The Largest Known Simultaneous Primes

Introduction
News: 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004
The largest known simultaneous primes
Credited programs and projects
Record history for k = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Rules
Submissions

Introduction
This page records the single largest known case of k simultaneous primes for each k, and the record history.
The idea is to show the best overall record for different types of sets with k primes.
p# (called p primorial) is the product of all primes ≤ p, e.g. 10# = 2 · 3 · 5 · 7 = 210.
An expression with p# is often used in prime searches to avoid factors ≤ p.

News
2014
April 6. New record: A second 23-digit AP20 by Jaroslaw Wroblewski.
April 3. New record: A third 30-digit CC-17 2nd kind by Raanan Chermoni & Jaroslaw Wroblewski.
April 2. New record: 22-digit AP21 by Jaroslaw Wroblewski.
April 2. New record: 23-digit AP20 by Jaroslaw Wroblewski.
March 29. New record: A second 21-digit AP20 by Jaroslaw Wroblewski.
March 23. New record: A second 29-digit CC-19 2nd kind by Raanan Chermoni & Jaroslaw Wroblewski.
March 21. New record: 21-digit AP20 by Jaroslaw Wroblewski.
March 20. New record: A sixth 20-digit AP20 by Jaroslaw Wroblewski.
March 19. New record: A fifth 20-digit AP20 by Jaroslaw Wroblewski.
March 15. New record: 29-digit CC-19 2nd kind by Raanan Chermoni & Jaroslaw Wroblewski.
March 10. New record: 651-digit CC-6 2nd kind by Oscar Östlin, NewPGen, PrimeForm.
March 9. New record: 30-digit CC-18 2nd kind by Raanan Chermoni & Jaroslaw Wroblewski. Also contains record CC17.
March 8. New record: 29-digit CC-18 2nd kind by Raanan Chermoni & Jaroslaw Wroblewski.
March 8. New record: 30-digit CC-17 2nd kind by Raanan Chermoni & Jaroslaw Wroblewski.
March 1. New record: A tenth 28-digit 18-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
February 11. New record: 112-digit CC12 1st kind by Primecoin.
January 20. New record: 108-digit CC13 1st kind by Primecoin.
January 3. New record: A ninth 28-digit 18-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
January 1. New record: 1443-digit quintuplet by Serge Batalov, NewPGen, PrimeForm, Primo.

2013
December 21. New record: 3503-digit quadruplet by Serge Batalov, NewPGen, PrimeForm, Primo.
November 28. New record: 1293-digit 5-tuplet by Reto Keiser, PrimeForm, Primo.
November 1. New record: 1209-digit CPAP-5 by David Broadhurst, PrimeForm, Primo.
September 29. New record: 3443-digit quadruplet by Serge Batalov, NewPGen, PrimeForm, Primo.
September 27. New record: 148-digit CC10 1st kind by Primecoin.
September 10. New record: 96-digit CC13 2nd kind by Primecoin.
August 25. New record: 101-digit BiTwin with 5 links (12 primes) by Primecoin.
August 3. New record: 141-digit CC11 1st kind  by Primecoin. Also contains record CC10.
July 29. New record: An eighth 28-digit 18-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
July 29. New record: 99-digit CC12 2nd kind  by Primecoin.
July 29. New record: 117-digit CC11 1st kind  by Primecoin.
July 29. New record: 139-digit BiTwin with 4 links (10 primes) by Primecoin.
April 30. New record: 16737-digit triplet by Peter Kaiser, NewPGen, Srsieve, PrimeForm, LLR, Primo.
April 14. New record: 3360-digit quadruplet by Reto Keiser, NewPGen, PrimeForm, LLR, Primo.
February 25. New record: A seventh 28-digit 18-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
February 17. New record: 30-digit 17-tuplet by Roger Thompson.
February 4. New record: 50-digit 14-tuplet by Roger Thompson. Also contains record 13-tuplet.
January 25. New record for largest known prime: 17425170-digit Mersenne prime by Curtis Cooper, GIMPS.

2012
December 31. New record: A second 28-digit 19-tuplet by Raanan Chermoni & Jaroslaw Wroblewski. Also contains record 18-tuplet.
December 15. New record: 28-digit 19-tuplet by Raanan Chermoni & Jaroslaw Wroblewski. Also contains record 18-tuplet.
December 2. New record: A fourth 28-digit 18-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
September 2. New record: 35-digit 15-tuplet by Roger Thompson.
August 9. New record: 31-digit 16-tuplet by Roger Thompson.
April 9. New record: 200701-digit Sophie Germain prime by Philipp Bliedung, PrimeGrid, TwinGen, LLR.
March 26. New record: 3024-digit quadruplet by Peter Kaiser, NewPGen, PrimeForm, Primo.
March 20. New record: A third 28-digit 18-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
March 4. New record: 1184-digit CC5 1st kind by Dirk Augustin, NewPGen, PrimeForm.
January 24. New record: A second 28-digit 18-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.

2011
December 31. New record: 29-digit 17-tuplet by Roger Thompson.
December 25. New record: 200700-digit twin prime by Timothy D. Winslow, PrimeGrid, TwinGen, LLR.
December 4. New record: A second 28-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
December 4. New record: 28-digit 18-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
August 25. New record: A second 28-digit 17-tuplet by Roger Thompson.
August 21. New record: 28-digit 17-tuplet by Roger Thompson.
August 9. New record: 28-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
June 20. New record: A seventeenth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
May 28. New record: A third 27-digit 19-tuplet by Raanan Chermoni & Jaroslaw Wroblewski. Also contains record 18-tuplet and 17-tuplet.
May 13. New record: A fifteenth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
April 18. New record: A fourteenth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
April 4. New record: A thirteenth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
March 15. New record: 27-digit 17-tuplet by Roger Thompson.
March 14. New record: A twelfth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
February 28. New record: An eleventh 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
February 19. New record: A tenth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
February 19. New record: A second 27-digit 19-tuplet by Raanan Chermoni & Jaroslaw Wroblewski. Also contains record 18-tuplet.
February 13. New record: 2835-digit CC4 1st kind by Michael Angel, NewPGen, PrimeForm.
February 11. New record: A ninth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
February 9. New record: 27-digit 19-tuplet by Raanan Chermoni & Jaroslaw Wroblewski. Also contains record 18-tuplet.
February 4. New record: An eighth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
February 4. New record: 27-digit 18-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
January 31. New record: A seventh 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
January 21. New record: A sixth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
January 13. New record: A fifth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
January 6. New record: 1141-digit CC5 2nd kind by Michael Angel, NewPGen, PrimeForm.
January 2. New record: A fourth 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.

2010
December 13. New record: A third 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
November 17. New record: A second 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
November 1. New record: 27-digit 17-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
August 10. New record: 225-digit CC8 2nd kind by Dirk Augustin, NewPGen, PrimeForm.
July 28. New record: 1116-digit CC5 2nd kind by David Broadhurst, NewPGen, PrimeForm.
July 17. New record: 357-digit CC7 1st kind by Dirk Augustin, NewPGen, PrimeForm.
April 26. New record: A second 27-digit 18-tuplet by Jaroslaw Wroblewski.
March 2. New record: 634-digit CC6 1st kind by Dirk Augustin, NewPGen, PrimeForm.
January 15. New record: 27-digit 18-tuplet by Jaroslaw Wroblewski.
January 9. New record: 10477-digit CC3 1st kind by Tom Wu, LLR.

2009
August 13. New record: 100355-digit twin prime by (SG Grid), Peter Kaiser, Keith Klahn, Twin Prime Search, PrimeGrid, NewPGen, tpsieve, LLR.
August 7. New record: 48-digit 13-tuplet by Jens K. Andersen.
July 12. New record: 110-digit CC10 2nd kind by Dirk Augustin, NewPGen, PrimeForm.
June 22. New record: 301-digit 7-tuplet by Jens K. Andersen.
May 1. New record: 559-digit 6-tuplet by Norman Luhn.
March 24. New record: 1107-digit 5-tuplet by Norman Luhn.
March 11. New record: A fifth 26-digit 18-tuplet by Jaroslaw Wroblewski.
February 20. New record: A fourth 26-digit 18-tuplet by Jaroslaw Wroblewski.
January 26. New record: A third 26-digit 18-tuplet by Jaroslaw Wroblewski.
January 23. This page is moved to http://users.cybercity.dk/~dsl522332/math/simultprime.htm.
January 16. New record: A second 26-digit 18-tuplet by Jaroslaw Wroblewski.

2008
December 30. New record: 64-digit CC12 2nd kind by Dirk Augustin, NewPGen, PrimeForm.
December 18. New record: 26-digit 18-tuplet by Jaroslaw Wroblewski.
December 14. New record: 25-digit 18-tuplet by Jaroslaw Wroblewski.
December 3. New record: 20-digit AP21 (first entry for 21) by Jaroslaw Wroblewski.
November 17. New record: 10047-digit triplet by Norman Luhn, François Morain, NewPGen, LLR, Primo, FastECPP.
October 13. Possible future record: A 10047-digit triplet by Norman Luhn. It contains an unproven probable prime (proof was announced November 17).
September 16. New record for largest known prime: 12978189-digit Mersenne prime by Edson Smith, GIMPS.
July 18. New record: A fourth 20-digit AP20 by Jaroslaw Wroblewski. Also contains record AP19.
July 17. New record: A third 20-digit AP20 by Jaroslaw Wroblewski. Also contains record AP19.
July 3. New record: A seventh 20-digit AP19 by Jaroslaw Wroblewski.
July 1. New record: 292-digit CC7 1st kind kind by Dirk Augustin, NewPGen, PrimeForm.
June 30. New record: A second 20-digit AP20 by Jaroslaw Wroblewski. Also contains record AP19.
June 30. New record: A fifth 20-digit AP19 by Jaroslaw Wroblewski.
June 29. New record: A fourth 20-digit AP19 by Jaroslaw Wroblewski.
June 29. New record: A third 20-digit AP19 by Jaroslaw Wroblewski.
June 29. New record: A second 20-digit AP19 by Jaroslaw Wroblewski.
June 28. New record: 20-digit AP20 by Jaroslaw Wroblewski. Also contains record AP19.
June 28. New record: A fourth 19-digit AP19 by Jaroslaw Wroblewski.
June 27. New record: A third 19-digit AP19 by Jaroslaw Wroblewski.
June 27. New record: 19-digit AP20 by Jaroslaw Wroblewski. Also contains record AP19.
June 26. New record: 30-digit CC16 2nd kind by Jaroslaw Wroblewski.
June 17. New record: 34-digit CC15 2nd kind by Jaroslaw Wroblewski.
June 12. New record: 28-digit CC16 2nd kind by Jaroslaw Wroblewski.
June 10. New records: 27-digit CC17 2nd kind by Jaroslaw Wroblewski. Also contains record CC16.
June 8. New record: A second 26-digit CC16 2nd kind by Jaroslaw Wroblewski.
June 5. New records: A second 26-digit CC17 2nd kind by Jaroslaw Wroblewski. Also contains record CC16.
June 5. New record: 26-digit CC17 2nd kind by Jaroslaw Wroblewski.
May 29. New record: 26-digit CC16 1st kind by Jaroslaw Wroblewski.
April 14. New record: 33-digit 15-tuplet by Jens K. Andersen.
February 29. New record: 218-digit 8-tuplet by Jens K. Andersen.

2007
December 28. New records: 46-digit 14-tuplet by Norman Luhn. Also contains record 13-tuplet.
March 1. New record: 18-digit AP20 by Jaroslaw Wroblewski.
February 27. New record: 19-digit AP19 by Jaroslaw Wroblewski.
January 15. New record: 58711-digit twin prime by Eric Vautier, Dmitri Gribenko, Patrick W. McKibbon, Twin Prime Search, PrimeGrid, NewPGen, LLR.

2006
December 30. New record: 17-digit AP20 (first entry for 20) by Jaroslaw Wroblewski.
December 30. New record: 17-digit AP19 by Jaroslaw Wroblewski.
December 30. New record: 15-digit AP19 (first entry for 19) by Jaroslaw Wroblewski.
September 11. New record for largest known prime: 9808358-digit Mersenne prime by Curtis Cooper, Steven Boone, GIMPS.
August 7. New record: 7937-digit CC3 1st kind by Michael Paridon, NewPGen, PrimeForm.
June 30. New record: 475-digit CC6 2nd kind by Dirk Augustin, NewPGen, PrimeForm.
May 3. New record: 51780-digit Sophie Germain prime by Zoltán Járai, Gabor Farkas, Timea Csajbok, Janos Kasza, Antal Járai.
April 7. New record: 1069-digit 5-tuplet by Norman Luhn.
February 8. New record: 58-digit CC12 2nd kind by Jens K. Andersen.
January 17. New record: 427-digit 6-tuplet by Norman Luhn.
January 4. New record: 282-digit 7-tuplet by Norman Luhn.

2005
December 25. New record for largest known prime: 9152052-digit Mersenne prime by Curtis Cooper, Steven Boone, GIMPS.
December 7. New record: 41-digit CC13 1st kind by Dirk Augustin, NewPGen, PrimeForm.
September 8. New record: 51779-digit twin prime by Zoltán Járai, Gabor Farkas, Timea Csajbok, Janos Kasza, Antal Járai.
August 7. New record: 187-digit CC9 1st kind by Dirk Augustin, NewPGen, PrimeForm.
August 6. New record: 206-digit 8-tuplet by Norman Luhn.
June 10. New record: 2354-digit CC4 1st kind by Jiong Sun, NewPGen, PrimeForm.
April 29. New record: 2058-digit quadruplet (4-tuplet) by Norman Luhn, Primo.
April 18. New record: 6038-digit CC3 1st kind by Jiong Sun, NewPGen, PrimeForm.
March 19. New record: 1770-digit CC4 2nd kind by Jiong Sun, NewPGen, PrimeForm.
February 27. New record for largest known prime: 7816230-digit Mersenne prime by Martin Nowak & GIMPS.
February 7. New record: 33-digit 14-tuplet by Christ van Willegen & Jens K. Andersen.
February 6. New record: 135-digit 9-tuplet by Norman Luhn.
January 19. New record: 180-digit 8-tuplet by Torbjörn Alm & Jens K. Andersen.

2004
December 1. New record: 32-digit 14- and 15-tuplet by Joerg Waldvogel & Peter Leikauf.
November 24. New record: 174-digit 8-tuplet by Norman Luhn.
November 7. New record: 418-digit CC6 1st kind by Dirk Augustin, NewPGen, PrimeForm.
October 24. New record: 5190-digit CC3 2nd kind by Jiong Sun, NewPGen, PrimeForm.
October 19. New record: 26-digit 16-tuplet by Jens K. Andersen.
October 16. This page is published at http://hjem.get2net.dk/jka/math/simultprime.htm.

The largest known simultaneous primes
k Primes Type Digits Year Discoverer
1 257885161-1 Mersenne 17425170 2013 Curtis Cooper, GIMPS
2 18543637900515 · 2666667· 2n - 1, n=0..1 CC, 1st kind (Sophie Germain) 200701 2012 Philipp Bliedung, PrimeGrid, TwinGen, LLR
3 6521953289619 · 255555 - 5, -1, +1 Tuplet 16737 2013 Peter Kaiser, NewPGen, Srsieve, PrimeForm, LLR, Primo
4 2339662057597 · 103490  + 1,3,7,9 Tuplet 3503 2013 Serge Batalov, NewPGen, PrimeForm, Primo
5 163252711105 · 3371#/2 -8, -4, -2, +2, +4 Tuplet 1443 2014 Serge Batalov, NewPGen, PrimeForm, Primo
6 480112483568 · 1511# · 2n + 1, n=0..5 CC, 2nd kind 651 2014 Oscar Östlin, NewPGen, PrimeForm
7 162597166369 · 827# · 2n - 1, n=0..6 CC, 1st kind 357 2010 Dirk Augustin, NewPGen, PrimeForm
8 1148424905221 · 509# · 2n + 1, n=0..7 CC, 2nd kind 225 2010 Dirk Augustin, NewPGen, PrimeForm
9 65728407627 · 431# · 2n - 1, n=0..8 CC, 1st kind 187 2005 Dirk Augustin, NewPGen, PrimeForm
10 x89 · 149# · 2n - 1, n=0..9 CC, 1st kind 148 2013 Primecoin
11 x80 · 151# · 2n - 1, n=0..10 CC, 1st kind 141 2013 Primecoin
12 x83c · 71# · 2n - 1, n=0..11 CC, 1st kind 112 2014 Primecoin
13 x84 · 61# · 2n - 1, n=0..12 CC, 1st kind 108 2014 Primecoin
14 14815550 · 107# + 4385574275277311 + 
0,2,6,8,12,18,20,26,30,32,36,42,48,50
Tuplet 50 2013 Roger Thompson
15 10004646546202610858599716515809907 + 0,2,6, 12,14,20,24,26,30,36,42,44,50,54,56 Tuplet 35 2012 Roger Thompson
16 1003234871202624616703163933853 + 0,4,6, 10,16,18,24,28,30,34,40,46,48,54,58,60 Tuplet 31 2012 Roger Thompson
17 1540797425367761006138858880 · 2n + 1, n=0..16 CC, 2nd kind 30 2014 Raanan Chermoni & Jaroslaw Wroblewski
18 658189097608811942204322720 · 2n + 1, n=0..17 CC, 2nd kind 30 2014 Raanan Chermoni & Jaroslaw Wroblewski
19 79910197721667870187016100 · 2n + 1, n=0..18 CC, 2nd kind 29 2014 Raanan Chermoni & Jaroslaw Wroblewski
20 35182855408632706168481 + 29# · n, n=0..19 AP 23 2014 Jaroslaw Wroblewski
21 5547796991585989797641 + 29# · n, n=0..20 AP 22 2014 Jaroslaw Wroblewski
The k value links to the record history. A year link is to an announcement.

Credited programs and projects
Programs:
NewPGen by Paul Jobling.
APSieve by Michael Bell and Jim Fougeron.
tpsieve by Geoff Reynolds.
TwinGen by David Underbakke.
Srsieve by Geoffrey Reynolds.
PRP by George Woltman.
PrimeForm by the OpenPFGW group with George Woltman.
Proth.exe by Yves Gallot.
LLR by Jean Penné.
Primo (formerly Titanix) by Marcel Martin.
VFYPR by Tony Forbes.
FastECPP (unpublished program) by François Morain.
The primality proving program is only credited above 300 digits.

Projects:
CP10 by Harvey Dubner, Tony Forbes, Nik Lygeros, Michel Mizony and Paul Zimmermann.
GIMPS by George Woltman, Scott Kurowski, et al.
Twin Prime Search and PrimeGrid, coordinated by Michael Kwok, Andrea Pacini, Rytis Slatkevicius.
Primecoin by Sunny King. The project does sometimes not state discoverers and precise dates of records.

Record history
k Primes Type Digits Year Discoverer
1 257885161-1 Mersenne 17425170 2013 Curtis Cooper, GIMPS
1 243112609-1 Mersenne 12978189 2008 Edson Smith, GIMPS
1 232582657-1 Mersenne 9808358 2006 Curtis Cooper, Steven Boone, GIMPS
1 230402457-1 Mersenne 9152052 2005 Curtis Cooper, Steven Boone, GIMPS
1 225964951-1 Mersenne 7816230 2005 Martin Nowak, GIMPS
1 224036583-1 Mersenne 7235733 2004 Josh Findley, GIMPS
1 220996011-1 Mersenne 6320430 2003 Michael Shafer, GIMPS
1 213466917-1 Mersenne 4053946 2001 Michael Cameron, GIMPS
1 26972593-1 Mersenne 2098960 1999 Nayan Hajratwala, GIMPS
 
2 18543637900515 · 2666667· 2n - 1, n=0..1 CC, 1st kind (Sophie Germain) 200701 2012 Philipp Bliedung, PrimeGrid, TwinGen, LLR
2 3756801695685 · 2666669 ± 1 Tuplet (twin) 200700 2011 Timothy D. Winslow, PrimeGrid, TwinGen, LLR
2 65516468355 · 2333333 ± 1 Tuplet (twin) 100355 2009 (SG Grid), Peter Kaiser, Keith Klahn, Twin Prime Search, PrimeGrid, NewPGen, tpsieve, LLR
2 2003663613 · 2195000 ± 1 Tuplet (twin) 58711 2007 Eric Vautier, Dmitri Gribenko, Patrick W. McKibbon, Twin Prime Search, PrimeGrid, NewPGen, LLR
2 137211941292195 · 2171960 · n - 1, n=1,2 CC, 1st kind (Sophie Germain) 51780 2006 Zoltán Járai, Gabor Farkas, Timea Csajbok, Janos Kasza, Antal Járai
2 16869987339975 · 2171960 ± 1 Tuplet 51779 2005 Zoltán Járai, Gabor Farkas, Timea Csajbok, Janos Kasza, Antal Járai
2 33218925 · 2169690 ± 1 Tuplet 51090 2002 Daniel Papp, NewPGen, PRP, Proth.exe
2 318032361 · 2107001 ± 1 Tuplet 32220 2001 David Underbakke, Phil Carmody, NewPGen, PRP, PrimeForm
2 1807318575 · 298305 ± 1 Tuplet 29603 2001 David Underbakke, Phil Carmody, NewPGen, PRP, Proth.exe
2 665551035 · 280025 ± 1 Tuplet 24099 2000 David Underbakke, Phil Carmody, NewPGen, PRP, Proth.exe
 
3 6521953289619 · 255555 - 5, -1, +1 Tuplet 16737 2013 Peter Kaiser, NewPGen, Srsieve, PrimeForm, LLR, Primo
3 914546877 · 234772 · 2n - 1, n=0..2 CC, 1st kind 10477 2010 Tom Wu, LLR
3 2072644824759 · 233333 -1, +1, +5 Tuplet 10047 2008 Norman Luhn, François Morain, NewPGen, LLR, Primo, FastECPP
3 164210699973 · 226326 · 2n - 1, n=0..2 CC, 1st kind 7937 2006 Michael Paridon, NewPGen, PrimeForm
3 3020255265 · 220023 · 2n - 1, n=0..2 CC, 1st kind 6038 2005 Jiong Sun, NewPGen, PrimeForm
3 2366867925 · 217206 · 2n + 1, n=0..2 CC, 2nd kind 5190 2004 Jiong Sun, NewPGen, PrimeForm
3 2288999415 · 215937 · 2n - 1, n=0..2 CC, 1st kind 4808 2004 Jiong Sun, NewPGen, PrimeForm
3 1110159213 · 215164 · 2n + 1, n=0..2 CC, 2nd kind 4575 2002 Michael Angel, Dirk Augustin, Paul Jobling, NewPGen, PRP, Proth.exe
3 (108748629354 · 4436 · 3251# · (4436·3251#+1) + 210) · (4436·3251#-1) / 35 + 7,11,13 Tuplet 4135 2002 David Broadhurst, PrimeForm
3 (61504372896 · 5119 · 3163# · (5119·3163#+1) + 210) · (5119·3163#-1) / 35 + 5, 7,11 Tuplet 4019 2002 David Broadhurst, PrimeForm
 
4 2339662057597 · 103490  + 1,3,7,9 Tuplet 3503 2013 Serge Batalov, NewPGen, PrimeForm, Primo
4 305136484659 · 211399 - 1, +1, +5, +7 Tuplet 3443 2013 Serge Batalov, NewPGen, PrimeForm, Primo
4 722047383902589 · 211111 - 1, +1, +5, +7 Tuplet 3360 2013 Reto Keiser, NewPGen, PrimeForm, LLR, Primo
4 43697976428649 · 29999 - 1, +1, +5, +7 Tuplet 3024 2012 Peter Kaiser, NewPGen, PrimeForm, Primo
4 1249097877 · 6599# · 2n - 1, n=0..3 CC, 1st kind 2835 2011 Michael Angel, NewPGen, PrimeForm
4 119184698 · 5501# · 2n - 1, n=0..3 CC, 1st kind 2354 2005 Jiong Sun, NewPGen, PrimeForm
4 4104082046 · 4799# + 5651 + 0,2,6,8 Tuplet 2058 2005 Norman Luhn, Primo
4 1453501013 · 4127# · 2n + 1, n=0..3 CC, 2nd kind 1770 2005 Jiong Sun, NewPGen, PrimeForm
4 18672891658 · 4099# + 1591788529 + 210n, n=2..5 CPAP 1763 2003 Jim Fougeron, Primo
4 853877841 · 3571# · 2n ± 1, n=0,1 BiTwin 1529 2002 Henri Lifchitz
4 1707223185 · 3049# · 2n - 1, n=0..3 CC, 2nd kind 1308 2002 Michael Angel, Dirk Augustin, NewPGen, PrimeForm
4 356701232 · 3041# · 2n + 1, n=0..3 CC, 1st kind 1304 2002 Michael Angel, Dirk Augustin, NewPGen, PrimeForm
4 10271674954 · 2999# + 3461 + 0,2,6,8 Tuplet 1284 2002 Michael Bell, Michael Davison, Matt Jack, Ronald Lau, Graeme Leese, Ben Lowing
 
5 163252711105 · 3371#/2 -8, -4, -2, +2, +4 Tuplet 1443 2014 Serge Batalov, NewPGen, PrimeForm, Primo
5 699549860111847 · 24244 - 1, +1, +5, +7, +11 Tuplet 1293 2013 Reto Keiser, PrimeForm, Primo
5 406463527990 · 2801# + 1633050283 + 30n, n=0..4 CPAP 1209 2013 David Broadhurst, PrimeForm, Primo
5 4250172704 · 2749# · 2n - 1, n=0..4 CC, 1st kind 1184 2012 Dirk Augustin, NewPGen, PrimeForm
5 80670856865 · 2677# · 2n + 1, n=0..4 CC, 2nd kind 1141 2011 Michael Angel, NewPGen, PrimeForm
5 45008010405 · 2621# · 2n + 1, n=0..4 CC, 2nd kind 1116 2010 David Broadhurst, NewPGen, PrimeForm
5 424232794973 · 2600# + 43777 + 0,4,6,10,12 Tuplet 1107 2009 Norman Luhn, Primo
5 283534892623 · 2500# + 1091261 + 0,2,6,8,12 Tuplet 1069 2006 Norman Luhn, Primo
5 142661157626 · 2411# + 71427757 + 30n, n=0..4 CPAP 1038 2002 Jim Fougeron, Primo
5 51946113 · 1193# · 2n + 1, n=0..4 CC, 2nd kind 509 2002 Dirk Augustin, NewPGen, PrimeForm
5 148809453 · 1069# · 2n - 1, n=0..4 CC, 1st kind 461 2001 Dirk Augustin, NewPGen, PrimeForm
 
6 480112483568 · 1511# · 2n + 1, n=0..5 CC, 2nd kind 651 2014 Oscar Östlin, NewPGen, PrimeForm
6 37488065464 · 1483# · 2n - 1, n=0..5 CC, 1st kind 634 2010 Dirk Augustin, NewPGen, PrimeForm
6 601545895935 · 1300# + 43777 + 0,4,6,10,12,16 Tuplet 559 2009 Norman Luhn
6 37783362904 · 1097# · 2n + 1, n=0..5 CC, 2nd kind 475 2006 Dirk Augustin, NewPGen, PrimeForm
6 328481121285 · 1000# + 16057 + 0,4,6,10,12,16 Tuplet 427 2006 Norman Luhn
6 33692909611 · 977# · 2n - 1, n=0..5 CC, 1st kind 418 2004 Dirk Augustin, NewPGen, PrimeForm
6 44770344615 · 859# + 1204600427 + 30n, n=0..5 CPAP 370 2003 Jens K. Andersen, Jim Fougeron, Primo
6 2121022995 · 859# + 1204600427 + 30n, n=0..5 CPAP 369 2003 Jim Fougeron, VFYPR
6 124605675 · 719# · 2n ± 1, n=3..5 BiTwin 308 2002 Dirk Augustin
6 110282080125 · 700# + 6005887 + 0,4,6,10,12,16 Tuplet 301 2001 Norman Luhn, Primo
 
7 162597166369 · 827# · 2n - 1, n=0..6 CC, 1st kind 357 2010 Dirk Augustin, NewPGen, PrimeForm
7 68841237 · 701# + 2525568581 + 0,2,6,8,12,18,20 Tuplet 301 2009 Jens K. Andersen
7 1178137903623 · 661# · 2n - 1, n=0..6 CC, 1st kind 292 2008 Dirk Augustin, NewPGen, PrimeForm
7 251733155478 · 650# + 1146779 + 0,2,8,12,14,18,20 Tuplet 282 2006 Norman Luhn
7 194688251849 · 601# + x155 + 210n, n=0..6 CPAP 259 2003 Jim Fougeron
7 7127829789350 · 460# + x177 + 210n, n=0..6 CPAP 201 2003 Torbjörn Alm & Jens K. Andersen
7 94552004441 · 410# + 165701 + 0,2,6,8,12,18,20 Tuplet 178 2003 Jens K. Andersen
7 497423806097 · 400# + 380284918609481+ 0,2,6,8,12,18,20 Tuplet 173 2001 Norman Luhn
 
8 1148424905221 · 509# · 2n + 1, n=0..7 CC, 2nd kind 225 2010 Dirk Augustin, NewPGen, PrimeForm
8 330846961 · 503# + 349129635971 + 0,2,6,8,12,18,20,26 Tuplet 218 2008 Jens K. Andersen
8 12874261020824 · 463# + 88793 + 0,6,8,14,18,20,24,26 Tuplet 206 2005 Norman Luhn
8 97510235 · 421# + 322355908991 + 0,2,6,8,12,18,20,26 Tuplet 180 2005 Torbjörn Alm & Jens K. Andersen
8 4319152256906 · 400# + 1277 + 0,2,6,12,14,20,24,26 Tuplet 174 2004 Norman Luhn
8 65677369861 · 380# + 18000020393471 + 0,2,6,8,12,18,20,26 Tuplet 165 2003 Torbjörn Alm & Jens K. Andersen
8 15234072433401 · 375# + 43813839521 + 0,2,6,8,12,18,20,26 Tuplet 164 2002 Norman Luhn
8 243551752728 · 320# + 1277 + 0,2,6,12,14,20,24,26 Tuplet 142 2001 Graeme Leese, Michael Bell, Matt Jack, Michael Davison, Ben Lowing, Tim Nightingale, APSieve
 
9 65728407627 · 431# · 2n - 1, n=0..8 CC, 1st kind 187 2005 Dirk Augustin, NewPGen, PrimeForm
9 90421624808713 · 293# + 103498931  + 0,2,6,8,12,18,20,26,30 Tuplet 135 2005 Norman Luhn
9 1619062142 · 255# + 53344165991 + 0,2,6,8,12,18,20,26,30 Tuplet 111 2003 Thomas Wolter & Jens K. Andersen
9 388793398651 · 250# + 1042090781 + 0,2,6,8,12,18,20,26,30 Tuplet 110 2001 Norman Luhn
 
10 x89 · 149# · 2n - 1, n=0..9 CC, 1st kind 148 2013 Primecoin
10 x80 · 151# · 2n - 1, n=1..10 CC, 1st kind 141 2013 Primecoin
10 x83a · 139# · 2n ± 1, n=0..4 BiTwin 139 2013 Primecoin
10 1070828503293 · 239# · 2n + 1, n=0..9 CC, 2nd kind 110 2009 Dirk Augustin, NewPGen, PrimeForm
10 24698258 · 239# + 28606476153371 + 0,2,6,8,12,18,20,26,30,32 Tuplet 104 2004 Jens K. Andersen
10 72613488698235 · 227# + 39058751 + 0,2,6,8,12,18,20,26,30,32 Tuplet 103 2004 Norman Luhn
10 507618446770482 · 193# + x77 + 210n, n=0..9 CPAP 93 1998 Manfred Toplic, CP10
 
11 x80 · 151# · 2n - 1, n=0..10 CC, 1st kind 141 2013 Primecoin
11 x81a · 89# · 2n - 1, n=0..10 CC, 1st kind 117 2013 Primecoin
11 24698258 · 239# + 28606476153371 + 0,2,6,8,12,18,20,26,30,32,36 Tuplet 104 2004 Norman Luhn & Jens K. Andersen
11 35078052 · 157# + 398861548425071 + 0,2,6,8,12,18,20,26,30,32,36 Tuplet 70 2004 Jens K. Andersen & Hans Rosenthal
11 92119245478633 · 130# + 21816911 + 0,2,6,8,12,18,20,26,30,32,36 Tuplet 63 2003 Norman Luhn
11 58187756 · 110# + 2320048690691 + 0,2,6,8,12,18,20,26,30,32,36 Tuplet 53 2003 Jens K. Andersen 
11 11450665899501 · 101# + 39058751 + 0,2,6,8,12,18,20,26,30,32,36 Tuplet 52 2003 Norman Luhn
11 946772106455 · 90# + 872141 + 0,2,6,8,12,18,20,26,30,32,36 Tuplet 47 2003 Jens K. Andersen 
11 3676296453875 · 80# + 10527733922591 + 0,2,6,8,12,18,20,26,30,32,36 Tuplet 44 2001 Norman Luhn
 
12 x83c · 71# · 2n - 1, n=0..11 CC, 1st kind 112 2014 Primecoin
12 x81c · 53# · 2n ± 1, n=0..5 BiTwin 101 2013 Primecoin
12 x81b · 43# · 2n + 1, n=0..11 CC, 2nd kind 99 2013 Primecoin
12 13931865163581 · 127# · 2n + 1, n=0..11 CC, 2nd kind 64 2008 Dirk Augustin, NewPGen, PrimeForm
12 (8428860 · 127# + 212148902055090) · 2n + 1, n=0..11 CC, 2nd kind 58 2006 Jens K. Andersen
12 (4691553 · 97# + 704765232261090) · 2n ± 1, n=0..5 BiTwin 44 2004 Jens K. Andersen
12 332352838383 · 80# + 38458151 + 0,2,6,8,12,18,20,26,30,32,36,42 Tuplet 43 2003 Jens K. Andersen
12 5027317106963 · 75# + 1418575498567 + 0,6,10,12,16,22,24,30,34,36,40,42 Tuplet 42 2001 Norman Luhn
 
13 x84 · 61# · 2n - 1, n=0..12 CC, 1st kind 108 2014 Primecoin
13 x83b · 31# · 2n + 1, n=0..12 CC, 2nd kind 96 2013 Primecoin
13 14815550 · 107# + 4385574275277311 + 
2,6,8,12,18,20,26,30,32,36,42,48,50
Tuplet 50 2013 Roger Thompson
13 61571 · 107# + 4803194122972361 + 
0,2,6,8,12,18,20,26,30,32,36,42,48
Tuplet 48 2009 Jens K. Andersen
13 381955327397348 · 79# + 18393209 + 
2,8,14,18,20,24,30,32,38,42,44,48,50
Tuplet 46 2007 Norman Luhn
13 1753286498051 · 71# · 2n - 1, n=0..12 CC, 1st kind 41 2005 Dirk Augustin, NewPGen, PrimeForm
13 (938719 · 67# + 56461354019070) · 2n+1, n=0..12 CC, 2nd kind 33 2004 Jens K. Andersen
13 129017282 · 65# + 3001560376931 + 0,2,6,8,12,18,20,26,30,32,36,42,48 Tuplet 32 2003 Torbjörn Alm & Jens K. Andersen
13 5953176232124 · 50# + 9564671 + 0,2,6,8,12,18,20,26,30,32,36,42,48 Tuplet 31 2003 Jens K. Andersen
13 1000000008282508019026959814211 + 2,6,8,12,18,20,26,30,32,36,42,48,50 Tuplet 31 2000 Joerg Waldvogel & Peter Leikauf
 
14 14815550 · 107# + 4385574275277311 + 
0,2,6,8,12,18,20,26,30,32,36,42,48,50
Tuplet 50 2013 Roger Thompson
14 381955327397348 · 79# + 18393209 + 
0,2,8,14,18,20,24,30,32,38,42,44,48,50
Tuplet 46 2007 Norman Luhn
14 26093748 · 67# + 383123187762431 + 0,2,6,8,12,18,20,26,30,32,36,42,48,50 Tuplet 33 2005 Christ van Willegen & Jens K. Andersen
14 99999999948164978600250563546400 + 11,13,17,19,23,29,31,37,41,43,47,53,59,61 Tuplet 32 2004 Joerg Waldvogel & Peter Leikauf
14 1251030012595955901312188450381 + 0,2,6,8,12,18,20,26,30,32,36,42,48,50 Tuplet 31 2003 Hans Rosenthal & Jens K. Andersen
14 1124495649695212998778414534811 + 0,2,6,8,12,18,20,26,30,32,36,42,48,50 Tuplet 31 2003 Thomas Wolter & Jens K. Andersen
14 1000000008282508019026959814211 + 0,2,6,8,12,18,20,26,30,32,36,42,48,50 Tuplet 31 2000 Joerg Waldvogel & Peter Leikauf
 
15 10004646546202610858599716515809907 + 0,2,6, 12,14,20,24,26,30,36,42,44,50,54,56 Tuplet 35 2012 Roger Thompson
15 28320350134887132315879689643840 · 2n + 1, n=0..14 CC, 2nd kind 34 2008 Jaroslaw Wroblewski
15 107173714602413868775303366934621 + 0,2,6,8,12,18,20,26,30,32,36,42,48,50,56 Tuplet 33 2008 Jens K. Andersen
15 99999999948164978600250563546400 + 11,13,17,19,23,29,31,37,41,43,47,53,59,61,67 Tuplet 32 2004 Joerg Waldvogel & Peter Leikauf
15 1251030012595955901312188450381 + 0,2,6,8,12,18,20,26,30,32,36,42,48,50,56 Tuplet 31 2003 Hans Rosenthal & Jens K. Andersen
15 999999999962618227626700812281 + 0,2,6,8,12,18,20,26,30,32,36,42,48,50,56 Tuplet 30 2000 Joerg Waldvogel & Peter Leikauf
 
16 1003234871202624616703163933853 + 0,4,6, 10,16,18,24,28,30,34,40,46,48,54,58,60 Tuplet 31 2012 Roger Thompson
16 2368823992523350998418445521 · 2n + 1, n=0..15 CC, 2nd kind 30 2008 Jaroslaw Wroblewski
16 20193491108493165642344880 · 2n + 1, n=0..15 CC, 2nd kind 28 2008 Jaroslaw Wroblewski
16 1302312696655394336638440 · 2n + 1, n=1..16 CC, 2nd kind 27 2008 Jaroslaw Wroblewski
16 258296136493222766530020 · 2n + 1, n=0..15 CC, 2nd kind 26 2008 Jaroslaw Wroblewski
16 127806074555607670094730 · 2n + 1, n=1..16 CC, 2nd kind 26 2008 Jaroslaw Wroblewski
16 91304653283578934559360 · 2n - 1, n=0..15 CC, 1st kind 26 2008 Jaroslaw Wroblewski
16 10252256693298561414756287 + 0,2,6, 12,14,20,26,30,32,36,42,44,50,54,56,60 Tuplet 26 2004 Jens K. Andersen
16 2845372542509911868266807 + 10,12, 16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 25 2000 Joerg Waldvogel & Peter Leikauf
 
17 1540797425367761006138858880 · 2n + 1, n=0..16 CC, 2nd kind 30 2014 Raanan Chermoni & Jaroslaw Wroblewski
17 658189097608811942204322720 · 2n + 1, n=1..17 CC, 2nd kind 30 2014 Raanan Chermoni & Jaroslaw Wroblewski
17 465463467291895470464386320 · 2n + 1, n=0..16 CC, 2nd kind 30 2014 Raanan Chermoni & Jaroslaw Wroblewski
17 100845391935878564991556707107 + 0,2,6, 12,14,20,24,26,30,36,42,44,50,54,56,62,66 Tuplet 30 2013 Roger Thompson
17 11413975438568556104209245223 + 0,4,6, 10,16,18,24,28,30,34,40,46,48,54,58,60,66 Tuplet 29 2011 Roger Thompson
17 1440214698782377829920161551 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 28 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 1193626642220508556578935357 + 0,2,6, 12,14,20,24,26,30,36,42,44,50,54,56,62,66 Tuplet 28 2011 Roger Thompson
17 1189738328255580204892107257 + 0,2,6, 12,14,20,24,26,30,36,42,44,50,54,56,62,66 Tuplet 28 2011 Roger Thompson
17 1022964394011851868818264017 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66 Tuplet 28 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 947007693039130553371313771 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 917810189564189435979968491 + 10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 865481269763090471673405217 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 783356226566404898275621751 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 772723255295737480928966771 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 766631303403477668452873513 + 0,4,6, 10,16,18,24,28,30,34,40,46,48,54,58,60,66 Tuplet 27 2011 Roger Thompson
17 730862462126306661846437737 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 711896327852024279416294841 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 663553629195874803746553191 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 646823491570043772214553321 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 635239540644425515747001047 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 597173610793158380251873601 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 572264871047109012711451507 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 528949036434611485053784421 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 506768097227010102028237687 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
17 446899237331752168867376467 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66 Tuplet 27 2010 Raanan Chermoni & Jaroslaw Wroblewski
17 388813564304223666130115591 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 27 2010 Raanan Chermoni & Jaroslaw Wroblewski
17 356357564387652563232359861 + 0,6,8, 12,18,20,26,32,36,38,42,48,50,56,60,62,66 Tuplet 27 2010 Raanan Chermoni & Jaroslaw Wroblewski
17 1302312696655394336638440 · 2n + 1, n=0..16 CC, 2nd kind 27 2008 Jaroslaw Wroblewski
17 127806074555607670094730 · 2n + 1, n=0..16 CC, 2nd kind 26 2008 Jaroslaw Wroblewski
17 40244844789379926979140 · 2n + 1, n=0..16 CC, 2nd kind 26 2008 Jaroslaw Wroblewski
17 2845372542509911868266807 + 4,10,12, 16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 25 2000 Joerg Waldvogel & Peter Leikauf
 
18 658189097608811942204322720 · 2n + 1, n=0..17 CC, 2nd kind 30 2014 Raanan Chermoni & Jaroslaw Wroblewski
18 182927793839529342111307800 · 2n + 1, n=0..17 CC, 2nd kind 29 2014 Raanan Chermoni & Jaroslaw Wroblewski
18 5621078036155517013724659007 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 28 2014 Raanan Chermoni & Jaroslaw Wroblewski
18 4668263977931056970475231217 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 28 2014 Raanan Chermoni & Jaroslaw Wroblewski
18 3361885098594416802447362317 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 28 2013 Raanan Chermoni & Jaroslaw Wroblewski
18 2650778861583720495199114537 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 28 2013 Raanan Chermoni & Jaroslaw Wroblewski
18 2406179998282157386567481191 + 6,10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 28 2012 Raanan Chermoni & Jaroslaw Wroblewski
18 2348190884512663974906615481 + 6,10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 28 2012 Raanan Chermoni & Jaroslaw Wroblewski
18 2152095346273291005088484977 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 28 2012 Raanan Chermoni & Jaroslaw Wroblewski
18 1752347810197939558619028007 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 28 2012 Raanan Chermoni & Jaroslaw Wroblewski
18 1657958103171451056593631007 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 28 2012 Raanan Chermoni & Jaroslaw Wroblewski
18 1378931799889412563577465677 + 0,4,10, 12,16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 28 2011 Raanan Chermoni & Jaroslaw Wroblewski
18 917810189564189435979968491 + 6,10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
18 656632460108426841186109951 + 6,10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
18 630134041802574490482213901 + 6,10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
18 601884606346328759496455407 + 0,4,10,12, 16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
18 183837276562811649018077773 + 0,4,6,10, 16,18,24,28,30,34,40,46,48,54,58,60,66,70 Tuplet 27 2010 Jaroslaw Wroblewski
18 159272023128204753638724847 + 0,4,10,12, 16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 27 2010 Jaroslaw Wroblewski
18 51342365971531191697537333 + 0,4,6,10, 16,18,24,28,30,34,40,46,48,54,58,60,66,70 Tuplet 26 2009 Jaroslaw Wroblewski
18 44453357465442632103684223 + 0,4,6,10, 16,18,24,28,30,34,40,46,48,54,58,60,66,70 Tuplet 26 2009 Jaroslaw Wroblewski
18 33755528632220819791319947 + 0,4,10,12, 16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 26 2009 Jaroslaw Wroblewski
18 23531820918273007548405133 + 0,4,6,10, 16,18,24,28,30,34,40,46,48,54,58,60,66,70 Tuplet 26 2009 Jaroslaw Wroblewski
18 11298510058634407483251313 + 0,4,6,10, 16,18,24,28,30,34,40,46,48,54,58,60,66,70 Tuplet 26 2008 Jaroslaw Wroblewski
18 4530085223434265844952597 + 0,4,10,12, 16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 25 2008 Jaroslaw Wroblewski
18 2845372542509911868266807 + 0,4,10,12, 16,22,24,30,36,40,42,46,52,54,60,64,66,70 Tuplet 25 2000 Joerg Waldvogel & Peter Leikauf
 
19 79910197721667870187016100 · 2n + 1, n=0..18 CC, 2nd kind 29 2014 Raanan Chermoni & Jaroslaw Wroblewski
19 42008163485623434922152330 · 2n + 1, n=0..18 CC, 2nd kind 29 2014 Raanan Chermoni & Jaroslaw Wroblewski
19 2406179998282157386567481191 + 0,6,10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 28 2012 Raanan Chermoni & Jaroslaw Wroblewski
19 2348190884512663974906615481 + 0,6,10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 28 2012 Raanan Chermoni & Jaroslaw Wroblewski
19 917810189564189435979968491 + 0,6,10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
19 656632460108426841186109951 + 0,6,10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
19 630134041802574490482213901 + 0,6,10,16, 18,22,28,30,36,42,46,48,52,58,60,66,70,72,76 Tuplet 27 2011 Raanan Chermoni & Jaroslaw Wroblewski
19 30702013451021547907 + 29# · n, n=1..19 AP 20 2008 Jaroslaw Wroblewski
19 28195514826922573189 + 29# · n, n=1..19 AP 20 2008 Jaroslaw Wroblewski
19 22855978072012553147 + 29# · n, n=0..18 AP 20 2008 Jaroslaw Wroblewski
19 19316011345882272017 + 29# · n, n=1..19 AP 20 2008 Jaroslaw Wroblewski
19 17196286091474921689 + 29# · n, n=0..18 AP 20 2008 Jaroslaw Wroblewski
19 14275160661224928539 + 29# · n, n=0..18 AP 20 2008 Jaroslaw Wroblewski
19 12167225693277514633 + 29# · n, n=0..18 AP 20 2008 Jaroslaw Wroblewski
19 11794878875045456989 + 29# · n, n=0..18 AP 20 2008 Jaroslaw Wroblewski
19 11512568504244030089 + 29# · n, n=1..19 AP 20 2008 Jaroslaw Wroblewski
19 8463643902010505569 + 29# · n, n=0..18 AP 19 2008 Jaroslaw Wroblewski
19 6619756800771371627 + 29# · n, n=0..18 AP 19 2008 Jaroslaw Wroblewski
19 2357208768504754823 + 29# · n, n=1..19 AP 19 2008 Jaroslaw Wroblewski
19 1464072733127278531 + 29# · n, n=0..18 AP 19 2007 Jaroslaw Wroblewski
19 21167397384723757 + 29# · n, n=0..18 AP 17 2006 Jaroslaw Wroblewski
19 206063865762371 + 29# · n, n=0..18 AP 15 2006 Jaroslaw Wroblewski
 
20 35182855408632706168481 + 29# · n, n=0..19 AP 23 2014 Jaroslaw Wroblewski
20 21237391176980112635587 + 29# · n, n=0..19 AP 23 2014 Jaroslaw Wroblewski
20 732521705233593674363 + 29# · n, n=0..19 AP 21 2014 Jaroslaw Wroblewski
20 112729427143771808611 + 29# · n, n=0..19 AP 21 2014 Jaroslaw Wroblewski
20 63499970321885347427 + 29# · n, n=0..19 AP 20 2014 Jaroslaw Wroblewski
20 55083559098541779413 + 29# · n, n=0..19 AP 20 2014 Jaroslaw Wroblewski
20 30702013451021547907 + 29# · n, n=0..19 AP 20 2008 Jaroslaw Wroblewski
20 28195514826922573189 + 29# · n, n=0..19 AP 20 2008 Jaroslaw Wroblewski
20 19316011345882272017 + 29# · n, n=0..19 AP 20 2008 Jaroslaw Wroblewski
20 11512568504244030089 + 29# · n, n=0..19 AP 20 2008 Jaroslaw Wroblewski
20 2357208768504754823 + 29# · n, n=0..19 AP 19 2008 Jaroslaw Wroblewski
20 843882398917750139 + 29# · n, n=0..19 AP 18 2007 Jaroslaw Wroblewski
20 19645711679859961 + 29# · n, n=0..19 AP 17 2006 Jaroslaw Wroblewski
 
21 5547796991585989797641 + 29# · n, n=0..20 AP 22 2014 Jaroslaw Wroblewski
21 28112131522731197609 + 19# · n, n=0..20 AP 20 2008 Jaroslaw Wroblewski

xN is an N-digit number which was used in a record but has no simple expression.
x77 = 545382416838875826681897035 90110659057865934764604873840781923513421103495579
x80 = 73853903764168979088206401473739410396455001112581722569026969860983656346568919
x81a = 566002435353389048470195154197633715327639809354150079355350346671860564824949963
x81b = 263663326886409378473341387047271336974122837948496277769621396327294641140893808
x81c = 223673331265817252994407640089592745163575915313761280958903819304727806835314518
x83a = 39027761902802007714618528725397363585108921377235848032440823132447464787653697269
x83b = 10756750720700195380397697188448178460115725467111771468875842964723844354555016704
x83c = 61592551716229060392971860549140211602858978086524024531871935735163762961673908480
x84 = 106680560818292299253267832484567360951928953599522278361651385665522443588804123392
x89 = 44598464649019035883154084128331646888059795218766083584048621139159337786287845212160000
x155 = 573501051193549030504900787301835825160485101511983854806 08646918133804223879167823802443758585361919599047776527963058 419047009660578164772858363185263809
x177 = 248780094097472243404896912 18520204523173891494265205671857771054034765718993 39316926569630394295966974033459801501769756510157 97243607875744813349096932598456481621971387004081

Rules
The listed number of digits is for the median prime, i.e. the i'th of 2i or 2i-1 primes. This prime determines the comparison to other sets. Using the median is more fair but means the digit count may vary from pages for CC's and BiTwins.
All primes must be above 1012 (mainly to avoid listing uninteresting k-tuplets of tiny primes).
All primes must be proven, i.e. not just probable primes.
The record for k=1 is simply the largest known prime.
There are restrictions for k>1 to satisfy a reasonable interpretation of "simultaneous".

Allowed forms include:
Tuplets (primes as closely together as possible).
CC's (Cunningham Chains) of the 1st or 2nd kind.
BiTwins (chains of twin primes).
AP-k (k primes in arithmetic progression): Only allowed with difference k# or p# or q#, where p and q are the smallest primes above k.
CPAP-k (k consecutive primes in arithmetic progression): Same restriction as AP-k.

Disallowed forms include:
AP-k and CPAP-k with other differences than explicitly allowed above.
Generalized BiTwins (at bottom of linked page).
Generalized CC's (Cunningham Chains).

I am not aware of a previous comparison of this type and chose rules which seem fair for the intended purpose. You can suggest rule changes, but arbitrary AP's will never be allowed.
The rules for allowed forms were made with the idea that k numbers on a specific predetermined form should be primes simultaneously. The form should usually only be able to vary one thing, e.g. the first prime.
It should not be possible to compute a large set of primes and then find some subset of k numbers with something in common, or choose a function which runs through k already known primes.
An AP search usually first computes a large set of primes and then tests for AP's by varying both one of the primes and the difference. This is much easier than finding simultaneous primes. Extreme example: Any 2 numbers are in AP, so the 2 largest known primes will always form an AP-2 which is obviously disallowed (unless it has an allowed difference).
The longest known AP has 26 primes. The largest known number of simultaneous primes satisfying the rules is an AP21 with difference 19# and 20 digits. The smallest 18-tuplet above 100 has 25 digits and may have been harder to find. The smallest AP's above 1000 are usually much smaller than the smallest case of other forms, because there are more small candidates without small prime factors. This makes it easier to find small examples of many simultaneous primes for AP's. Sieving methods means this should not give AP's an advantage when competing for the largest known case, when other forms have a known case.

Submissions
I would like to hear of all new records. Please mail any you find or know about, but note the AP/CPAP rule. Say who should be credited, and which program proved the primes if they are above 1000 digits.
If you are considering a form not mentioned then you can e-mail me and ask whether it will be allowed. If you think you have found a clever form which makes a search much easier than the explicitly allowed forms, then the form almost certainly has a property that will not be allowed. Extreme example: The n'th prime for k consecutive values of n.

Created and maintained by Jens Kruse Andersen, jens.k.a@get2net.dk   home
Last updated 7 April 2014.