The largest known CPAP-k for each k
k | Primes | n's | Digits | Year | Discoverer(s) |
3 | 197418203 · 225000 - 6091 + 6090n |
n=0..2 | 7535 | 2005 |
David Broadhurst, François Morain, FastECPP, PrimeForm |
4 | 18672891658 · 4099# + 1591788529 + 210n | n=2..5 | 1763 |
2003 | Jim Fougeron, Primo |
5 | 142661157626 · 2411# + 71427757 + 30n | n=0..4 |
1038 | 2002 | Jim Fougeron, Primo |
6 | 44770344615 · 859# + 1204600427 + 30n |
n=0..5 | 370 | 2003 |
Jens Kruse Andersen, Jim Fougeron, Primo |
7 | 194688251849 · 601# + x155 + 210n | n=0..6 |
259 | 2003 | Jim Fougeron |
8 | 10097274767216 · 250# + x99 + 210n | n=0..7 |
112 | 2003 | Jens Kruse Andersen |
9 | 73577019188277 · 199#·227·229 + x87 + 210n | n=0..8 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
10 | 507618446770482 · 193# + x77 + 210n | n=0..9 |
93
| 1998 |
Manfred Toplic, CP10 |
The largest known CPAP-3
Rank | Primes | n's | Digits | Year | Discoverer(s) |
1 | 197418203 · 225000 - 6091 + 6090n |
n=0..2 | 7535 | 2005 |
David Broadhurst, François Morain, FastECPP, PrimeForm |
2 | 87 · 224582 - 1 + 1290n |
n=0..2 | 7402 | 2004 |
Torbjörn Alm, Hans Rosenthal, Jens Kruse Andersen, Tom Kuechler,
PrimeForm, Proth.exe, Primo |
3 | 4811 · 220219 - 7475 + 3738n |
n=0..2 | 6091 | 2004 |
Christ van Willegen, Hans Rosenthal, Jens Kruse Andersen, Patrick Demichel,
PrimeForm, Primo |
4 | (84055657369 · 205881 · 4001# · (205881 · 4001# + 1) + 210)
· (205881 · 4001# - 1)/35 + 1 + 6n |
n=0..2 | 5132 | 2006 |
Ken Davis, PrimeForm, APTreeSieve |
5 | (61310346529 · 205881 · 4001# · (205881 · 4001# + 1) + 210)
· (205881 · 4001# - 1)/35 + 1 + 6n |
n=0..2 | 5132 | 2005 |
Ken Davis, PrimeForm, APTreeSieve |
6 | 1205 · 216165 - 869 + 870n |
n=0..2 | 4870 | 2003 |
Torbjörn Alm, Hans Rosenthal, Jens Kruse Andersen, Ray Ballinger, PrimeForm, Proth.exe, Primo |
7 | (114200191465398 · 3331# · (1037 · 3331# + 1) + 210)/35 · (1037 · 3331# - 1) + 1 + 6n |
n=0..2 | 4260 | 2003 |
David Broadhurst, PrimeForm |
8 | 9341# + 14371913 + 4068n |
n=0..2 | 4007 | 2003 | Ken Davis,
PrimeForm, Primo |
9 | 9337# + 582650759 + 1560n | n=0..2 | 4003 |
2004 | Hans Rosenthal, Primo |
10 | 9337# + 548450179 + 3492n | n=0..2 | 4003 |
2004 | Hans Rosenthal, Primo |
Verified certificates for all 9337# + ... available by e-mail request to
Hans.Rosenthal at t-online.de (replace at with @)
The largest known CPAP-4
Rank | Primes | n's | Digits | Year | Discoverer(s) |
1 | 18672891658 · 4099# + 1591788529 + 210n | n=2..5 | 1763 |
2003 | Jim Fougeron, Primo |
2 | 23963 + 1031388366 + 1500n | n=0..3 | 1312 |
2005 | Ken Davis, PrimeForm, Primo |
3 | 4919761805 · 3000# + 6673 + 30n | n=0..3 | 1284 |
2003 |
Torbjörn Alm & Jens Kruse Andersen, APSieve, PrimeForm, Primo |
4 | 111008 + 998672782 + 1080n | n=0..3 | 1050 |
2005 | Ken Davis, PrimeForm, Primo |
5 | 111005 + 260495358 + 60n | n=0..3 | 1047 |
2005 | Ken Davis, PrimeForm, Primo |
6 | 142661157626 · 2411# + 71427757 + 30n | n=1..4 | 1038 |
2002 | Jim Fougeron, Primo |
7 | 142661157626 · 2411# + 71427757 + 30n | n=0..3 | 1038 |
2002 | Jim Fougeron, Primo |
8 | 23332 + 445241605 + 396n | n=0..3 | 1004 |
2000 | Jim Fougeron, Primo |
9 | 23322 + 845219106973 + 600n | n=0..3 | 1001 |
2003 | Hans Rosenthal, Jim Fougeron, Jens Kruse Andersen, Primo |
10 | 23322 + 759534352753 + 1050n | n=0..3 | 1001 |
2003 | Hans Rosenthal, Jim Fougeron, Jens Kruse Andersen, Primo |
The largest known CPAP-5
Rank | Primes | n's | Digits | Year | Discoverer(s) |
1 | 142661157626 · 2411# + 71427757 + 30n | n=0..4 |
1038 | 2002 | Jim Fougeron, Primo |
2 | 9400734826 · 1499# + x632 + 2310n | n=0..4 |
645 | 2004 | Jim Fougeron, Primo |
3 | 60677170100 · 859# + 1204600427 + 30n |
n=0..4 | 370 | 2003 | Jens Kruse Andersen, Jim Fougeron, Primo |
4 | 51892636811 · 859# + 1204600427 + 30n |
n=0..4 | 370 | 2003 | Jens Kruse Andersen, Jim Fougeron, Primo |
5 | 46010092037 · 859# + 1204600427 + 30n |
n=0..4 | 370 | 2003 | Jens Kruse Andersen, Jim Fougeron, Primo |
6 | 44770344615 · 859# + 1204600427 + 30n |
n=1..5 | 370 | 2003 | Jens Kruse Andersen, Jim Fougeron, Primo |
7 | 44770344615 · 859# + 1204600427 + 30n |
n=0..4 | 370 | 2003 | Jens Kruse Andersen, Jim Fougeron, Primo |
8 | 32942330509 · 859# + 1204600427 + 30n |
n=1..5 | 370 | 2003 | Jens Kruse Andersen, Jim Fougeron, Primo |
9 | 31612974178 · 859# + 1204600427 + 30n |
n=1..5 | 370 | 2003 | Jens Kruse Andersen, Jim Fougeron, Primo |
10 | 24315544123 · 859# + 1204600427 + 30n |
n=0..4 | 370 | 2003 | Jim Fougeron, VFYPR |
The largest known CPAP-6
Rank | Primes | n's | Digits | Year | Discoverer(s) |
1 | 44770344615 · 859# + 1204600427 + 30n |
n=0..5 | 370 | 2003 |
Jens Kruse Andersen, Jim Fougeron, Primo |
2 | 2121022995 · 859# + 1204600427 + 30n |
n=0..5 | 369 | 2003 |
Jim Fougeron, VFYPR |
3 | 200605912613 · 700# + 2437704499910036551539466113407 + 30n |
n=0..5 | 301 | 2003 |
Torbjörn Alm & Jens Kruse Andersen, VFYPR |
4 | 261280286208 · 601# + x155 + 210n | n=1..6 |
259 | 2003 | Jim Fougeron |
5 | 246536360326 · 601# + x156 + 210n | n=1..6 |
259 | 2003 | Jim Fougeron |
6 | 226050459215 · 601# + x155 + 210n | n=0..5 |
259 | 2003 | Jim Fougeron |
7 | 225932147236 · 601# + x156 + 210n | n=0..5 |
259 | 2003 | Jim Fougeron |
8 | 194688251849 · 601# + x155 + 210n | n=1..6 |
259 | 2003 | Jim Fougeron |
9 | 194688251849 · 601# + x155 + 210n | n=0..5 |
259 | 2003 | Jim Fougeron |
10 | 97685004830 · 601# + x155 + 210n | n=0..5 |
259 | 2003 | Jim Fougeron |
The largest known CPAP-7
Rank | Primes | n's | Digits | Year | Discoverer(s) |
1 | 194688251849 · 601# + x155 + 210n | n=0..6 |
259 | 2003 | Jim Fougeron |
2 | 7127829789350 · 460# + x177 + 210n | n=0..6 |
201 | 2003 |
Torbjörn Alm & Jens Kruse Andersen |
3 | 7091037255023 · 460# + x177 + 210n | n=0..6 |
201 | 2003 | Torbjörn Alm & Jens Kruse Andersen |
4 | 7032468079552 · 460# + x177 + 210n | n=0..6 |
201 | 2003 | Torbjörn Alm & Jens Kruse Andersen |
5 | 10097274767216 · 250# + x99 + 210n | n=1..7 |
112 | 2003 | Jens Kruse Andersen |
6 | 10097274767216 · 250# + x99 + 210n | n=0..6 |
112 | 2003 | Jens Kruse Andersen |
7 | 10080119713620 · 250# + x99 + 210n | n=0..6 |
112 | 2003 | Jens Kruse Andersen |
8 | 10074509638938 · 250# + x99 + 210n | n=0..6 |
112 | 2003 | Jens Kruse Andersen |
9 | 10003305227518 · 250# + x99 + 210n | n=0..6 |
112 | 2003 | Jens Kruse Andersen |
10 | 121333717075627 · 199#·227·229 + x87 + 210n | n=0..7 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
The largest known CPAP-8
Rank | Primes | n's | Digits | Year | Discoverer(s) |
1 | 10097274767216 · 250# + x99 + 210n | n=0..7 |
112 | 2003 | Jens Kruse Andersen |
2 | 121333717075627 · 199#·227·229 + x87 + 210n | n=0..7 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
3 | 120293524089244 · 199#·227·229 + x87 + 210n | n=0..7 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
4 | 119845733530287 · 199#·227·229 + x87 + 210n | n=0..7 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
5 | 117686134150353 · 199#·227·229 + x87 + 210n | n=0..7 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
6 | 109571139518701 · 199#·227·229 + x87 + 210n | n=0..7 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
7 | 104072945625210 · 199#·227·229 + x87 + 210n | n=0..7 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
8 | 101107729483324 · 199#·227·229 + x87 + 210n | n=0..7 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
9 | 73577019188277 · 199#·227·229 + x87 + 210n | n=1..8 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
10 | 73577019188277 · 199#·227·229 + x87 + 210n | n=0..7 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
The largest known CPAP-9
Rank | Primes | n's | Digits | Year | Discoverer(s) |
1 | 73577019188277 · 199#·227·229 + x87 + 210n | n=0..8 |
101 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
2 | 25127352416973 · 199#·227·229 + x87 + 210n | n=0..8 |
101 | 2004 |
Hans Rosenthal & Jens Kruse Andersen |
3 | 1056761470535795 · 193# + x77 + 210n | n=0..8 |
93
| 2006 |
Manfred Toplic, CP10 |
4 | 1028784711070427 · 193# + x77 + 210n | n=1..9 |
93
| 2006 |
Manfred Toplic, CP10 |
5 | 580596232159174 · 193# + x77 + 210n | n=0..8 |
93 | 1998 |
Robert Piche, CP10 |
6 | 507618446770482 · 193# + x77 + 210n | n=1..9 |
93 | 1998 | Manfred Toplic, CP10 |
7 | 507618446770482 · 193# + x77 + 210n | n=0..8 |
93 | 1998 | Manfred Toplic, CP10 |
8 | 500996388736659 · 193# + x76 + 210n | n=0..8 |
92 | 1998 |
Manfred Toplic, CP09 |
9 | 124779708048481 · 167#·179·191·197 +
x72 + 210n | n=0..8 |
87 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
10 | 168890422879870 · 179#/(149·157) + x65 + 210n | n=0..8 |
81 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
The smallest known CPAP-k
k | Primes | n's | Digits | Year | Discoverer(s) |
7(1) | 1205967 · 61# + x32a + 210n | n=0..6 |
32 | 2004 | Laurent Fousse & Paul Zimmermann |
7(2) | 333936 · 67# + x32b + 210n | n=0..6 |
32 | 2004 | Laurent Fousse & Paul Zimmermann |
7(3) | 5722231 · 67# + x25 + 210n | n=0..6 |
32 | 2004 | Laurent Fousse & Paul Zimmermann |
8(1) | 2799806429564 · 83#·113 + x34 + 210n | n=0..7 |
47 | 2004 |
Hans Rosenthal & Jens Kruse Andersen |
8(2) | 5351738881202 · 83#·113 + x34 + 210n | n=0..7 |
48 | 2004 |
Hans Rosenthal & Jens Kruse Andersen |
8(3) | 16003606986539 · 83#·113 + x34 + 210n | n=0..7 |
48 | 2004 |
Hans Rosenthal & Jens Kruse Andersen |
9(1) | 3416716311814 · 179#/(149·157) + x65 + 210n | n=0..8 |
79 | 2004 |
Hans Rosenthal & Jens Kruse Andersen |
9(2) | 12606057030290 · 179#/(149·157) + x65 + 210n | n=0..8 |
80 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
9(3) | 52515434335080 · 179#/(149·157) + x65 + 210n | n=0..8 |
80 | 2005 |
Hans Rosenthal & Jens Kruse Andersen |
10 | 507618446770482 · 193# + x77 + 210n | n=0..9 |
93
| 1998 |
Manfred Toplic, CP10 |
The largest known CPAP-k difference
k | Primes | n's | Digits | Year | Discoverer(s) |
3 | x2506 + 21102n | n=0..2 |
2506 | 2004 | Torbjörn Alm & Jens Kruse Andersen,
PrimeForm, Primo |
4 | 46313478 · 1201#/1302643 + x498 + 2310n | n=0..3 |
505 | 2004 | Jens Kruse Andersen, PrimeForm,
Primo |
5 | 9400734826 · 1499# + x632 + 2310n | n=0..4 |
645 | 2004 | Jim Fougeron, Primo |
6 | x218 + 840n | n=0..5 |
218 | 2004 |
Torbjörn Alm & Jens Kruse Andersen |
7 | x133 + 420n | n=0..6 |
133 | 2004 |
Torbjörn Alm & Jens Kruse Andersen |
8 | x92 + 210n | n=0..7 |
92 | 1997 |
Harvey Dubner, Tony Forbes & Paul Zimmermann |
9 | 500996388736659 · 193# + x76 + 210n | n=0..8 |
92 | 1998 |
Manfred Toplic, CP09 |
10 | 507618446770482 · 193# + x77 + 210n | n=0..9 |
93
| 1998 |
Manfred Toplic, CP10 |
History of the largest known CPAP-k difference
k | Primes | n's | Digits | Year | Discoverer(s) |
3 | x2506 + 21102n | n=0..2 |
2506 | 2004 | Torbjörn Alm & Jens Kruse Andersen,
PrimeForm, Primo |
3 | 41#137 - 5576107 + 10164n | n=0..2 |
1985
|
2002 | David Broadhurst, Primo |
|
4 | 46313478 · 1201#/1302643 + x498 + 2310n | n=0..3 |
505 | 2004 | Jens Kruse Andersen, PrimeForm,
Primo |
4 | 78006074 · 883# + x371 + 2004n | n=0..3 |
379 | 2004 | Jim Fougeron |
4 | 23320 + 1308319536235 + 1470n | n=0..3 |
1000 | 2004 | Hans Rosenthal, Jim Fougeron, Primo |
|
5 | 9400734826 · 1499# + x632 + 2310n | n=0..4 |
645 | 2004 | Jim Fougeron, Primo |
5 | x272 + 1350n | n=0..4 |
272 | 2004 | Jens Kruse Andersen |
|
6 | x218 + 840n | n=0..5 |
218 | 2004 |
Torbjörn Alm & Jens Kruse Andersen |
|
7 | x133 + 420n | n=0..6 |
133 | 2004 |
Torbjörn Alm & Jens Kruse Andersen |
7 | x97 + 210n | n=0..6 |
97 | 1995 |
Harvey Dubner & Harry Nelson |
|
8 | x92 + 210n | n=0..7 |
92 | 1997 |
Harvey Dubner, Tony Forbes & Paul Zimmermann |
|
9 | 500996388736659 · 193# + x76 + 210n | n=0..8 |
92 | 1998 |
Manfred Toplic, CP09 |
|
10 | 507618446770482 · 193# + x77 + 210n | n=0..9 |
93
| 1998 |
Manfred Toplic, CP10 |