counterSince June 16, 2000STUDIO KAMADAEnglish text only.
Factorizations
Records2008-07-26(Sat) 17:36

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
3 200 P84 · P116 6·10200+1 Jul 4, 2008 Serge Batalov
4 197 P67 · P131 6·10196+1 Jul 21, 2008 Wataru Sakai
5 196 P56 · P140 (5·10195+7)/3 May 17, 2008 Sinkiti Sibata
6 195 P76 · P120 5·10194-1 Sep 20, 2007 Sinkiti Sibata
7 193 P52 · P141 10360+1 Jul 4, 2005 Tomoya Adachi
8 192 P89 · P104 (4·10192-13)/9 Feb 19, 2008 Jo Yeong Uk
9 192 P51 · P141 (2·10192-11)/9 Jan 30, 2007 Wataru Sakai
10 192 P51 · P141 (13·10191+41)/9 Jul 15, 2008 Jo Yeong Uk
11 191 P41 · P150 (14·10190-41)/9 Aug 5, 2007 Sinkiti Sibata
12 191 P83 · P108 (10192+53)/9 May 18, 2008 Wataru Sakai
13 190 P89 · P101 (4·10190-31)/9 Nov 2, 2007 Jo Yeong Uk
14 189 P47 · P51 · P93 (31·10189-13)/9 Jul 26, 2008 Wataru Sakai
15 189 P77 · P112 (4·10189-7)/3 Jun 16, 2006 Alexander Mkrtychyan
16 188 P37 · P67 · P86 5·10190-7 Jul 25, 2008 Kenji Ibusuki
17 188 P89 · P100 (4·10188-31)/9 Oct 17, 2007 Jo Yeong Uk
18 187 P59 · P129 8·10186-7 Dec 7, 2007 Jo Yeong Uk
19 187 P77 · P111 (32·10186-23)/9 Jul 7, 2007 Sinkiti Sibata
20 186 P53 · P133 (10186+71)/9 Jun 16, 2006 Alexander Mkrtychyan
21 186 P48 · P138 2·10186-3 Apr 29, 2008 matsui
22 185 P44 · P142 (7·10185-43)/9 May 28, 2005 Greg Childers
23 185 P40 · P43 · P43 · P61 (46·10186-1)/9 Jan 12, 2008 Sinkiti Sibata
24 185 P62 · P124 3·10184-1 Sep 12, 2007 Jo Yeong Uk
25 185 P45 · P66 · P75 (13·10184+23)/9 Mar 28, 2008 Robert Backstrom
26 184 P68 · P117 4·10185+3 Nov 21, 2007 Sinkiti Sibata
27 184 P45 · P139 (88·10186-7)/9 May 31, 2008 Wataru Sakai
28 184 P67 · P117 10184+3 Apr 23, 2008 Robert Backstrom
29 184 P88 · P96 (82·10185-1)/9 Jun 15, 2008 Robert Backstrom
30 184 P42 · P60 · P82 (28·10184+17)/9 Apr 30, 2008 Robert Backstrom
31 183 P59 · P62 · P63 10183-9 Oct 9, 2006 Wataru Sakai
32 183 P82 · P102 (17·10185-53)/9 Jun 3, 2008 Robert Backstrom
33 183 P48 · P48 · P87 (86·10182+31)/9 Sep 25, 2007 Robert Backstrom
34 182 P62 · P121 10182-3 Aug 25, 2007 Jo Yeong Uk
35 182 P48 · P135 8·10181-7 Nov 22, 2007 Jo Yeong Uk
36 182 P50 · P59 · P74 (7·10181-1)/3 Jul 27, 2007 Jo Yeong Uk
37 182 P86 · P96 (11·10181+43)/9 Mar 5, 2008 Jo Yeong Uk
38 182 P47 · P135 5·10182-3 Sep 12, 2007 Robert Backstrom
39 181 P85 · P97 10183+3 Mar 3, 2008 Robert Backstrom
40 181 P84 · P97 (16·10181-61)/9 Sep 9, 2007 Robert Backstrom
41 181 P41 · P140 (2·10184-17)/3 Mar 3, 2008 Robert Backstrom
42 181 P81 · P100 (52·10181-7)/9 Sep 20, 2007 Robert Backstrom
43 180 P76 · P105 7·10182+3 Jun 24, 2008 Sinkiti Sibata
44 180 P74 · P106 7·10179-3 Aug 13, 2007 Jo Yeong Uk
45 180 P86 · P94 4·10180+3 Jun 17, 2007 Sinkiti Sibata
46 180 P45 · P135 4·10179+9 Dec 10, 2007 Sinkiti Sibata
47 180 P63 · P118 6·10183-1 Jul 17, 2008 Wataru Sakai
48 179 P44 · P62 · P74 10179-3 Jan 1, 2006 Kenichiro Yamaguchi
49 179 P71 · P109 (55·10178-1)/9 May 16, 2007 Sinkiti Sibata
50 179 P46 · P62 · P72 10185-9 May 17, 2008 Wataru Sakai
51 179 P68 · P112 (31·10179-13)/9 May 17, 2008 matsui
52 179 P44 · P136 (79·10178-7)/9 Jul 17, 2008 Wataru Sakai
53 179 P76 · P104 (73·10178-1)/9 Jul 15, 2007 Robert Backstrom
54 179 P78 · P101 (8·10178+7)/3 Nov 12, 2007 Jo Yeong Uk
55 179 P88 · P91 (5·10179-17)/3 Jul 9, 2007 Robert Backstrom
56 179 P52 · P58 · P70 (19·10179+17)/9 Jun 20, 2008 Wataru Sakai
57 178 P54 · P55 · P70 3·10180+1 Mar 2, 2008 matsui
58 178 P45 · P133 (23·10178+1)/3 May 27, 2008 Sinkiti Sibata
59 178 P70 · P109 (14·10177+31)/9 May 9, 2008 Jo Yeong Uk
60 177 P38 · P40 · P101 (71·10176-17)/9 Apr 16, 2007 Sinkiti Sibata
61 177 P53 · P124 10179+7 Jun 9, 2007 Alexander Mkrtychyan
62 177 P42 · P136 (4·10177+41)/9 Jun 14, 2007 Jo Yeong Uk
63 177 P65 · P112 (13·10176+41)/9 Mar 24, 2008 Jo Yeong Uk
64 177 P81 · P96 (2·10178+1)/3 Jul 17, 2008 Wataru Sakai
65 176 P43 · P134 (16·10175-1)/3 Dec 15, 2004 Greg Childers
66 176 P80 · P96 (19·10175+71)/9 Jun 18, 2008 Jo Yeong Uk
67 176 P45 · P49 · P83 (14·10179+31)/9 Jul 26, 2008 matsui
68 175 P64 · P112 9·10174+1 Jun 5, 2007 Jo Yeong Uk
69 175 P82 · P94 (23·10174+1)/3 Mar 1, 2007 Tyler Cadigan
70 175 P69 · P106 8·10177-7 Apr 10, 2008 matsui
71 175 P45 · P131 6·10176+7 Jun 24, 2008 matsui
72 175 P38 · P137 (5·10174+1)/3 May 29, 2007 Jo Yeong Uk
73 175 P76 · P99 (25·10179-1)/3 Mar 28, 2008 Tyler Cadigan
74 174 P52 · P122 (4·10187-1)/3 Dec 3, 2007 Jo Yeong Uk
75 174 P76 · P98 (8·10175-71)/9 Jul 6, 2008 Wataru Sakai
76 174 P66 · P108 (7·10174-61)/9 Jul 9, 2007 Robert Backstrom
77 174 P35 · P139 8·10175-3 Mar 22, 2008 matsui
78 174 P66 · P108 (4·10174+23)/9 Jul 9, 2007 Robert Backstrom
79 173 P70 · P104 (22·10173+41)/9 Jul 22, 2008 Sinkiti Sibata
80 173 P46 · P128 (14·10175-41)/9 Jan 29, 2007 Sinkiti Sibata
81 173 P80 · P93 (5·10175+1)/3 Jun 15, 2008 Kenji Ibusuki
82 173 P81 · P93 8·10176+9 Feb 24, 2008 matsui
83 173 P38 · P57 · P79 (19·10173+17)/9 Jun 20, 2008 Robert Backstrom
84 172 P62 · P111 (22·10173-31)/9 Jul 7, 2008 Robert Backstrom
85 172 P68 · P104 (16·10173-1)/3 Jun 21, 2007 Robert Backstrom
86 172 P48 · P125 6·10171+1 Apr 22, 2007 Jo Yeong Uk
87 172 P47 · P51 · P75 4·10175+1 Feb 8, 2008 matsui
88 172 P43 · P130 (2·10172+43)/9 Apr 1, 2007 Robert Backstrom
89 172 P79 · P93 (13·10171+23)/9 Mar 12, 2008 Jo Yeong Uk
90 172 P61 · P111 (10172+53)/9 Dec 15, 2005 Sinkiti Sibata
91 171 P50 · P57 · P65 7·10173+9 Jul 1, 2008 Robert Backstrom
92 171 P80 · P92 (13·10171-1)/3 Jun 7, 2007 Robert Backstrom
93 171 P50 · P56 · P66 2·10170-7 Aug 28, 2007 Jo Yeong Uk
94 171 P67 · P104 (5·10170-11)/3 Apr 14, 2008 Jo Yeong Uk
95 171 P42 · P129 (5·10173-41)/9 Jun 25, 2007 Robert Backstrom
96 171 P41 · P51 · P80 (11·10172+61)/9 Jun 2, 2008 Robert Backstrom
97 170 P64 · P107 8·10169-1 Oct 24, 2005 Makoto Kamada
98 170 P77 · P94 (5·10170+31)/9 Nov 3, 2005 Makoto Kamada
99 170 P45 · P53 · P74 (10175-7)/3 Jul 9, 2008 matsui
100 170 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
1 140 P45 · P95 4·10200+7 Mar 6, 2008 Tyler Cadigan
2 139 P60 · P79 6·10199+1 Jul 10, 2008 Tyler Cadigan
3 138 P64 · P74 (7·10196-43)/9 May 9, 2008 Wataru Sakai
4 135 P49 · P86 (4·10195-1)/3 Nov 17, 2007 Jo Yeong Uk
5 134 P47 · P88 8·10190-1 May 28, 2008 Jo Yeong Uk
6 129 P61 · P69 3·10191+1 Jul 3, 2008 matsui
7 127 P39 · P89 8·10187-1 Apr 24, 2008 Jo Yeong Uk
8 126 P50 · P76 (16·10182-7)/9 Apr 22, 2008 Wataru Sakai
9 124 P62 · P63 8·10197+9 Jun 1, 2008 Tyler Cadigan
10 124 P59 · P65 (5·10190+13)/9 May 30, 2008 Tyler Cadigan
11 123 P59 · P65 3·10179-1 Feb 16, 2008 matsui
12 123 P53 · P71 6·10192+7 May 28, 2008 Tyler Cadigan
13 123 P59 · P64 (16·10190-61)/9 Feb 12, 2008 Tyler Cadigan
14 122 P39 · P41 · P43 (2·10188-17)/3 May 31, 2007 Sinkiti Sibata
15 122 P46 · P76 (2·10178+61)/9 Mar 12, 2008 Robert Backstrom
16 122 P51 · P71 5·10180-7 Jul 11, 2008 Sinkiti Sibata
17 121 P59 · P62 5·10179-7 Sep 28, 2007 Sinkiti Sibata
18 120 P44 · P77 (71·10182-17)/9 Jan 4, 2007 Alexander Mkrtychyan
19 120 P54 · P67 (2·10197+7)/9 Dec 4, 2006 Tyler Cadigan
20 120 P48 · P73 (4·10179-1)/3 Nov 15, 2006 Tyler Cadigan
21 120 P38 · P83 10187+9 Oct 7, 2006 Tyler Cadigan
22 120 P58 · P63 (22·10189-1)/3 Dec 13, 2006 Tyler Cadigan
23 120 P29 · P43 · P49 10177+9 Aug 11, 2007 Sinkiti Sibata
24 120 P43 · P78 (86·10171+31)/9 Jan 10, 2008 Jo Yeong Uk
25 120 P57 · P64 (8·10189-71)/9 Dec 21, 2006 Tyler Cadigan
26 120 P59 · P61 9·10184+1 May 23, 2007 Sinkiti Sibata
27 120 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 (52·10181-7)/9 Sep 20, 2007 Robert Backstrom
17 81 (67·10166+23)/9 Jan 12, 2008 Robert Backstrom
18 81 (2·10178+1)/3 Jul 17, 2008 Wataru Sakai
19 81 8·10176+9 Feb 24, 2008 matsui
20 80 (5·10175+1)/3 Jun 15, 2008 Kenji Ibusuki
21 80 (19·10175+71)/9 Jun 18, 2008 Jo Yeong Uk
22 80 (13·10171-1)/3 Jun 7, 2007 Robert Backstrom
23 79 (8·10164-71)/9 Aug 12, 2007 Robert Backstrom
24 79 5·10164+9 Dec 18, 2007 Jo Yeong Uk
25 79 (13·10171+23)/9 Mar 12, 2008 Jo Yeong Uk
26 79 (5·10165-11)/3 Apr 14, 2008 Robert Backstrom
27 79 8·10170-3 Jun 8, 2008 matsui
28 79 (4·10168+23)/9 Jun 13, 2008 Robert Backstrom
29 79 (4·10164-13)/9 Jun 26, 2007 Robert Backstrom
30 78 (83·10166+61)/9 Jan 17, 2008 Robert Backstrom
31 78 (8·10178+7)/3 Nov 12, 2007 Jo Yeong Uk
32 78 (13·10172+41)/9 Jun 27, 2008 Robert Backstrom
33 78 (19·10171+53)/9 Jun 7, 2008 Robert Backstrom
34 78 10181-9 May 12, 2008 Wataru Sakai
35 77 (17·10156-53)/9 May 5, 2008 Robert Backstrom
36 77 10155+3 Jun 12, 2006 Wojciech Florek
37 77 (88·10165-7)/9 Jul 14, 2006 Sinkiti Sibata
38 77 (17·10165-53)/9 May 10, 2008 Robert Backstrom
39 77 8·10171-7 May 29, 2008 Robert Backstrom
40 77 (4·10189-7)/3 Jun 16, 2006 Alexander Mkrtychyan
41 77 (32·10186-23)/9 Jul 7, 2007 Sinkiti Sibata
42 77 4·10168-3 Jul 2, 2008 Robert Backstrom
43 77 (13·10165-1)/3 Oct 22, 2007 Robert Backstrom
44 77 (5·10162+1)/3 Apr 29, 2007 Robert Backstrom
45 77 4·10162+9 Dec 1, 2007 Robert Backstrom
46 77 5·10157+3 Jul 16, 2007 Robert Backstrom
47 77 (79·10200-7)/9 Dec 25, 2006 Alexander Mkrtychyan
48 77 (5·10170+31)/9 Nov 3, 2005 Makoto Kamada
49 76 7·10182+3 Jun 24, 2008 Sinkiti Sibata
50 76 (8·10175-71)/9 Jul 6, 2008 Wataru Sakai
51 76 (7·10173-61)/9 Jun 22, 2008 Wataru Sakai
52 76 (67·10165+23)/9 Nov 8, 2007 Robert Backstrom
53 76 (25·10179-1)/3 Mar 28, 2008 Tyler Cadigan
54 76 5·10194-1 Sep 20, 2007 Sinkiti Sibata
55 76 (73·10178-1)/9 Jul 15, 2007 Robert Backstrom
56 76 10157-9 Sep 27, 2004 Makoto Kamada
57 76 2·10155+3 May 18, 2007 Robert Backstrom
58 75 (11·10167+43)/9 Feb 7, 2008 Robert Backstrom
59 75 (85·10167+41)/9 Apr 26, 2008 Robert Backstrom
60 75 (7·10161+17)/3 Jun 21, 2008 Robert Backstrom
61 75 8·10158-7 Oct 17, 2007 Robert Backstrom
62 75 9·10154+7 Nov 7, 2007 Robert Backstrom
63 75 (7·10174+11)/9 Jun 20, 2008 Wataru Sakai
64 75 (17·10154+1)/9 May 12, 2008 Robert Backstrom
65 75 (17·10150-71)/9 Oct 6, 2004 Greg Childers
66 74 (61·10167-7)/9 Jun 1, 2008 Wataru Sakai
67 74 7·10179-3 Aug 13, 2007 Jo Yeong Uk
68 74 2·10161+9 Nov 18, 2007 Robert Backstrom
69 74 (14·10158-41)/9 Apr 25, 2007 Robert Backstrom
70 74 8·10160-7 Oct 18, 2007 Robert Backstrom
71 74 (7·10170-1)/3 Jun 12, 2007 Robert Backstrom
72 73 9·10157-7 Oct 31, 2007 Robert Backstrom
73 73 (5·10160-17)/3 Jun 25, 2005 Samuel Chong
74 73 (16·10155-7)/9 Oct 5, 2005 Sinkiti Sibata
75 73 (7·10163-1)/3 Jul 30, 2007 Robert Backstrom
76 73 (4·10157+11)/3 Feb 20, 2008 Jo Yeong Uk
77 73 (34·10150-43)/9 Nov 17, 2004 Greg Childers
78 73 8·10153+3 Aug 11, 2007 Robert Backstrom
79 73 (25·10169-1)/3 Mar 8, 2008 Tyler Cadigan
80 73 (4·10167-13)/9 Dec 25, 2007 Robert Backstrom
81 73 9·10167-7 Jan 27, 2008 Robert Backstrom
82 72 (64·10181-1)/9 Feb 10, 2008 Tyler Cadigan
83 72 (2·10170+43)/9 May 25, 2007 Robert Backstrom
84 72 (11·10167+61)/9 Jun 20, 2008 Robert Backstrom
85 72 (4·10168+41)/9 Jul 5, 2008 Robert Backstrom
86 72 (19·10167+17)/9 Jun 9, 2008 Robert Backstrom
87 72 (34·10147-7)/9 Apr 9, 2005 Sinkiti Sibata
88 72 8·10165+9 Jan 20, 2008 Robert Backstrom
89 72 (2·10155+1)/3 Apr 3, 2007 Robert Backstrom
90 72 (61·10147-7)/9 May 9, 2005 Greg Childers
91 72 (19·10168+17)/9 May 30, 2008 Jo Yeong Uk
92 72 (4·10159+11)/3 Mar 8, 2008 Robert Backstrom
93 72 (13·10149+41)/9 Mar 14, 2008 Sinkiti Sibata
94 72 2·10155-1 Jan 26, 2006 Anton Korobeynikov
95 71 (46·10156-1)/9 Jan 22, 2007 suberi
96 71 (4·10156-13)/9 Apr 11, 2007 Robert Backstrom
97 71 (11·10146+61)/9 Feb 13, 2008 Robert Backstrom
98 71 (89·10163+1)/9 Oct 12, 2007 Robert Backstrom
99 71 (22·10164-31)/9 Jul 1, 2008 Robert Backstrom
100 71 8·10166-1 Jan 29, 2008 Robert Backstrom
101 71 (7·10164+17)/3 Jun 26, 2008 Robert Backstrom
102 71 (55·10178-1)/9 May 16, 2007 Sinkiti Sibata
103 70 (8·10160+7)/3 Oct 23, 2007 Robert Backstrom
104 70 (22·10173+41)/9 Jul 22, 2008 Sinkiti Sibata
105 70 8·10154+3 Aug 10, 2007 Robert Backstrom
106 70 (17·10161-71)/9 Oct 4, 2007 Robert Backstrom
107 70 5·10149+3 Jul 15, 2007 Jo Yeong Uk
108 70 (17·10162-71)/9 Jun 18, 2007 Robert Backstrom
109 70 (5·10166-11)/3 Apr 25, 2008 Robert Backstrom
110 70 (65·10158+43)/9 Apr 26, 2007 Robert Backstrom
111 70 (2·10157+61)/9 Apr 6, 2007 Sinkiti Sibata
112 70 10161-3 Jun 29, 2005 Samuel Chong
113 70 (5·10157-17)/3 Apr 19, 2007 Robert Backstrom
114 70 (14·10167-41)/9 Jul 19, 2005 Samuel Chong
115 70 (4·10165+41)/9 Feb 1, 2008 Robert Backstrom
116 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 (25·10165-7)/9 3000000 1593296484 Jul 25, 2007 JMB
10 47 (64·10234+53)/9 10757000 1312137675 Dec 3, 2007 Robert Backstrom
11 47 (55·10165-1)/9 3000000 1761471762 Mar 7, 2008 Jo Yeong Uk
12 46 4·10194+1 11000000 632711195 Jul 27, 2007 Wataru Sakai
13 45 8·10167+3 1000000 127447873 Jul 18, 2008 Jo Yeong Uk
14 45 (4·10189-1)/3 3000000 4103031508 Mar 27, 2007 suberi
15 45 5·10188+3 3000000 2524047625 Jul 4, 2008 suberi
16 45 (64·10202+53)/9 11000000 49343718 Jun 13, 2005 Wataru Sakai
17 45 (13·10177+41)/9 7318000 2046770327 Apr 2, 2008 Robert Backstrom
18 45 (86·10148+31)/9 2728500 679331778 Sep 22, 2003 Robert Backstrom
19 45 2·10191+9 3000000 3278687019 Nov 16, 2007 Jo Yeong Uk
20 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 (4·10148+41)/9 Jan 31, 2005 Samuel Chong
11 61 (8·10120+7)/3 Oct 20, 2007 Jo Yeong Uk
12 60 5·10118-9 Dec 4, 2007 Jo Yeong Uk
13 59 (43·10160-7)/9 Aug 1, 2007 Sinkiti Sibata
14 58 (67·10143+23)/9 Nov 17, 2004 Greg Childers
15 57 (7·10142+11)/9 Apr 28, 2005 Makoto Kamada
16 57 (22·10136+23)/9 Jul 10, 2008 Serge Batalov
17 56 4·10154+9 Dec 10, 2007 Robert Backstrom
18 56 (5·10113+7)/3 Sep 26, 2007 Jo Yeong Uk
19 55 (4·10143+41)/9 Jan 21, 2005 Samuel Chong
20 55 (5·10134-11)/3 Apr 12, 2008 Sinkiti Sibata
21 53 (22·10143-31)/9 Jun 27, 2008 Sinkiti Sibata
22 53 (4·10110-31)/9 May 22, 2004 Naoki Yamamoto
23 52 8·10107+3 Aug 9, 2007 Robert Backstrom
24 52 (16·10144-43)/9 Apr 17, 2008 Robert Backstrom
25 52 (19·10163+53)/9 Jun 3, 2008 Jo Yeong Uk
26 52 (88·10152-7)/9 Jun 22, 2006 Sinkiti Sibata
27 51 (64·10122+53)/9 Jul 2, 2003 Robert Backstrom

6. Unprovable near-repdigit PRPs

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


  digits PRP when searched who searched
1 53718 (1053718-7)/3 Oct 17, 2004 Makoto Kamada
2 30178 (1030178-7)/3 Mar 20, 2004 Makoto Kamada
3 26045 1026045-3 Nov 2002 Henri Lifchitz
4 25324 (1025324-7)/3 Feb 7, 2004 Makoto Kamada
5 24549 (1024549-7)/3 Feb 7, 2004 Makoto Kamada
6 24253 (1024253-7)/3 Feb 7, 2004 Makoto Kamada
7 23365 (1023365-7)/3 Feb 7, 2004 Makoto Kamada
8 22718 (1022718-7)/3 Feb 6, 2004 Makoto Kamada
9 22094 (61·1022093-7)/9 Jan 6, 2008 Maksym Voznyy
10 21873 1021873-3 Nov 2002 Henri Lifchitz

7. Unprovable Plateau and Depression PRPs

See 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

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