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
2019
October 28. A twenty-third 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
October 17. A twenty-second 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
September 25. A twenty-first 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
August 19. A twentieth 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
July 17. A nineteenth 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
June 17. New record: 527-digit 7-tuplet by Vidar Nakling, rieMiner.
April 23. New record: 20008-digit triplet by Peter Kaiser, PolySieve, LLR,
Primo.
February 25. New record: 10132-digit quadruplet by Peter Kaiser, PolySieve, LLR,
Primo.
February 17. An eighteenth 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
2018
December 27. A third 30-digit 21-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski. Also contains record 19-tuplet.
December 23. A seventeenth 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
December 7. New record for largest known prime: 24862048-digit Mersenne prime by Patrick Laroche, GIMPS.
August 30. A sixteenth 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
May 23. A fifteenth 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
March 15. A fourteenth 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
January 28. A thirteenth 30-digit 20-tuplet by Raanan Chermoni & Jaroslaw Wroblewski.
January 17. New record: 515-digit 7-tuplet by Norman Luhn, Primo.
2017
December 26. New record for largest known prime: 23249425-digit Mersenne prime by Jonathan Pace, GIMPS.
December 7. A twelfth 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
May 24. New record: An eleventh 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
2016
December 7. New record: A tenth 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
November 18. New record: 35-digit 16-tuplet by Roger Thompson.
November 8. New record: 2018-digit CC-5 2nd kind by Andrey Balyakin.
November 3. New record: 1766-digit CC-5 1st kind by Andrey Balyakin.
November 3. New record: 151-digit CC-11 2nd kind by Andrey Balyakin.
October 15. New record: 1680-digit CC-5 1st kind by Michael Angel, Dirk Augustin,
NewPGen, PrimeForm.
September 29. New record: 1631-digit CC-5 2nd kind by Michael Angel, Dirk Augustin,
NewPGen, PrimeForm.
September 14. New record: 388342-digit twin prime by Tom Greer, PrimeGrid, TwinGen, LLR.
August 1. New record: A second 30-digit 21-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski. Also contains record 20-tuplet and 19-tuplet.
May 31. New record: An eighth 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
March 16. New record: A seventh 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
March 14. New record: 1037-digit sextuplet by Norman Luhn, Primo.
March 10. New record: 152-digit CC-10 1st kind by Andrey Balyakin.
March 10. New record: 261-digit CC-9 1st kind by Andrey Balyakin.
March 10. New record: 338-digit CC-8 2nd kind by Andrey Balyakin.
March 10. New record: 1535-digit CC-5 2nd kind by Andrey Balyakin.
March 8. New record: 5003-digit quadruplet by Peter Kaiser, NewPGen, PolySieve, LLR,
Primo.
March 2. New record: 1493-digit CC-5 1st kind by Oscar Östlin, NewPGen,
PrimeForm.
February 29. New record: 388342-digit Sophie Germain prime by Scott
Brown, PrimeGrid, TwinGen, LLR.
January 7. New record for largest known prime: 22338618-digit Mersenne prime by Curtis Cooper, GIMPS.
January 3. New record: A sixth 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
2015
December 31. New record: 509-digit CC7 1st kind by Andrey
Balyakin.
December 31. New record: 151-digit CC10 1st kind by Andrey
Balyakin.
December 31. New record: 47-digit CC15 1st kind by Andrey
Balyakin.
December 17. New record: 454-digit CC7 2nd kind by Andrey
Balyakin.
December 17. New record: 266-digit CC8 1st kind by Andrey
Balyakin.
December 17. New record: 191-digit CC9 1st kind by Andrey
Balyakin.
December 17. New record: 44-digit CC15 1st kind by Andrey
Balyakin.
December 16. New record: A fifth 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
November 20. New record: 239-digit CC-8 1st kind by Oscar Östlin, NewPGen,
PrimeForm.
October 8. New record: A fourth 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
October 8. New record: 30-digit 21-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski. Also contains record 19-tuplet.
September 13. New record: 3598-digit quadruplet by Serge Batalov, NewPGen, PrimeForm, Primo.
September 9. New record: A third 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
September 3. New record: A second 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
August 12. New record: 30-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
July 11. New record: A sixth 29-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
May 15. New record: 382-digit CC7 1st kind by Andrey
Balyakin.
May 15. New record: 189-digit CC9 2nd kind by Andrey
Balyakin.
May 15. New record: 147-digit CC11 2nd kind by Andrey
Balyakin.
May 15. New record: 123-digit CC12 2nd kind by Andrey
Balyakin.
April 22. New record: A fifth 29-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
April 6. New record: 150-digit BiTwin with 4 links (10 primes) by Andrey
Balyakin.
March 31. New record: 1016-digit CC6 1st kind by Serge Batalov, NewPGen,
PrimeForm.
February 6. New record: A fourth 29-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
January 23. New record: 700-digit 6-tuplet by
Vidar Nakling, Primo.
January 8. New record: 29-digit 21-tuplet by Raanan Chermoni & Jaroslaw Wroblewski. Also contains record
20-tuplet.
2014
December 11. New record: A second 29-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
November 24. New record: 654-digit 6-tuplet by Riecoin, Primo.
October 6. New record: 29-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
July 24. New record: 368-digit CC7 1st kind by Serge Batalov, NewPGen,
PrimeForm.
June 24. New record: 28-digit 20-tuplet by Raanan Chermoni &
Jaroslaw Wroblewski.
June 22. New record: 236-digit 8-tuplet by Norman Luhn.
June 11. This page is moved to http://primerecords.dk/simultprime.htm.
May 16. New record: 102-digit CC14 2nd kind by Primecoin.
April 25. New record: 43-digit CC-15 1st kind by
Jaroslaw Wroblewski.
April 6. New record: A second 23-digit AP20 by
Jaroslaw Wroblewski.
April 6. New record: 118-digit BiTwin with 5 links (12 primes) by Primecoin.
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 (moved again in 2014).
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.
| k | Primes | Type | Digits | Year | Discoverer |
|---|---|---|---|---|---|
| 1 | 282589933-1 | Mersenne | 24862048 | 2018 | Patrick Laroche, GIMPS |
| 2 | 2996863034895 · 21290000 ± 1 | Tuplet (twin) | 388342 | 2016 | Tom Greer, PrimeGrid, TwinGen, LLR |
| 3 | 4111286921397 · 266420 -1, +1, +5 | Tuplet | 20008 | 2019 | Peter Kaiser, PolySieve, LLR, Primo |
| 4 | 667674063382677 · 233608 - 1, +1, +5, +7 | Tuplet | 10132 | 2019 | Peter Kaiser, PolySieve, LLR, Primo |
| 5 | 181439827616655015936 · 4673# · 2n + 1, n=0..4 | CC, 2nd kind | 2018 | 2016 | Andrey Balyakin |
| 6 | 28993093368077 · 2399# + 19417 + 0, 4, 6, 10, 12, 16 | Tuplet | 1037 | 2016 | Norman Luhn, Primo |
| 7 | x397 · 317# + 1068701 + 0, 2, 6, 8, 12, 18, 20 | Tuplet | 527 | 2019 | Vidar Nakling, rieMiner |
| 8 | 2373007846680317952 · 761# · 2n + 1, n=0..7 | CC, 2nd kind | 338 | 2016 | Andrey Balyakin |
| 9 | 553374939996823808 · 593# · 2n - 1, n=0..8 | CC, 1st kind | 261 | 2016 | Andrey Balyakin |
| 10 | 3696772637099483023015936 · 311# · 2n - 1, n=0..9 | CC, 1st kind | 152 | 2016 | Andrey Balyakin |
| 11 | 341841671431409652891648 · 311# · 2n + 1, n=0..10 | CC, 2nd kind | 151 | 2016 | Andrey Balyakin |
| 12 | 906644189971753846618980352 · 233# · 2n + 1, n=0..11 | CC, 2nd kind | 123 | 2015 | Andrey Balyakin |
| 13 | x84 · 61# · 2n - 1, n=0..12 | CC, 1st kind | 108 | 2014 | Primecoin |
| 14 | x82 · 47# · 2n + 1, n=0..13 | CC, 2nd kind | 102 | 2014 | Primecoin |
| 15 | 14354792166345299956567113728 · 43# · 2n - 1, n=0..14 | CC, 1st kind | 47 | 2015 | Andrey Balyakin |
| 16 | 322255 · 73# + 1354238543317302647 + 0,2,6,12,14,20,26,30,32,36,42,44,50,54,56,60 | Tuplet | 35 | 2016 | 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 | 622803914376064301858782434517 + 0,4,6,10,12, 16,24,30,34,40,42,46,52,54,60,66,70,72,76 | Tuplet | 30 | 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 839013472011818416634745523991 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2019 | Raanan Chermoni & Jaroslaw Wroblewski |
| 21 | 622803914376064301858782434517 + 0,4,6,10,12, 16,24,30,34,40,42,46,52,54,60,66,70,72,76,82,84 | Tuplet | 30 | 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
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.
PolySieve by
Robert Gerbicz.
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.
by Thomas Nguyen and other contributors.
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.
Riecoin
| k | Primes | Type | Digits | Year | Discoverer |
|---|---|---|---|---|---|
| 1 | 282589933-1 | Mersenne | 24862048 | 2018 | Patrick Laroche, GIMPS |
| 1 | 277232917-1 | Mersenne | 23249425 | 2017 | Jonathan Pace, GIMPS |
| 1 | 274207281-1 | Mersenne | 22338618 | 2016 | Curtis Cooper, GIMPS |
| 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 | 2996863034895 · 21290000 ± 1 | Tuplet (twin) | 388342 | 2016 | Tom Greer, PrimeGrid, TwinGen, LLR |
| 2 | 2618163402417 · 21290000 · 2n - 1, n=0..1 | CC, 1st kind (Sophie Germain) | 388342 | 2016 | Scott Brown, PrimeGrid, TwinGen, LLR |
| 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 | 4111286921397 · 266420 -1, +1, +5 | Tuplet | 20008 | 2019 | Peter Kaiser, PolySieve, LLR, Primo |
| 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 | 667674063382677 · 233608 - 1, +1, +5, +7 | Tuplet | 10132 | 2019 | Peter Kaiser, PolySieve, LLR, Primo |
| 4 | 4122429552750669 · 216567 - 1, +1, +5, +7 | Tuplet | 5003 | 2016 | Peter Kaiser, NewPGen, PolySieve, LLR, Primo |
| 4 | 2673092556681 · 153048 - 4, -2, +2, +4 | Tuplet | 3598 | 2015 | Serge Batalov, NewPGen, PrimeForm, Primo |
| 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 | 181439827616655015936 · 4673# · 2n + 1, n=0..4 | CC, 2nd kind | 2018 | 2016 | Andrey Balyakin |
| 5 | 31017701152691334912 · 4091# · 2n - 1, n=0..4 | CC, 1st kind | 1766 | 2016 | Andrey Balyakin |
| 5 | 3387614923 · 3917# · 2n - 1, n=0..4 | CC, 1st kind | 1680 | 2016 | Michael Angel, Dirk Augustin, NewPGen, PrimeForm |
| 5 | 6413732664 · 3797# · 2n + 1, n=0..4 | CC, 2nd kind | 1631 | 2016 | Michael Angel, Dirk Augustin, NewPGen, PrimeForm |
| 5 | 646737879652976640 · 3559# · 2n + 1, n=0..4 | CC, 2nd kind | 1535 | 2016 | Andrey Balyakin |
| 5 | 199949435137 · 3499# · 2n - 1, n=0..4 | CC, 1st kind | 1493 | 2016 | Oscar Östlin, NewPGen, PrimeForm |
| 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 | 28993093368077 · 2399# + 19417 + 0, 4, 6, 10, 12, 16 | Tuplet | 1037 | 2016 | Norman Luhn, Primo |
| 6 | 2799873605326 · 2371# · 2n - 1, n=0..5 | CC, 1st kind | 1016 | 2015 | Serge Batalov, NewPGen, PrimeForm |
| 6 | x279 · 1013# + 6503587 + 0,4,6,10,12,16 | Tuplet | 700 | 2015 | Vidar Nakling, Primo |
| 6 | x586 · 173# + 16057 + 0,4,6,10,12,16 | Tuplet | 654 | 2014 | Riecoin, Primo |
| 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 | x397 · 317# + 1068701 + 0, 2, 6, 8, 12, 18, 20 | Tuplet | 527 | 2019 | Vidar Nakling, rieMiner |
| 7 | 115828580393941 · 1200# + 5132201 + 0,2,6,8,12,18,20 | Tuplet | 515 | 2018 | Norman Luhn, Primo |
| 7 | 82466536397303904 ·1171# · 2n - 1, n=0..6 | CC, 1st kind | 509 | 2015 | Andrey Balyakin |
| 7 | 25802590081726373888 ·1033# · 2n + 1, n=0..6 | CC, 2nd kind | 454 | 2015 | Andrey Balyakin |
| 7 | 3931472185692005387730944 · 857# · 2n - 1, n=0..6 | CC, 1st kind | 382 | 2015 | Andrey Balyakin |
| 7 | 14317181455772 · 853# · 2n - 1, n=0..6 | CC, 1st kind | 368 | 2014 | Serge Batalov, NewPGen, PrimeForm |
| 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 | 2373007846680317952 · 761# · 2n + 1, n=0..7 | CC, 2nd kind | 338 | 2016 | Andrey Balyakin |
| 8 | 89628063633698570895360 · 593# · 2n - 1, n=0..7 | CC, 1st kind | 266 | 2015 | Andrey Balyakin |
| 8 | 5175268103676 · 557# · 2n - 1, n=0..7 | CC, 1st kind | 239 | 2015 | Oscar Östlin, NewPGen, PrimeForm |
| 8 | 29995576270632 · 550# + 1277 + 0,2,6,12,14,20,24,26 | Tuplet | 236 | 2014 | 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 | 553374939996823808 · 593# · 2n - 1, n=0..8 | CC, 1st kind | 261 | 2016 | Andrey Balyakin |
| 9 | 40912747216912409971130368 · 401# · 2n - 1, n=0..8 | CC, 1st kind | 191 | 2015 | Andrey Balyakin |
| 9 | 173129832252242394185728 · 401# · 2n + 1, n=0..8 | CC, 2nd kind | 189 | 2015 | Andrey Balyakin |
| 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 | 3696772637099483023015936 · 311# · 2n - 1, n=0..9 | CC, 1st kind | 152 | 2016 | Andrey Balyakin |
| 10 | 380036435653000196587520 · 311# · 2n - 1, n=0..9 | CC, 1st kind | 151 | 2015 | Andrey Balyakin |
| 10 | 144941178918272079102115840 · 307# · 2n ± 1, n=0..4 | BiTwin | 150 | 2015 | Andrey Balyakin |
| 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 | 341841671431409652891648 · 311# · 2n + 1, n=0..10 | CC, 2nd kind | 151 | 2016 | Andrey Balyakin |
| 11 | 19298029794843054654 · 311# · 2n + 1, n=0..10 | CC, 2nd kind | 147 | 2015 | Andrey Balyakin |
| 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 | 906644189971753846618980352 · 233# · 2n + 1, n=0..11 | CC, 2nd kind | 123 | 2015 | Andrey Balyakin |
| 12 | x81d · 61# · 2n ± 1, n=45..50 | BiTwin | 118 | 2014 | Primecoin |
| 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 | x82 · 47# · 2n + 1, n=0..13 | CC, 2nd kind | 102 | 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 |
| 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 | 14354792166345299956567113728 · 43# · 2n - 1, n=0..14 | CC, 1st kind | 47 | 2015 | Andrey Balyakin |
| 15 | 14366587870229772953764096 · 43# · 2n - 1, n=0..14 | CC, 1st kind | 44 | 2015 | Andrey Balyakin |
| 15 | 27353790674175627273118204975428644651730 · 2n - 1, n=0..14 | CC, 1st kind | 43 | 2014 | Jaroslaw Wroblewski |
| 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 | 322255 · 73# + 1354238543317302647 + 0,2,6,12,14,20,26,30,32,36,42,44,50,54,56,60 | Tuplet | 35 | 2016 | 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 |
| 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 | 622803914376064301858782434517 + 0,4,6,10,12, 16,24,30,34,40,42,46,52,54,60,66,70,72,76 | Tuplet | 30 | 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| 19 | 248283957683772055928836513589 + 8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80,84 | Tuplet | 30 | 2016 | Raanan Chermoni & Jaroslaw Wroblewski |
| 19 | 138433730977092118055599751669 + 8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80,84 | Tuplet | 30 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 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 | 839013472011818416634745523991 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2019 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 831504454982803270879178298359 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2019 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 807462397198198801670343382679 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2019 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 789292095021856634277511882469 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2019 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 764364269069907627842423582909 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2019 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 667424014858149638371951648871 + 0,2,6,8, 12,20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2019 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 639121700726230052098229452019 + 0,2,8,12, 14,18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 562422394447827908154562532159 + 0,2,8,12, 14,18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 494179332730633784520908832239 + 0,2,8,12, 14,18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 466435879660522367654413675211 + 0,2,6,8, 12,20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 452101241612347545944528242469 + 0,2,8,12, 14,18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 403065917762608576939692599261 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2017 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 352259532126245901475150592651 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2017 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 260786413629117930695179308299 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2016 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 248283957683772055928836513589 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2016 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 220974232729147341120519932981 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2016 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 187976201367296936422347098471 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2016 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 161375347518710752668754312691 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2016 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 154016910009801751265474541311 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 140661282456312925227370009589 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 121888742383899006588229597469 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 114601431611676407654036210321 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 30 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 111286948968140923889225384099 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 30 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 97344384991448238094880899499 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 29 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 69611500022230424427263424221 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 29 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 40814702190384518551961455541 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 29 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 39433867730216371575457664399 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 29 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 17546231261175189855273591491 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 29 | 2014 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 14374153072440029138813893241 + 0,2,6,8,12, 20,26,30,36,38,42,48,50,56,62,66,68,72,78,80 | Tuplet | 29 | 2014 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 3941119827895253385301920029 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80 | Tuplet | 28 | 2014 | Raanan Chermoni & 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 | 622803914376064301858782434517 + 0,4,6,10,12, 16,24,30,34,40,42,46,52,54,60,66,70,72,76,82,84 | Tuplet | 30 | 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| 21 | 248283957683772055928836513589 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80,84 | Tuplet | 30 | 2016 | Raanan Chermoni & Jaroslaw Wroblewski |
| 21 | 138433730977092118055599751669 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80,84 | Tuplet | 30 | 2015 | Raanan Chermoni & Jaroslaw Wroblewski |
| 21 | 39433867730216371575457664399 + 0,2,8,12,14, 18,24,30,32,38,42,44,50,54,60,68,72,74,78,80,84 | Tuplet | 29 | 2015 | Raanan Chermoni & 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
x81d = 386727562407905441323542867468313504832835283009085268004408453725770596763660073
x82 = 5819411283298069803200936040662511327268486153212216998535044251830806354124236416
x83a = 39027761902802007714618528725397363585108921377235848032440823132447464787653697269
x83b = 10756750720700195380397697188448178460115725467111771468875842964723844354555016704
x83c = 61592551716229060392971860549140211602858978086524024531871935735163762961673908480
x84 = 106680560818292299253267832484567360951928953599522278361651385665522443588804123392
x89 = 44598464649019035883154084128331646888059795218766083584048621139159337786287845212160000
x155 =
573501051193549030504900787301835825160485101511983854806
08646918133804223879167823802443758585361919599047776527963058
419047009660578164772858363185263809
x177 = 248780094097472243404896912 18520204523173891494265205671857771054034765718993
39316926569630394295966974033459801501769756510157 97243607875744813349096932598456481621971387004081
x279 = 39192012090354765012032937869
63620446183193864072395084531670244391789850454987
90600310298931245078011665141488718221144402728008
84198554607462042723509866995108041645298700784996
91992151722541551955298630979698530841904537286500
37452220380184681391570092753684727879715473377537
x397 = 32821868878860201045633341031688415601401701228
32878265333984717524446848642006351778066196724473
92249620201536539259942023218972369026762290403609
01005487309186655777663859063397693729163631275766
07799875309038457637116938538279395260265064447747
74261236889041020217108597484837589978261046949778
71991825164994665583879769659044973939714534960362
41885200541893611077817261813672809971503287259089
x586 = 414011906395692562707625916642009279
19784381401630770332154929293398379732931526432717
68110685094930596054056039071084677868651232321497
06387759691959890180822248736604808055974283449242
04717278233388912711575086138672038905509854691940
89965337548559187345043456954721787760988692205272
93364477300012589402397085151427849425715928696400
18730515113148148353596839911851088674650293533764
53558170146445192639606953562379978691400614099121
92788772270248979414914544447140290584313409867748
76659101771881199524569126026881866340566377525162
48275209509392841432650248795223050106564589182501
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, found in 2008. 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. A 21-tuplet with 29 digits was found in 2015. It may be the smallest
above 100.
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 29 October 2019.