti Sibata
76 73 (7·10163-1)/3 Jul 30, 2007 Robert Backstrom
77 73 (4·10157+11)/3 Feb 20, 2008 Jo Yeong Uk
78 73 (82·10187-1)/9 Aug 1, 2008 Robert Backstrom
79 73 (34·10150-43)/9 Nov 17, 2004 Greg Childers
80 73 8·10153+3 Aug 11, 2007 Robert Backstrom
81 73 (25·10169-1)/3 Mar 8, 2008 Tyler Cadigan
82 73 (4·10167-13)/9 Dec 25, 2007 Robert Backstrom
83 73 9·10167-7 Jan 27, 2008 Robert Backstrom
84 72 (64·10181-1)/9 Feb 10, 2008 Tyler Cadigan
85 72 (2·10170+43)/9 May 25, 2007 Robert Backstrom
86 72 (11·10167+61)/9 Jun 20, 2008 Robert Backstrom
87 72 (4·10168+41)/9 Jul 5, 2008 Robert Backstrom
88 72 (23·10166-41)/9 Aug 3, 2008 Robert Backstrom
89 72 (19·10167+17)/9 Jun 9, 2008 Robert Backstrom
90 72 (34·10147-7)/9 Apr 9, 2005 Sinkiti Sibata
91 72 8·10165+9 Jan 20, 2008 Robert Backstrom
92 72 (2·10155+1)/3 Apr 3, 2007 Robert Backstrom
93 72 (61·10147-7)/9 May 9, 2005 Greg Childers
94 72 (19·10168+17)/9 May 30, 2008 Jo Yeong Uk
95 72 (4·10159+11)/3 Mar 8, 2008 Robert Backstrom
96 72 (13·10149+41)/9 Mar 14, 2008 Sinkiti Sibata
97 72 2·10155-1 Jan 26, 2006 Anton Korobeynikov
98 71 (46·10156-1)/9 Jan 22, 2007 suberi
99 71 (4·10156-13)/9 Apr 11, 2007 Robert Backstrom
100 71 (11·10146+61)/9 Feb 13, 2008 Robert Backstrom
101 71 (89·10163+1)/9 Oct 12, 2007 Robert Backstrom
102 71 (22·10164-31)/9 Jul 1, 2008 Robert Backstrom
103 71 8·10166-1 Jan 29, 2008 Robert Backstrom
104 71 (7·10164+17)/3 Jun 26, 2008 Robert Backstrom
105 71 (55·10178-1)/9 May 16, 2007 Sinkiti Sibata
106 70 (8·10160+7)/3 Oct 23, 2007 Robert Backstrom
107 70 (22·10173+41)/9 Jul 22, 2008 Sinkiti Sibata
108 70 8·10154+3 Aug 10, 2007 Robert Backstrom
109 70 (64·10232+53)/9 Aug 13, 2008 Serge Batalov
110 70 (17·10161-71)/9 Oct 4, 2007 Robert Backstrom
111 70 5·10149+3 Jul 15, 2007 Jo Yeong Uk
112 70 (55·10190-1)/9 Aug 11, 2008 Robert Backstrom
113 70 (17·10162-71)/9 Jun 18, 2007 Robert Backstrom
114 70 (22·10200-31)/9 Aug 1, 2008 Serge Batalov
115 70 (5·10166-11)/3 Apr 25, 2008 Robert Backstrom
116 70 (65·10158+43)/9 Apr 26, 2007 Robert Backstrom
117 70 (2·10157+61)/9 Apr 6, 2007 Sinkiti Sibata
118 70 10161-3 Jun 29, 2005 Samuel Chong
119 70 (5·10157-17)/3 Apr 19, 2007 Robert Backstrom
120 70 (14·10167-41)/9 Jul 19, 2005 Samuel Chong
121 70 (4·10165+41)/9 Feb 1, 2008 Robert Backstrom
122 70 (14·10177+31)/9 May 9, 2008 Jo Yeong Uk

4. Large factors found by ECM

Large factors which have 45 digits at least and were found by ECM.


  digits prime factor from B1 sigma when who
1 58 (8·10141-17)/9 3897500 2735675386 Oct 31, 2003 Robert Backstrom
2 56 3·10166-1 44000000 3068145495 Sep 14, 2005 Wataru Sakai
3 52 (10178+53)/9 11000000 1762451977 Jul 18, 2008 suberi
4 48 (86·10192+31)/9 44000000 896044946 Aug 4, 2006 JMB
5 48 10192+9 11000000 413694509 Oct 7, 2007 Jo Yeong Uk
6 47 (64·10215+53)/9 11000000 1048397889 Jul 7, 2008 Serge Batalov
7 47 (22·10155+41)/9 3870000 219387156 Jul 22, 2008 Robert Backstrom
8 47 10196+9 11000000 2570867251 Nov 11, 2006 Wataru Sakai
9 47 8·10206-1 3000000 1065804300 Aug 1, 2008 Sinkiti Sibata
10 47 (25·10165-7)/9 3000000 1593296484 Jul 25, 2007 JMB
11 47 (64·10234+53)/9 10757000 1312137675 Dec 3, 2007 Robert Backstrom
12 47 (22·10179-13)/9 3000000 1048915276 Aug 18, 2008 Sinkiti Sibata
13 47 (55·10165-1)/9 3000000 1761471762 Mar 7, 2008 Jo Yeong Uk
14 46 (68·10169+13)/9 3744000 1706818246 Jul 27, 2008 Robert Backstrom
15 46 4·10194+1 11000000 632711195 Jul 27, 2007 Wataru Sakai
16 45 8·10167+3 1000000 127447873 Jul 18, 2008 Jo Yeong Uk
17 45 (4·10189-1)/3 3000000 4103031508 Mar 27, 2007 suberi
18 45 5·10188+3 3000000 2524047625 Jul 4, 2008 suberi
19 45 (64·10202+53)/9 11000000 49343718 Jun 13, 2005 Wataru Sakai
20 45 (13·10177+41)/9 7318000 2046770327 Apr 2, 2008 Robert Backstrom
21 45 (86·10148+31)/9 2728500 679331778 Sep 22, 2003 Robert Backstrom
22 45 2·10191+9 3000000 3278687019 Nov 16, 2007 Jo Yeong Uk
23 45 (64·10215+53)/9 43000000 1801021090 Jul 7, 2008 Serge Batalov

5. Nice split

Large factor and cofactor which have 50 digits at least with the same length.


  digits prime factor prime cofactor from when who
1 69 (22·10139-1)/3 May 5, 2005 Greg Childers
2 69 (28·10146-1)/9 Apr 19, 2005 Sinkiti Sibata
3 67 (19·10163+71)/9 Jul 13, 2008 Robert Backstrom
4 66 (5·10159-41)/9 Oct 8, 2007 Jo Yeong Uk
5 65 (22·10163-13)/9 Jul 10, 2008 Robert Backstrom
6 65 (16·10145-43)/9 Apr 19, 2008 Robert Backstrom
7 62 (14·10145+13)/9 Mar 29, 2008 Jo Yeong Uk
8 62 5·10126+9 Dec 16, 2007 Jo Yeong Uk
9 62 (22·10125-1)/3 Oct 24, 2004 Sander Hoogendoorn
10 61 (8·10178-53)/9 Aug 12, 2008 Serge Batalov
11 61 (4·10148+41)/9 Jan 31, 2005 Samuel Chong
12 61 (46·10174-1)/9 Aug 8, 2008 Serge Batalov
13 61 (8·10120+7)/3 Oct 20, 2007 Jo Yeong Uk
14 60 5·10118-9 Dec 4, 2007 Jo Yeong Uk
15 59 (43·10160-7)/9 Aug 1, 2007 Sinkiti Sibata
16 58 (67·10143+23)/9 Nov 17, 2004 Greg Childers
17 57 (7·10142+11)/9 Apr 28, 2005 Makoto Kamada
18 57 (22·10136+23)/9 Jul 10, 2008 Serge Batalov
19 56 4·10154+9 Dec 10, 2007 Robert Backstrom
20 56 (5·10113+7)/3 Sep 26, 2007 Jo Yeong Uk
21 55 (4·10143+41)/9 Jan 21, 2005 Samuel Chong
22 55 (5·10134-11)/3 Apr 12, 2008 Sinkiti Sibata
23 53 (22·10143-31)/9 Jun 27, 2008 Sinkiti Sibata
24 53 (4·10110-31)/9 May 22, 2004 Naoki Yamamoto
25 52 8·10107+3 Aug 9, 2007 Robert Backstrom
26 52 (16·10144-43)/9 Apr 17, 2008 Robert Backstrom
27 52