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Table of contents

  1. Top 100 large numbers factored by SNFS
  2. Large numbers factored by GNFS
  3. Top 100 large factors found by NFS
  4. Large factors found by ECM
  5. Nice split
  6. Unprovable near-repdigit PRPs
  7. Unprovable quasi-repdigit PRPs
  8. Quasi-repdigit twin primes

1. Top 100 large numbers factored by SNFS

  digits composite number prime factors from when who
1 222 P55 · P55 · P114 (25·10223-1)/3 Nov 7, 2008 Serge Batalov
2 222 P51 · P51 · P120 (10222+17)/9 Jul 9, 2009 Dmitry Domanov
3 218 P54 · P165 4·10217-9 Jun 27, 2009 Robert Backstrom
4 216 P77 · P139 4·10219-9 May 1, 2009 Robert Backstrom
5 212 P87 · P125 2·10216-1 Jul 5, 2009 Robert Backstrom
6 211 P57 · P154 4·10217+1 Apr 17, 2009 Robert Backstrom
7 211 P57 · P154 (64·10321-1)/9 Apr 8, 2009 Robert Backstrom
8 208 P100 · P108 4·10209+1 Feb 17, 2009 Serge Batalov
9 207 P60 · P148 (10211+53)/9 Mar 20, 2009 Serge Batalov
10 206 P50 · P157 (19·10205-7)/3 Jun 9, 2009 Wataru Sakai
11 206 P67 · P139 (16·10205-1)/3 Nov 10, 2008 Robert Backstrom
12 206 P103 · P104 (14·10205-11)/3 Feb 22, 2009 Wataru Sakai
13 206 P53 · P75 · P79 (37·10205+17)/9 Feb 26, 2009 Robert Backstrom
14 206 P68 · P139 (25·10205-43)/9 Nov 20, 2008 Robert Backstrom
15 206 P58 · P148 (7·10207-43)/9 Jun 16, 2009 Robert Backstrom
16 205 P100 · P106 (4·10207-1)/3 Jul 19, 2008 Serge Batalov
17 205 P51 · P73 · P82 (64·10211-1)/9 Jun 10, 2009 Robert Backstrom
18 205 P48 · P71 · P88 (11·10204-17)/3 Dec 16, 2008 Robert Backstrom
19 205 P102 · P103 (37·10204+17)/9 Feb 5, 2009 Robert Backstrom
20 204 P52 · P153 (52·10204+11)/9 Jun 17, 2009 Markus Tervooren
21 204 P56 · P149 (47·10204+7)/9 Mar 24, 2009 Robert Backstrom
22 204 P79 · P126 (13·10203+17)/3 Feb 8, 2009 Wataru Sakai
23 204 P66 · P138 (64·10203-1)/9 Nov 4, 2008 Robert Backstrom
24 204 P40 · P164 (38·10203+61)/9 Jan 26, 2009 Wataru Sakai
25 203 P54 · P67 · P83 (10207+17)/9 Mar 30, 2009 Robert Backstrom
26 203 P42 · P59 · P102 (53·10203-17)/9 Jun 2, 2009 Robert Backstrom
27 203 P93 · P110 (41·10203+31)/9 Feb 20, 2009 Robert Backstrom
28 202 P80 · P123 (22·10203+41)/9 Sep 10, 2008 Serge Batalov
29 202 P60 · P143 (56·10202+43)/9 Jun 28, 2009 Dmitry Domanov
30 202 P58 · P144 (44·10202-17)/9 Mar 10, 2009 Robert Backstrom
31 202 P86 · P117 (41·10203-23)/9 Mar 16, 2009 Robert Backstrom
32 202 P47 · P55 · P100 (35·10202-17)/9 Mar 5, 2009 Robert Backstrom
33 201 P77 · P125 (79·10200-7)/9 Dec 25, 2006 Alexander Mkrtychyan
34 201 P53 · P70 · P79 (22·10200-31)/9 Aug 1, 2008 Serge Batalov
35 201 P37 · P41 · P123 (52·10200+11)/9 May 28, 2009 Wataru Sakai
36 200 P73 · P128 4·10203+1 May 8, 2009 Wataru Sakai
37 200 P47 · P62 · P92 (32·10204-41)/9 Dec 7, 2008 Robert Backstrom
38 200 P41 · P76 · P84 (46·10202+17)/9 Jun 11, 2009 matsui
39 200 P84 · P116 6·10200+1 Jul 4, 2008 Serge Batalov
40 200 P52 · P65 · P84 (14·10200-23)/9 Oct 30, 2008 Robert Backstrom
41 200 P60 · P67 · P73 (56·10200+61)/9 May 28, 2009 Robert Backstrom
42 199 P54 · P73 · P74 (7·10199-61)/9 Nov 23, 2008 Wataru Sakai
43 199 P61 · P138 (2·10199-17)/3 Aug 31, 2008 Wataru Sakai
44 199 P52 · P148 (53·10198-17)/9 May 16, 2009 Jo Yeong Uk
45 199 P34 · P80 · P86 (29·10198+61)/9 Nov 30, 2008 Wataru Sakai
46 199 P82 · P118 3·10198+1 Sep 8, 2008 Serge Batalov
47 199 P48 · P69 · P83 (23·10198-41)/9 Nov 14, 2008 Wataru Sakai
48 199 P46 · P154 (7·10200+11)/9 Apr 25, 2009 Wataru Sakai
49 199 P90 · P110 (5·10198-17)/3 Dec 1, 2008 Jo Yeong Uk
50 199 P60 · P66 · P74 (8·10199-17)/9 Dec 15, 2008 Wataru Sakai
51 199 P55 · P144 4·10200-3 Dec 6, 2008 Wataru Sakai
52 198 P40 · P158 (28·10198+53)/9 Dec 28, 2008 Wataru Sakai
53 198 P87 · P112 4·10198+9 Feb 18, 2009 matsui
54 197 P54 · P144 (8·10197+1)/9 Nov 4, 2008 Wataru Sakai
55 197 P96 · P102 (2·10197+1)/3 Nov 1, 2008 Wataru Sakai
56 197 P67 · P131 6·10196+1 Jul 21, 2008 Wataru Sakai
57 197 P52 · P146 (16·10197-7)/9 May 26, 2009 Dmitry Domanov
58 197 P76 · P122 (47·10196+61)/9 Apr 17, 2009 Jo Yeong Uk
59 197 P52 · P60 · P87 2·10200-3 Feb 14, 2009 matsui
60 197 P57 · P66 · P74 (37·10196+53)/9 Dec 28, 2008 Wataru Sakai
61 197 P54 · P54 · P90 3·10196-1 Oct 3, 2008 Jo Yeong Uk
62 197 P78 · P119 (5·10197-11)/3 May 22, 2009 Robert Backstrom
63 197 P49 · P148 (32·10196+31)/9 Feb 12, 2009 Robert Backstrom
64 197 P73 · P124 (31·10196-13)/9 Feb 9, 2009 Robert Backstrom
65 196 P60 · P136 4·10198+1 Mar 3, 2009 Wataru Sakai
66 196 P44 · P49 · P104 (13·10195+17)/3 Feb 13, 2009 Jo Yeong Uk
67 196 P63 · P134 (38·10195+61)/9 Jan 6, 2009 Wataru Sakai
68 196 P73 · P124 (37·10195+53)/9 Apr 4, 2009 Jo Yeong Uk
69 196 P88 · P108 (19·10196+71)/9 Jan 19, 2009 Wataru Sakai
70 196 P55 · P141 (64·10197-1)/9 Oct 23, 2008 Robert Backstrom
71 196 P87 · P109 (82·10198-1)/9 May 19, 2009 Robert Backstrom
72 196 P48 · P149 (22·10195+41)/9 Sep 21, 2008 Robert Backstrom
73 196 P56 · P140 (5·10195+7)/3 May 17, 2008 Sinkiti Sibata
74 196 P64 · P132 10196+3 Dec 9, 2008 Wataru Sakai
75 196 P91 · P105 (22·10198-1)/3 May 15, 2009 Robert Backstrom
76 196 P51 · P145 (38·10196-11)/9 May 13, 2009 Robert Backstrom
77 195 P44 · P53 · P99 (82·10195+71)/9 Apr 14, 2009 Wataru Sakai
78 195 P75 · P121 (73·10194-1)/9 Sep 29, 2008 Wataru Sakai
79 195 P55 · P141 (13·10195-1)/3 Apr 21, 2009 Sinkiti Sibata
80 195 P44 · P151 (47·10195+7)/9 May 5, 2009 Robert Backstrom
81 195 P88 · P108 5·10194+9 Sep 6, 2008 Jo Yeong Uk
82 195 P76 · P120 5·10194-1 Sep 20, 2007 Sinkiti Sibata
83 195 P49 · P147 (34·10194+11)/9 Dec 15, 2008 Wataru Sakai
84 195 P96 · P100 (25·10195-61)/9 Oct 8, 2008 Tyler Cadigan
85 195 P55 · P140 8·10196+3 May 6, 2009 Robert Backstrom
86 195 P74 · P121 (26·10195-17)/9 May 2, 2009 Robert Backstrom
87 195 P71 · P124 2·10197-3 May 14, 2009 Wataru Sakai
88 194 P40 · P155 5·10195-7 Feb 28, 2009 Wataru Sakai
89 194 P73 · P122 9·10198+1 May 23, 2009 Wataru Sakai
90 194 P90 · P105 (38·10193+43)/9 Jan 8, 2009 Jo Yeong Uk
91 194 P49 · P145 (13·10193+41)/9 Sep 12, 2008 Robert Backstrom
92 194 P97 · P97 6·10198+1 Mar 14, 2009 matsui
93 193 P57 · P136 (4·10193-31)/9 Aug 12, 2008 Jo Yeong Uk
94 193 P54 · P140 8·10197-3 Jun 9, 2009 Wataru Sakai
95 193 P92 · P102 (68·10192+13)/9 Sep 1, 2008 Robert Backstrom
96 193 P43 · P66 · P85 9·10193-1 Sep 17, 2008 Robert Backstrom
97 193 P36 · P60 · P98 5·10194-9 Oct 18, 2008 Wataru Sakai
98 193 P52 · P141 10360+1 Jul 4, 2005 Tomoya Adachi
99 192 P65 · P128 (34·10193+11)/9 Feb 10, 2009 Wataru Sakai
100 192 P64 · P64 · P66 (13·10193+23)/9 Oct 1, 2008 Robert Backstrom

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
1 148 P63 · P85 (16·10220-61)/9 Dec 24, 2008 Serge Batalov
2 145 P52 · P93 4·10212+9 May 12, 2009 Markus Tervooren
3 144 P70 · P74 (64·10232+53)/9 Aug 13, 2008 Serge Batalov
4 140 P53 · P88 (16·10214-61)/9 Aug 4, 2008 Serge Batalov
5 140 P49 · P92 (26·10203+1)/9 Jun 11, 2009 Dmitry Domanov
6 140 P45 · P95 4·10200+7 Mar 6, 2008 Tyler Cadigan
7 139 P60 · P79 6·10199+1 Jul 10, 2008 Tyler Cadigan
8 138 P60 · P79 (10196+53)/9 Feb 25, 2009 Tyler Cadigan
9 138 P49 · P89 (10198+53)/9 Aug 1, 2008 Tyler Cadigan
10 138 P64 · P74 (7·10196-43)/9 May 9, 2008 Wataru Sakai
11 137 P49 · P88 (55·10199+53)/9 Jun 5, 2009 Sinkiti Sibata
12 137 P47 · P91 2·10207-1 Jun 17, 2009 Andreas Tete
13 136 P59 · P78 9·10249-1 May 29, 2009 matsui
14 135 P49 · P86 (4·10195-1)/3 Nov 17, 2007 Jo Yeong Uk
15 134 P47 · P88 8·10190-1 May 28, 2008 Jo Yeong Uk
16 134 P50 · P84 8·10193-9 May 23, 2009 Sinkiti Sibata
17 133 P43 · P91 (2·10200+61)/9 May 15, 2009 Sinkiti Sibata
18 133 P45 · P88 (25·10190-7)/9 Mar 26, 2009 Andreas Tete
19 132 P51 · P81 6·10194+1 Apr 27, 2009 Tyler Cadigan
20 131 P60 · P72 (22·10186-31)/9 Jul 29, 2008 Sinkiti Sibata
21 131 P44 · P87 (52·10188+11)/9 Apr 21, 2009 Andreas Tete
22 130 P46 · P84 (4·10203-1)/3 May 5, 2009 Sinkiti Sibata
23 130 P60 · P70 (85·10186+41)/9 Feb 15, 2009 Erik Branger
24 129 P61 · P69 3·10191+1 Jul 3, 2008 matsui
25 128 P46 · P83 4·10187-9 Nov 11, 2008 Sinkiti Sibata
26 128 P63 · P66 2·10191+3 May 7, 2009 Ignacio Santos
27 127 P39 · P89 8·10187-1 Apr 24, 2008 Jo Yeong Uk
28 127 P43 · P84 (73·10191-1)/9 May 6, 2009 Ignacio Santos
29 126 P60 · P67 (64·10309-1)/9 Feb 16, 2009 Wataru Sakai
30 126 P44 · P82 (4·10241-1)/3 Mar 25, 2009 Ignacio Santos
31 126 P50 · P76 (16·10182-7)/9 Apr 22, 2008 Wataru Sakai
32 126 P55 · P71 (5·10185-23)/9 Aug 10, 2008 Serge Batalov
33 125 P57 · P68 (49·10181+23)/9 May 4, 2009 Ignacio Santos
34 125 P56 · P70 4·10199+9 Feb 20, 2009 Erik Branger
35 125 P58 · P68 (31·10168+41)/9 Mar 9, 2009 Andreas Tete
36 125 P49 · P76 (16·10189-7)/9 May 26, 2009 Dmitry Domanov
37 125 P46 · P79 (10181+17)/9 Sep 30, 2008 Justin Card
38 124 P57 · P68 2·10177-3 May 17, 2009 Dmitry Domanov
39 124 P43 · P82 (35·10181-53)/9 Nov 19, 2008 Erik Branger
40 124 P59 · P65 (5·10198-11)/3 Aug 4, 2008 Tyler Cadigan
41 124 P62 · P63 8·10197+9 Jun 1, 2008 Tyler Cadigan
42 124 P59 · P65 (5·10190+13)/9 May 30, 2008 Tyler Cadigan
43 124 P61 · P63 (35·10176-71)/9 Apr 23, 2009 Ignacio Santos
44 123 P59 · P65 3·10179-1 Feb 16, 2008 matsui
45 123 P53 · P71 6·10192+7 May 28, 2008 Tyler Cadigan
46 123 P51 · P72 (17·10179-11)/3 May 21, 2009 Sinkiti Sibata
47 123 P48 · P75 (29·10199-11)/9 Apr 1, 2009 Andreas Tete
48 123 P49 · P75 (53·10179-17)/9 May 18, 2009 Erik Branger
49 123 P59 · P64 (16·10190-61)/9 Feb 12, 2008 Tyler Cadigan
50 123 P58 · P65 (25·10157+11)/9 Sep 22, 2008 Sinkiti Sibata
51 123 P50 · P73 (37·10194+71)/9 Apr 28, 2009 Ignacio Santos
52 122 P40 · P83 (8·10173-11)/3 Apr 22, 2009 Ignacio Santos
53 122 P41 · P82 (44·10200-53)/9 Apr 25, 2009 Sinkiti Sibata
54 122 P51 · P72 7·10187-9 May 12, 2009 Dmitry Domanov
55 122 P41 · P82 (26·10176-71)/9 Oct 1, 2008 Sinkiti Sibata
56 122 P39 · P41 · P43 (2·10188-17)/3 May 31, 2007 Sinkiti Sibata
57 122 P40 · P82 (49·10173-31)/9 Apr 21, 2009 Ignacio Santos
58 122 P39 · P84 (25·10173+11)/9 Apr 21, 2009 Ignacio Santos
59 122 P51 · P71 (52·10183+11)/9 Apr 20, 2009 Ignacio Santos
60 122 P54 · P68 (37·10186+17)/9 Apr 19, 2009 Ignacio Santos
61 122 P44 · P79 (32·10194+13)/9 Apr 18, 2009 Ignacio Santos
62 122 P55 · P67 (85·10185+41)/9 Aug 12, 2008 Serge Batalov
63 122 P45 · P77 (19·10176+53)/9 Aug 13, 2008 Serge Batalov
64 122 P46 · P76 (2·10178+61)/9 Mar 12, 2008 Robert Backstrom
65 122 P61 · P61 (8·10178-53)/9 Aug 12, 2008 Serge Batalov
66 122 P51 · P71 5·10180-7 Jul 11, 2008 Sinkiti Sibata
67 122 P44 · P78 (28·10176+71)/9 Apr 17, 2009 Ignacio Santos
68 121 P33 · P45 · P45 (47·10187+61)/9 Apr 16, 2009 Ignacio Santos
69 121 P57 · P64 (37·10178+17)/9 Apr 16, 2009 Ignacio Santos
70 121 P54 · P68 5·10188+9 Apr 22, 2009 Sinkiti Sibata
71 121 P59 · P63 (43·10180+11)/9 Apr 15, 2009 Jeff Gilchrist
72 121 P56 · P66 (16·10199-43)/9 Aug 4, 2008 Serge Batalov
73 121 P44 · P78 (47·10182+61)/9 Apr 15, 2009 Jeff Gilchrist
74 121 P44 · P78 (43·10177-61)/9 Apr 14, 2009 Jeff Gilchrist
75 121 P38 · P84 8·10185+9 Nov 28, 2008 Serge Batalov
76 121 P50 · P71 (35·10190+1)/9 Feb 1, 2009 Ignacio Santos
77 121 P40 · P81 (55·10200+17)/9 May 3, 2009 Sinkiti Sibata
78 121 P59 · P62 5·10179-7 Sep 28, 2007 Sinkiti Sibata
79 120 P44 · P77 (71·10182-17)/9 Jan 4, 2007 Alexander Mkrtychyan
80 120 P54 · P67 (2·10197+7)/9 Dec 4, 2006 Tyler Cadigan
81 120 P48 · P73 (4·10179-1)/3 Nov 15, 2006 Tyler Cadigan
82 120 P51 · P70 (14·10170-23)/9 Dec 4, 2008 Jo Yeong Uk
83 120 P38 · P83 10187+9 Oct 7, 2006 Tyler Cadigan
84 120 P58 · P63 (22·10189-1)/3 Dec 13, 2006 Tyler Cadigan
85 120 P29 · P43 · P49 10177+9 Aug 11, 2007 Sinkiti Sibata
86 120 P43 · P78 (86·10171+31)/9 Jan 10, 2008 Jo Yeong Uk
87 120 P44 · P76 (5·10172+31)/9 Aug 15, 2008 Jo Yeong Uk
88 120 P57 · P64 (8·10189-71)/9 Dec 21, 2006 Tyler Cadigan
89 120 P54 · P66 (25·10192+11)/9 Oct 4, 2008 Jo Yeong Uk
90 120 P59 · P62 (25·10165+11)/9 Sep 23, 2008 Sinkiti Sibata
91 120 P59 · P61 (49·10161-31)/9 Apr 5, 2009 Andreas Tete
92 120 P35 · P85 (28·10165+71)/9 Nov 26, 2008 Jo Yeong Uk
93 120 P57 · P64 (25·10172+11)/9 Oct 1, 2008 Jo Yeong Uk
94 120 P51 · P69 (56·10186+61)/9 May 29, 2009 Jo Yeong Uk
95 120 P54 · P66 (49·10199-13)/9 Mar 24, 2009 Ignacio Santos
96 120 P51 · P69 (47·10170+43)/9 Mar 24, 2009 Robert Backstrom
97 120 P59 · P61 9·10184+1 May 23, 2007 Sinkiti Sibata
98 120 P38 · P82 (61·10169-7)/9 Oct 6, 2007 Bryan Koen

3. Top 100 large factors found by NFS

  digits prime factor from when who
1 103 (14·10205-11)/3 Feb 22, 2009 Wataru Sakai
2 102 (37·10204+17)/9 Feb 5, 2009 Robert Backstrom
3 100 (4·10207-1)/3 Jul 19, 2008 Serge Batalov
4 100 4·10209+1 Feb 17, 2009 Serge Batalov
5 97 6·10198+1 Mar 14, 2009 matsui
6 96 (2·10197+1)/3 Nov 1, 2008 Wataru Sakai
7 96 (25·10195-61)/9 Oct 8, 2008 Tyler Cadigan
8 94 (17·10192+1)/9 Aug 25, 2008 Robert Backstrom
9 93 (41·10203+31)/9 Feb 20, 2009 Robert Backstrom
10 92 (68·10192+13)/9 Sep 1, 2008 Robert Backstrom
11 91 (22·10198-1)/3 May 15, 2009 Robert Backstrom
12 90 (26·10183-17)/9 Oct 29, 2008 Jo Yeong Uk
13 90 (47·10191+7)/9 Jun 28, 2009 Wataru Sakai
14 90 (38·10193+43)/9 Jan 8, 2009 Jo Yeong Uk
15 90 (5·10198-17)/3 Dec 1, 2008 Jo Yeong Uk
16 89 (4·10190-31)/9 Nov 2, 2007 Jo Yeong Uk
17 89 (4·10192-13)/9 Feb 19, 2008 Jo Yeong Uk
18 89 9·10185+7 Nov 22, 2008 Wataru Sakai
19 89 (4·10188-31)/9 Oct 17, 2007 Jo Yeong Uk
20 88 (82·10185-1)/9 Jun 15, 2008 Robert Backstrom
21 88 (19·10196+71)/9 Jan 19, 2009 Wataru Sakai
22 88 5·10194+9 Sep 6, 2008 Jo Yeong Uk
23 88 (5·10179-17)/3 Jul 9, 2007 Robert Backstrom
24 87 (10183+53)/9 Jan 23, 2009 Tyler Cadigan
25 87 (82·10198-1)/9 May 19, 2009 Robert Backstrom
26 87 2·10216-1 Jul 5, 2009 Robert Backstrom
27 87 4·10198+9 Feb 18, 2009 matsui
28 86 4·10180+3 Jun 17, 2007 Sinkiti Sibata
29 86 (32·10190+31)/9 Jun 16, 2009 Wataru Sakai
30 86 (11·10181+43)/9 Mar 5, 2008 Jo Yeong Uk
31 86 (41·10203-23)/9 Mar 16, 2009 Robert Backstrom
32 85 10183+3 Mar 3, 2008 Robert Backstrom
33 84 6·10192-1 Mar 16, 2009 matsui
34 84 (16·10181-61)/9 Sep 9, 2007 Robert Backstrom
35 84 (25·10181-43)/9 Sep 30, 2008 Robert Backstrom
36 84 (8·10196+1)/9 Apr 27, 2009 Jo Yeong Uk
37 84 6·10200+1 Jul 4, 2008 Serge Batalov
38 84 (52·10175+11)/9 Apr 18, 2009 Ignacio Santos
39 84 4·10183-9 Nov 12, 2008 Serge Batalov
40 84 (56·10190-11)/9 May 24, 2009 Robert Backstrom
41 84 (29·10184+43)/9 Dec 20, 2008 Robert Backstrom
42 83 (52·10180+11)/9 Apr 24, 2009 Ignacio Santos
43 83 (67·10175+23)/9 Oct 9, 2008 Jo Yeong Uk
44 83 (44·10180+1)/9 Mar 12, 2009 Sinkiti Sibata
45 83 (26·10170-53)/9 Oct 8, 2008 Serge Batalov
46 83 (10192+53)/9 May 18, 2008 Wataru Sakai
47 83 (38·10186+61)/9 Jan 12, 2009 Sinkiti Sibata
48 82 (5·10171-23)/9 Oct 16, 2008 Robert Backstrom
49 82 (23·10188+13)/9 Nov 4, 2008 Wataru Sakai
50 82 (16·10177+11)/9 Sep 9, 2008 Robert Backstrom
51 82 (37·10173+17)/9 Dec 21, 2008 Jo Yeong Uk
52 82 3·10198+1 Sep 8, 2008 Serge Batalov
53 82 (17·10185-53)/9 Jun 3, 2008 Robert Backstrom
54 82 (14·10180+1)/3 Mar 28, 2009 Ignacio Santos
55 82 (23·10174+1)/3 Mar 1, 2007 Tyler Cadigan
56 81 (37·10167-1)/9 May 14, 2007 Robert Backstrom
57 81 (2·10185+1)/3 Aug 5, 2008 matsui
58 81 (85·10180+41)/9 Apr 26, 2009 Ignacio Santos
59 81 (52·10181-7)/9 Sep 20, 2007 Robert Backstrom
60 81 (67·10166+23)/9 Jan 12, 2008 Robert Backstrom
61 81 (2·10178+1)/3 Jul 17, 2008 Wataru Sakai
62 81 8·10176+9 Feb 24, 2008 matsui
63 81 (43·10184-7)/9 Jan 6, 2009 Tyler Cadigan
64 80 6·10180+1 Jul 5, 2009 Tyler Cadigan
65 80 (5·10175+1)/3 Jun 15, 2008 Kenji Ibusuki
66 80 (29·10198+61)/9 Nov 30, 2008 Wataru Sakai
67 80 (19·10175+71)/9 Jun 18, 2008 Jo Yeong Uk
68 80 (13·10171-1)/3 Jun 7, 2007 Robert Backstrom
69 80 (25·10186-43)/9 Oct 14, 2008 Robert Backstrom
70 80 2·10190-1 May 24, 2009 Jo Yeong Uk
71 80 (22·10203+41)/9 Sep 10, 2008 Serge Batalov
72 79 (8·10164-71)/9 Aug 12, 2007 Robert Backstrom
73 79 5·10164+9 Dec 18, 2007 Jo Yeong Uk
74 79 (13·10165-7)/3 Dec 25, 2008 Serge Batalov
75 79 5·10181-7 Sep 28, 2008 Robert Backstrom
76 79 (37·10166+17)/9 Dec 11, 2008 Serge Batalov
77 79 (13·10171+23)/9 Mar 12, 2008 Jo Yeong Uk
78 79 (25·10169-43)/9 Sep 15, 2008 Serge Batalov
79 79 (64·10177+53)/9 Sep 9, 2008 Robert Backstrom
80 79 (13·10203+17)/3 Feb 8, 2009 Wataru Sakai
81 79 (5·10165-11)/3 Apr 14, 2008 Robert Backstrom
82 79 8·10170-3 Jun 8, 2008 matsui
83 79 7·10180+9 Feb 8, 2009 Wataru Sakai
84 79 (4·10168+23)/9 Jun 13, 2008 Robert Backstrom
85 79 (4·10164-13)/9 Jun 26, 2007 Robert Backstrom
86 78 5·10183-1 Jun 9, 2009 Wataru Sakai
87 78 (83·10166+61)/9 Jan 17, 2008 Robert Backstrom
88 78 (5·10197-11)/3 May 22, 2009 Robert Backstrom
89 78 (8·10178+7)/3 Nov 12, 2007 Jo Yeong Uk
90 78 (13·10172+41)/9 Jun 27, 2008 Robert Backstrom
91 78 (8·10166-11)/3 Sep 2, 2008 Robert Backstrom
92 78 (28·10179+71)/9 Nov 28, 2008 Robert Backstrom
93 78 (19·10185+11)/3 Jun 28, 2009 Robert Backstrom
94 78 (29·10191-11)/9 Nov 23, 2008 Kenji Ibusuki
95 78 (44·10173-71)/9 Mar 5, 2009 Serge Batalov
96 78 (19·10171+53)/9 Jun 7, 2008 Robert Backstrom
97 78 10181-9 May 12, 2008 Wataru Sakai
98 77 (17·10156-53)/9 May 5, 2008 Robert Backstrom
99 77 (47·10168-11)/9 Mar 25, 2009 Ignacio Santos
100 77 4·10219-9 May 1, 2009 Robert Backstrom

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 51 (32·10205+13)/9 110000000 3446144840 Jun 15, 2009 Wataru Sakai
5 51 (4·10163+17)/3 11000000 861666340 Aug 21, 2008 nuggetprime
6 50 (43·10190+11)/9 11000000 1301257518 Feb 24, 2009 Wataru Sakai
7 49 (49·10164+41)/9 3316000 27217913 Mar 28, 2009 Robert Backstrom
8 49 (7·10188-43)/9 43000000 3499185670 May 22, 2009 Dmitry Domanov
9 49 (13·10169+17)/3 20000000 2331681453 Mar 6, 2009 Robert Backstrom
10 49 (4·10229-1)/3 11000000 2062470196 Sep 6, 2008 Serge Batalov
11 49 (5·10176+1)/3 43000000 3476594416 Mar 14, 2009 Wataru Sakai
12 49 (41·10150-23)/9 3000000 4014584566 Jan 29, 2009 Serge Batalov
13 49 (2·10175+1)/3 3000000 1712934266 Oct 4, 2008 Jo Yeong Uk
14 48 (86·10192+31)/9 44000000 896044946 Aug 4, 2006 JMB
15 48 (67·10172+23)/9 7600000 3670869563 Oct 19, 2008 Robert Backstrom
16 48 10192+9 11000000 413694509 Oct 7, 2007 Jo Yeong Uk
17 48 (73·10192-1)/9 43000000 1770093265 May 22, 2009 Dmitry Domanov
18 48 (2·10171-17)/3 3000000 1868644906 Jul 5, 2009 Wataru Sakai
19 47 (64·10215+53)/9 11000000 1048397889 Jul 7, 2008 Serge Batalov
20 47 (52·10169-61)/9 3000000 616297871 Jun 15, 2009 Wataru Sakai
21 47 (22·10155+41)/9 3870000 219387156 Jul 22, 2008 Robert Backstrom
22 47 (25·10171-61)/9 3000000 3132305148 Sep 4, 2008 Serge Batalov
23 47 10196+9 11000000 2570867251 Nov 11, 2006 Wataru Sakai
24 47 8·10206-1 3000000 1065804300 Aug 1, 2008 Sinkiti Sibata
25 47 (32·10169+31)/9 3000000 1504946988 May 28, 2009 Wataru Sakai
26 47 (10199+17)/9 11000000 1005177743 Feb 14, 2009 Serge Batalov
27 47 (43·10245-7)/9 3000000 45451499 Jan 28, 2009 Serge Batalov
28 47 (25·10165-7)/9 3000000 1593296484 Jul 25, 2007 JMB
29 47 (64·10234+53)/9 10757000 1312137675 Dec 3, 2007 Robert Backstrom
30 47 (22·10179-13)/9 3000000 1048915276 Aug 18, 2008 Sinkiti Sibata
31 47 (55·10165-1)/9 3000000 1761471762 Mar 7, 2008 Jo Yeong Uk
32 47 (64·10297-1)/9 43000000 3599812418 Feb 9, 2009 Serge Batalov
33 47 (43·10190+11)/9 43000000 1827407922 Feb 24, 2009 Wataru Sakai
34 47 (64·10227-1)/9 11000000 2234649575 Jan 21, 2009 Jo Yeong Uk
35 46 (53·10183+1)/9 1000000 761703653 Apr 23, 2009 Makoto Kamada
36 46 (68·10169+13)/9 3744000 1706818246 Jul 27, 2008 Robert Backstrom
37 46 (4·10239-1)/3 11000000 4266053392 Jul 8, 2009 Dmitry Domanov
38 46 (28·10167+71)/9 3000000 3590283382 Nov 13, 2008 Jo Yeong Uk
39 46 4·10222+1 11000000 2238052366 Nov 7, 2008 Serge Batalov
40 46 8·10190-9 3000000 3143978648 Apr 21, 2009 Wataru Sakai
41 46 (10203-7)/3 43000000 4169885631 May 25, 2009 Wataru Sakai
42 46 4·10194+1 11000000 632711195 Jul 27, 2007 Wataru Sakai
43 46 (49·10168-31)/9 3000000 408812994 May 29, 2009 Wataru Sakai
44 46 (16·10199-7)/9 11000000 540716867 Jun 3, 2009 Dmitry Domanov
45 46 (64·10333-1)/9 3000000 3772275269 May 26, 2009 Jo Yeong Uk
46 46 (44·10132-53)/9 20000000 2504866877 Mar 8, 2009 Robert Backstrom
47 45 (8·10186-71)/9 6016000 513170549 Oct 18, 2008 Robert Backstrom
48 45 (32·10165-41)/9 2114000 2117395774 Nov 25, 2008 Robert Backstrom
49 45 (35·10157-17)/9 3000000 2131351972 Dec 7, 2008 Serge Batalov
50 45 8·10167+3 1000000 127447873 Jul 18, 2008 Jo Yeong Uk
51 45 (55·10164+17)/9 4640000 1859142445 May 2, 2009 Robert Backstrom
52 45 (4·10189-1)/3 3000000 4103031508 Mar 27, 2007 suberi
53 45 5·10188+3 3000000 2524047625 Jul 4, 2008 suberi
54 45 (14·10197-11)/3 3000000 4276860758 Feb 9, 2009 Serge Batalov
55 45 (64·10202+53)/9 11000000 49343718 Jun 13, 2005 Wataru Sakai
56 45 (2·10171+61)/9 3000000 1058474660 Feb 22, 2009 Serge Batalov
57 45 (13·10177+41)/9 7318000 2046770327 Apr 2, 2008 Robert Backstrom
58 45 (46·10153+17)/9 3000000 1271141060 Mar 9, 2009 Robert Backstrom
59 45 (38·10153+7)/9 3000000 1546770427 Dec 18, 2008 Serge Batalov
60 45 (86·10148+31)/9 2728500 679331778 Sep 22, 2003 Robert Backstrom
61 45 2·10191+9 3000000 3278687019 Nov 16, 2007 Jo Yeong Uk
62 45 (29·10167+61)/9 3000000 1566598641 Nov 18, 2008 Serge Batalov
63 45 (64·10215+53)/9 43000000 1801021090 Jul 7, 2008 Serge Batalov
64 45 (52·10175-7)/9 11000000 4191283557 Oct 11, 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 97 6·10198+1 Mar 14, 2009 matsui
2 84 (8·10196+1)/9 Apr 27, 2009 Jo Yeong Uk
3 78 (44·10173-71)/9 Mar 5, 2009 Serge Batalov
4 76 (79·10169-7)/9 Oct 1, 2008 Robert Backstrom
5 69 (22·10139-1)/3 May 5, 2005 Greg Childers
6 69 (28·10146-1)/9 Apr 19, 2005 Sinkiti Sibata
7 68 (34·10137+11)/9 Dec 3, 2008 Serge Batalov
8 67 (19·10163+71)/9 Jul 13, 2008 Robert Backstrom
9 66 (5·10159-41)/9 Oct 8, 2007 Jo Yeong Uk
10 65 (22·10163-13)/9 Jul 10, 2008 Robert Backstrom
11 65 (16·10145-43)/9 Apr 19, 2008 Robert Backstrom
12 64 (13·10193+23)/9 Oct 1, 2008 Robert Backstrom
13 62 (23·10184+13)/9 Sep 10, 2008 Sinkiti Sibata
14 62 (14·10145+13)/9 Mar 29, 2008 Jo Yeong Uk
15 62 5·10126+9 Dec 16, 2007 Jo Yeong Uk
16 62 (22·10125-1)/3 Oct 24, 2004 Sander Hoogendoorn
17 61 (8·10178-53)/9 Aug 12, 2008 Serge Batalov
18 61 (4·10148+41)/9 Jan 31, 2005 Samuel Chong
19 61 (46·10174-1)/9 Aug 8, 2008 Serge Batalov
20 61 (8·10120+7)/3 Oct 20, 2007 Jo Yeong Uk
21 60 5·10118-9 Dec 4, 2007 Jo Yeong Uk
22 59 (43·10160-7)/9 Aug 1, 2007 Sinkiti Sibata
23 58 (67·10143+23)/9 Nov 17, 2004 Greg Childers
24 57 (7·10142+11)/9 Apr 28, 2005 Makoto Kamada
25 57 (22·10136+23)/9 Jul 10, 2008 Serge Batalov
26 57 (53·10149-71)/9 Apr 19, 2009 Robert Backstrom
27 56 4·10154+9 Dec 10, 2007 Robert Backstrom
28 56 (5·10113+7)/3 Sep 26, 2007 Jo Yeong Uk
29 55 (4·10143+41)/9 Jan 21, 2005 Samuel Chong
30 55 (41·10109+31)/9 Feb 3, 2009 Erik Branger
31 55 (5·10134-11)/3 Apr 12, 2008 Sinkiti Sibata
32 55 (25·10223-1)/3 Nov 7, 2008 Serge Batalov
33 54 3·10196-1 Oct 3, 2008 Jo Yeong Uk
34 53 (22·10143-31)/9 Jun 27, 2008 Sinkiti Sibata
35 53 (58·10139-13)/9 Jun 29, 2009 Sinkiti Sibata
36 53 (4·10110-31)/9 May 22, 2004 Naoki Yamamoto
37 52 8·10107+3 Aug 9, 2007 Robert Backstrom
38 52 (16·10144-43)/9 Apr 17, 2008 Robert Backstrom
39 52 (19·10163+53)/9 Jun 3, 2008 Jo Yeong Uk
40 52 (88·10152-7)/9 Jun 22, 2006 Sinkiti Sibata
41 51 (10222+17)/9 Jul 9, 2009 Dmitry Domanov
42 51 (64·10122+53)/9 Jul 2, 2003 Robert Backstrom
43 51 (32·10111-41)/9 Nov 22, 2008 Sinkiti Sibata
44 50 (31·10147+41)/9 Nov 25, 2008 Sinkiti Sibata

6. Unprovable near-repdigit PRPs

Unprovable near-repdigit PRPs which have 20000 digits at least.

  digits PRP when searched who searched
1 84239 (2·1084239+1)/3 Jul 6, 2009 Serge Batalov
2 56545 (19·1056544-1)/9 Mar 13, 2009 Serge Batalov
3 56454 (55·1056453-1)/9 Mar 12, 2009 Serge Batalov
4 55544 (2·1055544+1)/3 Jun 17, 2009 Serge Batalov
5 53718 (1053718-7)/3 Oct 17, 2004 Makoto Kamada
6 53411 (8·1053411+1)/9 Dec 18, 2008 Serge Batalov
7 53050 (19·1053049-1)/9 Mar 9, 2009 Serge Batalov
8 52764 (61·1052763-7)/9 Feb 27, 2009 Serge Batalov
9 43754 (25·1043753-1)/3 Jan 18, 2009 Serge Batalov
10 43272 (61·1043271-7)/9 Jan 2008 Maksym Voznyy
11 40890 (16·1040889-1)/3 Jan 24, 2009 Serge Batalov
12 39606 (2·1039606+1)/3 Jun 20, 2009 Serge Batalov
13 39464 (5·1039464+31)/9 Jan 6, 2009 Serge Batalov
14 38690 (5·1038690+31)/9 Jan 6, 2009 Serge Batalov
15 37597 1037597-9 Jan 2008 Jason Earls
16 35925 1035925-9 Jan 2008 Jason Earls
17 35754 (16·1035753-1)/3 Jan 23, 2009 Serge Batalov
18 31632 (61·1031631-7)/9 Jan 2008 Maksym Voznyy
19 30977 (61·1030976-7)/9 Jan 2008 Maksym Voznyy
20 30178 (1030178-7)/3 Mar 20, 2004 Makoto Kamada
21 26045 1026045-3 Nov 2002 Henri Lifchitz
22 25324 (1025324-7)/3 Feb 7, 2004 Makoto Kamada
23 24549 (1024549-7)/3 Feb 7, 2004 Makoto Kamada
24 24253 (1024253-7)/3 Feb 7, 2004 Makoto Kamada
25 23365 (1023365-7)/3 Feb 7, 2004 Makoto Kamada
26 22973 (1022973+53)/9 Oct 2008 Lelio R Paula
27 22718 (1022718-7)/3 Feb 6, 2004 Makoto Kamada
28 22094 (61·1022093-7)/9 Jan 6, 2008 Maksym Voznyy
29 21873 1021873-3 Nov 2002 Henri Lifchitz
30 20016 (1020016+17)/9 Oct 2008 Lelio R Paula

7. Unprovable quasi-repdigit PRPs

Unprovable quasi-repdigit PRPs except Plateau and Depression PRPs, which have 20000 digits at least.

  digits PRP when searched who searched
1 96744 (28·1096743+71)/9 Dec 8, 2008 Serge Batalov
2 59136 (28·1059135+53)/9 Nov 19, 2008 Serge Batalov
3 56899 (35·1056898-17)/9 Feb 28, 2009 Serge Batalov
4 50712 1050711+7 Dec 2007 Jason Earls
5 48110 1048109+9 Dec 2007 Jason Earls
6 43187 1043186+9 Dec 2007 Jason Earls
7 40744 (76·1040743-31)/9 Feb 27, 2009 Serge Batalov
8 39856 (38·1039855+61)/9 Oct 15, 2008 Serge Batalov
9 35991 (31·1035990+23)/9 Feb 23, 2009 Serge Batalov
10 35428 (76·1035427-31)/9 Feb 25, 2009 Serge Batalov
11 31811 1031810+9 Oct 14, 2006 Dirk Augustin
12 30222 1030221+7 Nov 2007 Jason Earls
13 27223 (19·1027222+53)/9 Oct 15, 2008 Serge Batalov
14 26928 1026927+3 Dec 2007 Jason Earls
15 26264 (58·1026263-31)/9 Nov 2, 2008 Serge Batalov
16 26195 (67·1026194-13)/9 Oct 15, 2008 Serge Batalov
17 23637 1023636+7 Nov 2007 Jason Earls
18 22049 (13·1022048-7)/3 Feb 23, 2009 Serge Batalov
19 21718 1021717+7 Feb 2004 Thomas Masser
20 20892 7·1020891+9 Jan 12, 2008 Sinkiti Sibata
21 20865 (64·1020864+17)/9 Oct 14, 2008 Serge Batalov
22 20764 (28·1020763+71)/9 Nov 17, 2008 Serge Batalov

See also Plateau and Depression Primes maintained by Patrick De Geest.

8. Quasi-repdigit twin primes

Quasi-repdigit twin primes which have 100 digits at least.

  digits p, p+2 when searched who searched when certified who certified
1 3884 (13·103883+23)/9
(13·103883+41)/9
Dec 17, 2004 Makoto Kamada May 27, 2006 Tyler Cadigan
2 413 (4·10412+11)/3
(4·10412+17)/3
Sep 20, 2004 Makoto Kamada Dec 7, 2004 Julien Peter Benney