# Primes in Arithmetic Progression Records

23 September 2019 Rob Gahan and PrimeGrid found the first known AP27: 224584605939537911 + 81292139·23#·n, for n = 0..26.

Introduction
News: 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005
Submissions
The largest known AP-k
Credited programs and projects
Record history for the largest known AP-k:
k = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Smallest AP-k with minimal difference
Record history for smallest AP-k with minimal difference: k = 18 19 20 21 22 23 24 25 26 27
Smallest AP-k with minimal start
Record history for smallest AP-k with minimal start: k = 16 17 18 19 20 21 22 23 24 25 26 27
AP-k with minimal end
Record history for AP-k with minimal end
All known AP24 to AP27

Introduction
This page shows the largest known case of k primes in AP (arithmetic progression) for each k, with a record history. It also shows the minimal or smallest known difference, start and end in an AP-k, with record histories. Finally it shows all known AP24 until an AP26 was found, and all known AP25. Record histories begin with the record when the page opened in January 2005.
An AP-k is k primes of the form p + d·n for some d (the difference between the primes) and k consecutive values of n. Technically any 2 primes form an AP2 but this page is only about AP3 and longer. Some sources say PAP-k instead of AP-k to signal it is primes in AP.
The Largest Known CPAP's is a different page with records for consecutive primes in AP.

Dirichlet's Theorem on Primes in Arithmetic Progressions says there are always infinitely many primes of the form c + d·n, when c and d are relatively prime - and consecutive n's are not demanded.
Ben Green & Terence Tao presented a proof in 2004 that The primes contain arbitrarily long arithmetic progressions. It shows existence of AP's but does not help in finding them.

January 18 2007 Jaroslaw Wroblewski discovered the first known AP24 with 75 computers: 468395662504823 + 205619·23#·n, for n = 0..23.
Before that the longest known AP was 23 primes in arithmetic progression by Markus Frind, Paul Jobling & Paul Underwood in 2004.
May 17 2008 Raanan Chermoni & Jaroslaw Wroblewski discovered the first known AP25 with a lot of computing power: 6171054912832631 + 366384·23#·n, for n = 0..24.
April 12 2010 Benoãt Perichon and PrimeGrid discovered the first known AP26 with the distributed AP26 Search: 43142746595714191 + 23681770·23#·n, for n = 0..25.
September 23 2019 Rob Gahan and PrimeGrid discovered the first known AP27 with the AP26 program: 224584605939537911 + 81292139·23#·n, for n = 0..26.

k# (called k primorial) is the product of all primes ≤ k, e.g. 10# = 2 · 3 · 5 · 7.
2# = 2, 3# = 6, 5# =30, 7# = 210, 11# = 2310, 13# = 30030, 17# = 510510, 19# = 9699690, 23# = 223092870.
Unless k is prime and starts an AP-k, the difference in an AP-k is always a multiple of k# to avoid factors ≤ k. Expressions with larger primorials are often used in AP searches to avoid more small factors. Most large AP's are found roughly like this:
First compute a large set of primes a·q#+1 for fixed q. Then find AP's among the a's.
This gives an AP formula like (4941928071 + 176836494·n)·2411#+1, for n=0..7
It can be written on the form p + d·n: (4941928071·2411#+1) + (176836494·2411#)·n

News
2019
December 27. AP14 record with 103 digits by Norman Luhn, NewPGen, PrimeForm.
December 27. A second AP13 record with 103 digits by Norman Luhn, NewPGen, PrimeForm.
September 23. First known AP27 by Rob Gahan, PrimeGrid, AP26. It has 18 digits and is also the largest known AP24, AP25 and AP26.
August 28. AP13 record with 103 digits by Norman Luhn, NewPGen, PrimeForm.
August 25. AP10 record with 450 digits by Norman Luhn, NewPGen, PrimeForm.
August 11. AP8 record with 2271 digits by Norman Luhn, Paul Underwood, Ken Davis, Primeform e-group, NewPGen, PrimeForm.
July 27. AP19 (also AP18) record with 31 digits by Norman Luhn.
July 24. AP18 record with 31 digits by Norman Luhn.
July 4. A second AP4 record with 25992 digits by Ken Davis, NewPGen, PrimeForm.
June 21. A second AP18 record with 30 digits by Norman Luhn.
June 18. AP8 record with 1101 digits by Mike Oakes, NewPGen, PrimeForm.
June 18. AP11 record with 289 digits by Norman Luhn.
June 8. AP12 record with 180 digits by Norman Luhn.
May 23. AP15 record with 68 digits by Norman Luhn.
May 14. AP10 record with 340 digits by Norman Luhn.
April 20. AP15 record with 60 digits by Mike Oakes.
March 24. AP10 record with 327 digits by Mike Oakes.
March 8. AP4 record with 25992 digits by Ken Davis, NewPGen, PrimeForm.
February 28. AP13 record with 101 digits by Norman Luhn.
February 25. AP18 record with 30 digits by Norman Luhn.
February 20. AP17 (also AP16) record with 43 digits by Norman Luhn.
February 19. AP15 record with 57 digits by Norman Luhn.
January 25. AP14 record with 74 digits by Norman Luhn.
January 19. AP10 record with 300 digits by Norman Luhn and Gerd Lamprecht.

2018
November 1. AP5 record with 10378 digits by Ken Davis, NewPGen, PrimeForm.
August 12. AP26 (also AP25 and AP24) record with 18 digits by Syracuse University, PrimeGrid, AP26.
July 19. AP5 record with 10377 digits by Ken Davis, NewPGen, PrimeForm.
May 5. AP13 record with 93 digits by Norman Luhn, NewPGen, PrimeForm.
April 22. AP6 record with 7036 digits by Ken Davis, NewPGen, PrimeForm.

2017
December 1. First known AP20 with the minimal start 23 found by Wojciech Izykowski. Also AP20 record (largest known end) with 29 digits.
November 10. AP25 (also AP24) record with 18 digits by Bill Brandt-Gasuen, PrimeGrid, AP26.
August 21. AP25 (also AP24) record with 18 digits by David E. Miller, PrimeGrid, AP26.
August 19. AP6 record with 3343 digits by Michael Stocker, PrimeForm.
June 22. AP5 record with 10114 digits by Michael Stocker, NewPGen, PrimeForm.
June 17. AP25 (also AP24) record with 18 digits by William Donovan, PrimeGrid, AP26.
March 25. AP5 record with 7657 digits by Michael Stocker, NewPGen, PrimeForm.

2016
December 18. AP3 record with 435054 digits by David Broadhurst, NewPGen, PrimeForm, et al.
June 17. AP5 record with 7035 digits by Ken Davis, NewPGen, PrimeForm.
June 12. AP3 record with 388342 digits by Serge Batalov, NewPGen, LLR, et al.
April 1. A fifth AP24 record with 18 digits by Bryan Little, AP26.
January 21. AP3 record with 388342 digits by Serge Batalov, NewPGen, LLR, et al.

2015
December 4. AP5 record with 7026 digits by Serge Batalov, NewPGen, PrimeForm.
September 29. AP3 record with 388342 digits by David Broadhurst, NewPGen, PrimeForm, et al.
February 20. A second AP26 (also AP25 and AP24) record with 18 digits by Bryan Little, AP26.

2014
September 2. AP17 (also AP16) record with 42 digits by Jaroslaw Wroblewski.
July 9. A third AP25 record with 18 digits by Bryan Little, AP26.
June 24. AP24 with smallest known difference (65073·23#) by Bryan Little, AP26.
May 25. A third AP24 record with 18 digits by Bryan Little, AP26.
April 25. AP20 record with 25 digits by Jaroslaw Wroblewski.
April 16. AP23 (also AP22) record with 20 digits by Jaroslaw Wroblewski.
April 13. AP19 (also AP18) record with 30 digits by Jaroslaw Wroblewski.
April 2. AP21 record with 22 digits by Jaroslaw Wroblewski.
March 14. A fourth AP21 record with 20 digits by Jaroslaw Wroblewski.
March 12. A third AP21 record with 20 digits by Jaroslaw Wroblewski.
March 7. AP20 record with 23 digits by Jaroslaw Wroblewski.
February 23. AP26 (also AP25 and AP24) record with 18 digits by Bryan Little, AP26.
January 13. AP24 record with 18 digits by Bryan Little, AP26.

2013
October 17. AP25 record with 18 digits by Bryan Little, AP26.
April 5. Smallest AP19 with the minimal start 19 found by Wojciech Izykowski. April 10 he completed showing it is the smallest.
February 26. First known AP19 with the minimal start 19 found by Wojciech Izykowski. The difference (13234551541698967679·17#) is not the smallest possible.

2012
October 31. Smallest AP18 with the minimal start 19 found by Gennady Gusev.
March 16. AP26 with smallest known difference (1666981·23#), start (3486107472997423) and end (12783396861134173) by James Fry. It is the second known AP26.
February 8. AP7 (also AP6) record with 3019 digits by Ken Davis, NewPGen, PrimeForm.
January 3. A second AP9 record with 1014 digits by Ken Davis, Paul Underwood, PrimeForm egroup, NewPGen, PrimeForm.

2011
August 1. AP9 record with 1014 digits (the first known titanic AP9) by Ken Davis, Paul Underwood, PrimeForm egroup, NewPGen, PrimeForm.
June 8. A second AP6 record with 3019 digits by Ken Davis, NewPGen, PrimeForm.
March 1. AP3 record with 200701 digits by David Broadhurst, NewPGen, PrimeForm, et al.

2010
December 22. AP13 record with 85 digits by Mike Oakes, NewPGen, PrimeForm.
October 24. AP4 record with 24092 digits by David Broadhurst, NewPGen, PrimeForm.
August 18. AP6 record with 3019 digits by Ken Davis, NewPGen, PrimeForm.
August 15. AP7 record with 1402 digits by Mike Oakes, NewPGen, PrimeForm.
July 28. AP4 record with 15004 digits by Mike Oakes, NewPGen, PrimeForm.
July 15. AP9 record with 446 digits by Mike Oakes, NewPGen, PrimeForm.
June 5. A second AP4 record with 13556 digits by David Broadhurst, NewPGen, PrimeForm.
June 3. AP4 record with 13556 digits by David Broadhurst, NewPGen, PrimeForm.
May 22. AP6 record with 3004 digits by Mike Oakes, NewPGen, PrimeForm.
May 20. AP13 record with 83 digits by Ken Davis, NewPGen, PrimeForm.
May 18. A second AP4 record with 12050 digits by David Broadhurst, NewPGen, PrimeForm.
May 17. AP4 record with 12050 digits by David Broadhurst, NewPGen, PrimeForm.
April 30. AP11 (also AP10) record with 283 digits by Ken Davis, NewPGen, PrimeForm.
April 30. AP3 record with 159382 digits by David Broadhurst, PrimeForm, et al.
April 29. AP7 record with 1335 digits by Ken Davis, NewPGen, PrimeForm.
April 20. AP3 record with 155300 digits by David Broadhurst, PrimeForm, et al.
April 12. First known AP26 by Benoãt Perichon and PrimeGrid. It has 18 digits.
April 2. AP25 record with 18 digits by Chris Wingate, PrimeGrid, AP26.
March 14. AP25 record with 18 digits by Dave Sunderland, PrimeGrid, AP26.
February 28. AP3 record with 154804 digits by David Broadhurst, PrimeForm, et al.
February 25. AP25 record with 18 digits by Keith Pattenden, PrimeGrid, AP26.
February 24. AP24 record with 18 digits by John Petterson, PrimeGrid, AP26.
February 24. AP24 record with 18 digits by Edward Gordon, PrimeGrid, AP26.

2009
December 21. AP24 record with 18 digits by Dave Mumper, PrimeGrid, AP26.
December 19. AP24 record with 18 digits by Jesper Kågefors, PrimeGrid, AP26.
December 16. AP25 (also AP24) record with 18 digits by Rune Nordbøe Skillingstad, PrimeGrid, AP26.
December 13. AP7 record with 1328 digits by Mike Oakes, NewPGen, PrimeForm.
December 11. AP14 record with 71 digits by Mike Oakes, NewPGen, PrimeForm.
December 4. AP24 record with 18 digits by Piotr M. Zalewski, PrimeGrid, AP26.
November 25. AP25 record with 17 digits by Ian Dickinson, PrimeGrid, AP26. It is the fifth known AP25.
November 18. AP6 record with 2153 digits by Ken Davis, NewPGen, PrimeForm.
November 14. AP17 (also AP16) record with 42 digits by Mike Oakes, NewPGen, PrimeForm.
November 13. AP24 record with 18 digits by Roald Solbjørg, PrimeGrid, AP26.
November 8. AP24 record with 17 digits by Marcus Rosario, PrimeGrid, AP26.
November 5. AP24 record with 17 digits by Chris Wingate, PrimeGrid, AP26.
November 1. AP24 record with 17 digits by Ian Dickinson, PrimeGrid, AP26.
October 10. AP24 record with 17 digits by Anonymous, PrimeGrid, AP26.
October 4. AP24 record with 17 digits by John S Morris III, PrimeGrid, AP26.
September 24. AP15 record with 54 digits by Mike Oakes, NewPGen, PrimeForm.
September 18. AP24 record with 17 digits by Kevin Erickson, PrimeGrid, AP26.
September 8. AP25 record with 17 digits by Keith Dale, PrimeGrid, AP26. It is the fourth known AP25.
September 2. AP25 record with 17 digits by Jochen Beck, PrimeGrid, AP26. It is the third known AP25.
September 1. AP10 record with 274 digits by Mike Oakes, NewPGen, PrimeForm.
August 23. AP24 record with 17 digits by Bryan Little, PrimeGrid, AP26.
August 3. AP11 record with 196 digits by Jeff Anderson-Lee, NewPGen, PrimeForm.
July 19. AP24 record with 17 digits by Jan-Cornelius Molnar, PrimeGrid, AP26.
July 13. AP6 record with 2145 digits by Mike Oakes, NewPGen, PrimeForm.
July 9. AP24 smallest known start (39421708111691) by Mark Codding, PrimeGrid, AP26.
July 4. AP24 record with 17 digits by Carsten Hartwig, PrimeGrid, AP26.
June 30. AP24 record with 17 digits by Anonymous, PrimeGrid, AP26.
June 1. AP10 record with 265 digits by Ken Davis, NewPGen, PrimeForm.
May 29. AP23 with smallest known start (20389023122473) by Eric Markle, PrimeGrid, AP26.
May 29. AP22 with smallest known start (1322554958713) by Jacek Kotnowski, PrimeGrid, AP26.
May 16. AP9 record with 425 digits by Ken Davis, NewPGen, PrimeForm.
May 6. AP24 record with 17 digits by Andreas Kobara, PrimeGrid, AP26. Also AP24 with smallest known start (167806194923077).
April 21. AP8 record with 1057 digits by Ken Davis, NewPGen, PrimeForm.
April 9. AP25 record with 17 digits by BOINC@Poland, PrimeGrid, AP26. It is the second known AP25 and also has the smallest known start (2960886048458003).
April 7. AP24 record with 17 digits by Pawel Stachowiak, PrimeGrid, AP26.
March 4. AP5 record with 7009 digits by Ken Davis, NewPGen, PrimeForm.
February 22. AP21 with smallest known start (124701216737) by Ryszard Walczak from BOINC@Poland, Jaroslaw Wroblewski.
February 22. Three new tables added with record histories for the smallest known difference, start and end in an AP-k.
February 19. AP20 with smallest known start (566547019) by Aleksander Parkitny from BOINC@Poland, Jaroslaw Wroblewski.
February 1. AP20 with smallest known start (24670154221) by Sebastian Jaworowicz from BOINC@Poland, Jaroslaw Wroblewski.
January 26. AP19 with smallest known start (275525353) by Mariusz Szafranski from BOINC@Poland, Jaroslaw Wroblewski.
January 23. This page is moved to http://users.cybercity.dk/~dsl522332/math/aprecords.htm (moved again in 2014).
January 21. AP19 with smallest known start (275955343) by Mariusz Szafranski from BOINC@Poland, Jaroslaw Wroblewski.
January 18. Table of all known AP24 and AP25 added.
January 8. AP19 with smallest known start (1358498353) by Machloj from BOINC@Poland, Jaroslaw Wroblewski.

2008
December 3. Smallest AP21 with the minimal difference 19# by Jaroslaw Wroblewski. Also a second AP21 record with 20 digits.
December 2. Smallest AP19 and AP20 with the minimal difference 19# by Jaroslaw Wroblewski.
December 1. AP22 record with 19 digits by Jaroslaw Wroblewski.
August 26. AP23 (also AP22) record with 19 digits by Raanan Chermoni & Jaroslaw Wroblewski.
August 10. A sixth AP22 record with 18 digits by Raanan Chermoni & Jaroslaw Wroblewski.
August 7. AP23 (also a fifth AP22) record with 18 digits by Raanan Chermoni & Jaroslaw Wroblewski.
August 4. A fourth AP22 record with 18 digits by Raanan Chermoni & Jaroslaw Wroblewski.
July 26. A third AP22 record with 18 digits by Raanan Chermoni & Jaroslaw Wroblewski.
July 3. A second AP22 record with 18 digits by Raanan Chermoni & Jaroslaw Wroblewski.
June 29. AP22 record with 18 digits by Raanan Chermoni & Jaroslaw Wroblewski.
June 24. AP5 record with 6913 digits by David Broadhurst, NewPGen, PrimeForm.
May 23. AP19 with smallest known start (2027663243) by Jaroslaw Wroblewski.
May 17. First known AP25 by Raanan Chermoni & Jaroslaw Wroblewski. It has 16 digits.
April 21. AP24 with smallest known start (401516288036293) by Raanan Chermoni & Jaroslaw Wroblewski.
April 18. AP24 with smallest known difference (136831·23#) and end (1217585417914253) by Raanan Chermoni & Jaroslaw Wroblewski.
April 15. A fifth AP23 record with 17 digits by Raanan Chermoni & Jaroslaw Wroblewski.
April 10. A fourth AP23 record with 17 digits by Raanan Chermoni & Jaroslaw Wroblewski.
March 22. AP24 record with 17 digits by Raanan Chermoni & Jaroslaw Wroblewski.
March 19. A third AP23 record with 17 digits by Raanan Chermoni & Jaroslaw Wroblewski.
March 2. A second AP23 record with 17 digits by Raanan Chermoni & Jaroslaw Wroblewski.
February 27. AP16 record with 38 digits by Jeff Anderson-Lee, NewPGen, PrimeForm.
February 25. AP23 record with 17 digits by Raanan Chermoni & Jaroslaw Wroblewski. Also AP23 with smallest known start (43760869165417).
January 28. A second AP23 record with 16 digits by Raanan Chermoni & Jaroslaw Wroblewski.
January 8. A third AP4 record with 11961 digits by Ken Davis, NewPGen, PrimeForm.

2007
December 31. AP21 with smallest known difference (208·19#) by Pawel Nowak & Jaroslaw Wroblewski.
October 5. A second AP4 record with 11961 digits by Ken Davis, NewPGen, PrimeForm.
September 26. AP4 record with 11961 digits by Ken Davis, NewPGen, PrimeForm.
August 31. AP24 (also AP23) record with 16 digits by Raanan Chermoni & Jaroslaw Wroblewski.
August 27. AP3 record with 137514 digits by Jens Kruse Andersen, PrimeForm, et al.
August 15. AP14 record with 69 digits by Jens Kruse Andersen.
August 4. AP18 record with 29 digits by Jens Kruse Andersen.
August 3. AP17 record with 29 digits by Jens Kruse Andersen.
July 27. AP4 record with 10544 digits by Jim Fougeron, PrimeForm.
February 21. AP22 record with 18 digits by Jaroslaw Wroblewski.
February 20. AP20 record with 21 digits by Jaroslaw Wroblewski.
February 10. AP19 record (also AP18 and AP17) with 27 digits by Jaroslaw Wroblewski.
February 9. AP5 record with 5132 digits by Ken Davis, APTreeSieve, PrimeForm.
February 9. AP19 record with 21 digits by Jaroslaw Wroblewski.
February 8. AP21 (also AP20) record with 20 digits by Jaroslaw Wroblewski.
February 7. AP20 record with 19 digits by Jaroslaw Wroblewski.
February 7. A third AP20 record with 18 digits by Jaroslaw Wroblewski.
February 6. AP21 record with 18 digits by Jaroslaw Wroblewski.
February 4. A fifth AP21 record with 17 digits by Jaroslaw Wroblewski.
February 4. A second AP22 (also a fourth AP21) record with 17 digits by Jaroslaw Wroblewski.
February 4. AP22 (also a third AP21) record with 17 digits by Jaroslaw Wroblewski.
February 3. A second AP21 record with 17 digits by Jaroslaw Wroblewski.
January 31. A second AP23 record with 16 digits by Jaroslaw Wroblewski.
January 26. AP11 record with 195 digits by Jeff Anderson-Lee, NewPGen, PrimeForm.
January 18. First known AP24 (also largest AP23 with 16 digits) by Jaroslaw Wroblewski.
January 11. AP22 with smallest known start (1365385579783) by Jaroslaw Wroblewski.
January 9. AP18 record with 24 digits and also smallest known start (47) by Gennady Gusev.
January 9. AP23 record with 16 digits by Markus Frind (found June 24 2006 but unpublished).
January 6. AP18 record with 22 digits by Jaroslaw Wroblewski.
January 4. AP20 (also AP19) with smallest known difference (5·19#) by Jaroslaw Wroblewski.
January 3. AP19 with smallest known difference (11·19#) by Jaroslaw Wroblewski.
January 1. AP21 record with 17 digits by Jaroslaw Wroblewski.

2006
December 28. AP18 record with 21 digits by Jaroslaw Wroblewski.
December 28. AP9 record with 401 digits by Mike Oakes, NewPGen, PrimeForm.
December 21. A second AP20 record with 18 digits by Jaroslaw Wroblewski.
December 18. AP20 record with 18 digits by Jaroslaw Wroblewski.
December 17. AP4 record with 10004 digits by Mike Oakes, NewPGen, PrimeForm.
December 11. AP12 (also AP11) record with 173 digits by Jeff Anderson-Lee, NewPGen, PrimeForm.
October 4. AP11 record with 150 digits by Jeff Anderson-Lee, NewPGen, PrimeForm.
September 25. AP12 (also AP11) record with 128 digits by Jeff Anderson-Lee, NewPGen, PrimeForm.
September 24. AP14 record with 60 digits by Mike Oakes, NewPGen, PrimeForm.
September 14. AP13 record with 78 digits by Mike Oakes, NewPGen, PrimeForm.
August 7. AP10 record with 260 digits by Mike Oakes, NewPGen, PrimeForm.
June 28. AP16 record with 36 digits by Mike Oakes, NewPGen, PrimeForm.
May 8. AP22 with smallest known difference (9959·19#) by Markus Frind.
April 28. AP6 record with 1606 digits by Ken Davis, NewPGen, PrimeForm.
April 6. AP9 record with 325 digits by Jens Kruse Andersen.
April 1. Another AP22 (also AP21 this time) record with 16 digits by Markus Frind.
April 1. AP23 with smallest known difference (9523·23#) and end (449924511422857) by Markus Frind.
March 31. AP6 record with 1503 digits by Mike Oakes, NewPGen, PrimeForm.
March 25. AP12 record with 100 digits by Jens Kruse Andersen.
March 23. AP13 record with 64 digits by Jens Kruse Andersen.
March 15. AP22 record with 16 digits by Markus Frind.
March 11. AP21 record with 16 digits by Markus Frind.
February 26. AP23 with smallest known difference (156722·23#) and end (869507044019447) by Markus Frind.
February 18. A third AP7 (also AP6) record with 1290 digits by Ken Davis, NewPGen, PrimeForm.
February 15. A second AP7 (also AP6) record with 1290 digits by Ken Davis, NewPGen, PrimeForm.
February 12. AP12 record with 91 digits by Norman Luhn.
February 12. AP9 record with 301 digits by Mike Oakes, APSieve, PrimeForm.
February 11. AP7 (also AP6) record with 1290 digits by Ken Davis, NewPGen, PrimeForm.
February 10. AP9 record with 215 digits by Norman Luhn.
February 7. AP13 record with 57 digits by Norman Luhn.
February 2. AP12 record with 77 digits by Mike Oakes, PrimeForm.

2005
December 8. AP18 with smallest known start 602521111 by Gennady Gusev.
May 8. AP5 record with 5132 digits by Ken Davis, PrimeForm.
April 24. Smallest AP18 with minimal difference found by Gennady Gusev & Jens Kruse Andersen.
February 18. AP3 record with 129240 digits by David Broadhurst, PrimeForm, et al.
February 3. Smallest AP16 with the minimal start 17 found by Phil Carmody.
February 2. Two new tables with minimal (or smallest known) starting and ending prime in an AP-k.
January 24. This page is published at http://hjem.get2net.dk/jka/math/aprecords.htm. New records for AP9 to AP19 by Jens Kruse Andersen.

Submissions
I would like to hear of all new records. Please mail any you find or know about to jens.k.a@get2net.dk. Say who should be credited, and which program proved the primes if they are above 500 digits.
All primes must be proven, i.e. prp's (probable primes) are not allowed.
The largest prime in an AP determines which AP is judged largest, so an AP3 record could start at 3.
An AP-k is also considered to be an AP-(k-1), so it can hold the record for different k's.

n's not starting at 0 indicates the end of a longer AP. The listed number of digits is for the largest prime in all tables. A year link is to an announcement. The k value links to the record history.

The largest known AP-k
k Primes n's Digits Year Discoverer
3 (2723880039837 · 21290000-1) + (4125·21445205-2723880039837·21290000)·n 0..2 435054 2016 David Broadhurst, David Abrahmi, David Metcalfe, TwinGen, NewPGen, srsieve, PSieve, Rieselprime, PrimeGrid, LLR, PrimeForm
4 (1021747532 + 7399459·n)·60013#+1 0..3 25992 2019 Ken Davis, NewPGen, PrimeForm
5 (161291608 + 59874860·n)·24001#+1 0..4 10378 2018 Ken Davis, NewPGen, PrimeForm
6 (1445494494 + 141836149·n)·16301#+1 0..5 7036
2018 Ken Davis, NewPGen, PrimeForm
7 (234043271 + 481789017·n)·7001#+1 0..6 3019 2012 Ken Davis, NewPGen, PrimeForm
8 (48098104751 + 3026809034·n)·5303#+1 0..7 2271 2019 Norman Luhn, Paul Underwood, Ken Davis, Primeform e-group, NewPGen, PrimeForm
9 (65502205462 + 6317280828·n)·2371#+1 0..8 1014 2012 Ken Davis, Paul Underwood, PrimeForm egroup, NewPGen, PrimeForm
10 (20794561384 + 1638155407·n)·1050#+1 0..9 450
2019 Norman Luhn, NewPGen, PrimeForm
11 (16533786790 + 1114209832·n)·666#+1 0..10 289 2019 Norman Luhn
12 (15079159689 + 502608831·n)·420#+1 0..11 180 2019 Norman Luhn
13 (50448064213 + 4237116495·n)·229#+1 0..12 103
2019 Norman Luhn, NewPGen, PrimeForm
14 (55507616633 + 670355577·n)·229#+1 0..13 103
2019 Norman Luhn, NewPGen, PrimeForm
15 (14512034548 + 87496195·n)·149#+1
0..14 68 2019 Norman Luhn
16 (9700128038 + 75782144·n)·83#+1 1..16 43 2019 Norman Luhn
17 (9700128038 + 75782144·n)·83#+1 0..16 43 2019 Norman Luhn
18 (33277396902 + 139569962·n)·53#+1 1..18 31 2019 Norman Luhn, NewPGen, PrimeForm
19 (33277396902 + 139569962·n)·53#+1 0..18 31 2019 Norman Luhn, NewPGen, PrimeForm
2023 + 134181089232118748020·19#·n0..1929
2017Wojciech Izykowski
21 5547796991585989797641 + 29#·n 0..20 22 2014 Jaroslaw Wroblewski
22 22231637631603420833 + 8·41#·n 1..22 20 2014 Jaroslaw Wroblewski
23 22231637631603420833 + 8·41#·n 0..22 20 2014 Jaroslaw Wroblewski
24 224584605939537911 + 81292139·23#·n 3..26 18 2019 Rob Gahan, PrimeGrid, AP26
25 224584605939537911 + 81292139·23#·n 2..26 18 2019 Rob Gahan, PrimeGrid, AP26
26 224584605939537911 + 81292139·23#·n 1..26 18 2019 Rob Gahan, PrimeGrid, AP26
27 224584605939537911 + 81292139·23#·n 0..26 18 2019 Rob Gahan, PrimeGrid, AP26

Credited programs and projects
Programs:
NewPGen by Paul Jobling.
APSieve by Michael Bell and Jim Fougeron.
APTreeSieve by Jens Kruse Andersen.
srsieve by Geoffrey Reynolds.
TwinGen by David Underbakke.
PSieve by Geoff Reynolds and Ken Brazier.
FermFact by Jim Fougeron.
LLR by Jean Penné.
PrimeForm by the OpenPFGW group with George Woltman.
Proth.exe by Yves Gallot.
PRP by George Woltman.
AP26 by Jaroslaw Wroblewski and Geoff Reynolds.
The primality proving program is only credited above 500 digits.

Projects:
BOINC@Poland (in Polish)
PrimeGrid
Riesel Prime Search
Primeform e-group

The below table contains (to the best of my knowledge) the records per January 1, 2005, and all records set since then.

Record history for the largest known AP-k
k Primes n's Digits Year Discoverer
3 (2723880039837 · 21290000-1) + (4125·21445205-2723880039837·21290000)·n 0..2 435054 2016 David Broadhurst, David Abrahmi, David Metcalfe, TwinGen, NewPGen, srsieve, PSieve, Rieselprime, PrimeGrid, LLR, PrimeForm
3 (731362328595 + 1986593776260·n)·21290000-1 0..2 388342 2016 Serge Batalov, Randy Ready, Simon Geis, NewPGen, TwinGen, PrimeGrid, LLR
3 (907717371825 + 1312259228802·n)·21290000-1 0..2 388342 2016 Serge Batalov, James Scott Brown, Simon Geis, NewPGen, TwinGen, PrimeGrid, LLR
3 (483590093385 + 1367824406910·n)·21290000-1 0..2 388342 2015 David Broadhurst, Ernst Fluttert, Randall Scalise, PrimeGrid, TwinGen, LLR, NewPGen, PrimeForm
3 (8175435610410 + 32289415560495·n)·2666666-1 0..2 200701 2011 David Broadhurst, Tony Gott, Ulrich Fries, PrimeGrid, TwinGen, LLR, NewPGen, PrimeForm
3 (1539·2263359+1) + (1185·2529444-1539·2263359)·n 0..2 159382 2010 David Broadhurst, Sascha Dinkel, Steven Harvey, FermFact, srsieve, PrimeGrid, PrimeForm, LLR
3 (907·2338934+1) + (71·2515885-907·2338934)·n 0..2 155300 2010 David Broadhurst, Steven Harvey, NewPGen, srsieve, PRP, PrimeForm
3 (11347·2508209-1) + (103939·2514229-11347·2508209)·n 0..2 154804 2010 David Broadhurst, Thomas Ritschel, Lei Zhou, Riesel Prime Search, NewPGen, srsieve, LLR, PrimeForm
3 (1769267·2340000-1) + (1061839·2456789-1769267·2340000)·n 0..2 137514 2007 Jens Kruse Andersen, Jiong Sun, Daniel Heuer, NewPGen, LLR, PrimeForm
3 (197·2202534-1) + (17·2429318-197·2202534)·n 0..2 129240 2005 David Broadhurst, Peter Grobstich, Mark Anderson, Proth.exe, LLR, PrimeForm
3 (405769059·2180009-1) + (45·2368553-405769059·2180009)·n 0..2 110948 2003 Jiong Sun, NewPGen, LLR, PrimeForm

4 (1021747532 + 7399459·n)·60013#+1 0..3 25992 2019 Ken Davis, NewPGen, PrimeForm
4(1006521663 + 6205834·n)·60013#+10..3259922019Ken Davis, NewPGen, PrimeForm
4 (1631979959·225000-1) + (164196977·280000-1631979959·225000)·n 0..3 24092 2010 David Broadhurst, NewPGen, PrimeForm
4 (1000362700 + 2571033·n)·34687#+1 0..3 15004 2010 Mike Oakes, NewPGen, PrimeForm
4 (487069965·225001-1) + (87940527·245001-487069965·225001)·n 0..3 13556 2010 David Broadhurst, NewPGen, PrimeForm
4 (183009063·225002-1) + (1367721·245007-183009063·225002)·n 0..3 13556 2010 David Broadhurst, NewPGen, PrimeForm
4 (464049135·225001-1) + (181836669·240000-464049135·225001)·n 0..3 12050 2010 David Broadhurst, NewPGen, PrimeForm
4 (222139713·225000-1) + (165710943·240000-222139713·225000)·n 0..3 12050 2010 David Broadhurst, NewPGen, PrimeForm
4 (100997770 + 3624707·n)·27751#+1 0..3 11961 2008 Ken Davis, NewPGen, PrimeForm
4 (100668506 + 809963·n)·27751#+1 0..3 11961 2007 Ken Davis, NewPGen, PrimeForm
4 (101056849 + 412064·n)·27751#+1 0..3 11961 2007 Ken Davis, NewPGen, PrimeForm
4 (18271126 + 9548007·n)·235000+1 0..3 10544 2007 Jim Fougeron, PrimeForm
4 (2024725 + 197732·n)·23159#+1 0..3 10004 2006 Mike Oakes, NewPGen, PrimeForm
4 (3897833 + 19575072·n)·225000-1 0..3 7534 2004 David Broadhurst, PrimeForm

5(161291608 + 59874860·n)·24001#+10..410378 2018Ken Davis, NewPGen, PrimeForm
5 (130673984 + 22703701·n)·24001#+1 0..4 10377 2018 Ken Davis, NewPGen, PrimeForm
5(39062872 + 8829881·n)·23431#-10..410114
2017Michael Stocker, NewPGen, PrimeForm
5 (101390511 + 36694699·n)·17761#-1 0..4 7657 2017 Michael Stocker, NewPGen, PrimeForm
5 (988418181 + 7078086·n)·16301#+1 0..4 7035 2016 Ken Davis, NewPGen, PrimeForm
5 (43728051 + 18797279·n)·16267#-1 0..4 7026 2015 Serge Batalov, NewPGen, PrimeForm
5 (82751511 + 20333209·n)·16229#+1 0..4 7009 2009 Ken Davis, NewPGen, PrimeForm
5 (2799788209 + 13265760·n)·16001#/5+1 0..4 6913 2008 David Broadhurst, NewPGen, PrimeForm
5 ((49077426729 + 681402540·n) · 205881·4001#/35·(205881·4001#+1) + 6) · (205881·4001#-1) + 7 0..4 5132 2007 Ken Davis, APTreeSieve, PrimeForm
5 ((3433500709 + 8222924605·n) · 205881·4001#/35·(205881·4001#+1) + 6) · (205881·4001#-1) + 7 0..4 5132 2005 Ken Davis, PrimeForm
5 (207727829 + 280455315·n)·5113#/35+1 0..4 2197 2002 Jim Fougeron, Hans Rosenthal, PrimeForm

6 (1445494494 + 141836149·n)·16301#+1 0..5 7036
2018 Ken Davis, NewPGen, PrimeForm
6
(44003657 + 12009836·n)·7759#-10..533432017Michael Stocker, PrimeForm
6 (234043271 + 481789017·n)·7001#+1 1..6 3019 2012 Ken Davis, NewPGen, PrimeForm
6 (987502724 + 41489812·n)·7001#+1 0..5 3019 2011 Ken Davis, NewPGen, PrimeForm
6 (967858482 + 19401803·n)·7001#+1 0..5 3019 2010 Ken Davis, NewPGen, PrimeForm
6 (1020460444 + 21411611·n)·6977#+1 0..5 3004 2010 Mike Oakes, NewPGen, PrimeForm
6 (19303382 + 41724940·n)·5011#+1 0..5 2153 2009 Ken Davis, NewPGen, PrimeForm
6 (36543956 + 6632285·n)·5003#+1 0..5 2145 2009 Mike Oakes, NewPGen, PrimeForm
6 (32649185 + 3884057·n)·3739#+1 0..5 1606 2006 Ken Davis, NewPGen, PrimeForm
6 (27477652 + 3603821·n)·3529#+1 0..5 1503 2006 Mike Oakes, NewPGen, PrimeForm
6 (143850392 + 114858412·n)·3011#+1 1..6 1290 2006 Ken Davis, NewPGen, PrimeForm
6 (135477657 + 114379137·n)·3011#+1 1..6 1290 2006 Ken Davis, NewPGen, PrimeForm
6 (479778674 + 1679489·n)·3011#+1 1..6 1290 2006 Ken Davis, NewPGen, PrimeForm
6 (21054583 + 8440140·n)·3011#+1 0..5 1289 2005 Ken Davis, NewPGen, PrimeForm
6 (17239418 + 8274192·n)·3011#+1 0..5 1289 2005 Ken Davis, NewPGen, PrimeForm
6 (18015883 + 2611270·n)·3011#+1 0..5 1288 2004 Ken Davis, NewPGen, PrimeForm

7 (234043271 + 481789017·n)·7001#+1 0..6 3019 2012 Ken Davis, NewPGen, PrimeForm
7 (280120647 + 30017636·n)·3301#+1 0..6 1402 2010 Mike Oakes, NewPGen, PrimeForm
7 (1198555389 + 5893725·n)·3121#+1 0..6 1335 2010 Ken Davis, NewPGen, PrimeForm
7 (1246733996 + 35777939·n)·3109#+1 0..6 1328 2009 Mike Oakes, NewPGen, PrimeForm
7 (143850392 + 114858412·n)·3011#+1 0..6 1290 2006 Ken Davis, NewPGen, PrimeForm
7 (135477657 + 114379137·n)·3011#+1 0..6 1290 2006 Ken Davis, NewPGen, PrimeForm
7 (479778674 + 1679489·n)·3011#+1 0..6 1290 2006 Ken Davis, NewPGen, PrimeForm
7 (347855843 + 230408192·n)·3001#+1 0..6 1287 2004 Jim Fougeron, Hans Rosenthal, PrimeForm

8 (48098104751 + 3026809034·n)·5303#+1 0..7 2271 2019 Norman Luhn, Paul Underwood, Ken Davis, Primeform e-group, NewPGen, PrimeForm
8 (753610389 + 60355670·n)·2591#+1 0..7 1101 2019 Mike Oakes, NewPGen, PrimeForm
8 (452558752 + 359463429·n)·2459#+1 0..7 1057 2009 Ken Davis, NewPGen, PrimeForm
8 (4941928071 + 176836494·n)·2411#+1 0..7 1037 2003 Paul Underwood, Markus Frind, PrimeForm

9 (65502205462 + 6317280828·n)·2371#+1 0..8 1014 2012 Ken Davis, Paul Underwood, PrimeForm egroup, NewPGen, PrimeForm
9 (58928599133 + 1298717501·n)·2371#+1 0..8 1014 2011 Ken Davis, Paul Underwood, PrimeForm egroup, NewPGen, PrimeForm
9 (758144320 + 247707761·n)·1039#+1 0..8 446 2010 Mike Oakes, NewPGen, PrimeForm
9 (190556231 + 138880294·n)·997#+1 0..8 425 2009 Ken Davis, NewPGen, PrimeForm
9 (805227062 + 54790161·n)·941#+1 0..8 401 2006 Mike Oakes, NewPGen, PrimeForm
9 (582170448 + 7977192·n)·757#+1 0..8 325 2006 Jens Kruse Andersen
9 (20475784 + 18458425·n)·701#+1 0..8 301 2006 Mike Oakes, APSieve, PrimeForm
9 (105628556 + 7914782·n)·499#+1 0..8 215 2006 Norman Luhn
9 (501788528 + 12970338·n)·463#+1 1..9 202 2005 Jens Kruse Andersen
925127352416973 · 199#·227·229 + x87 + 210n 0..8 101 2004 Hans Rosenthal & Jens Kruse Andersen

10 (20794561384 + 1638155407·n)·1050#+1 0..9 450
2019 Norman Luhn, NewPGen, PrimeForm
10(5375864877 + 721683·n)·800#+10..9340
2019Norman Luhn
10(42918719 + 23865878·n)·761#+10..9327
2019Mike Oakes
10(3843864037 + 35500601·n)·691#+10..9300
2019Norman Luhn and Gerd Lamprecht
10 (3186700865 + 61959394·n)·653#+1 1..10 283 2010 Ken Davis, NewPGen, PrimeForm
10 (565429078 + 147743546·n)·641#+1 0..9 274 2009 Mike Oakes, NewPGen, PrimeForm
10 (1600616052 + 52323192·n)·617#+1 0..9 265 2009 Ken Davis, NewPGen, PrimeForm
10 (1079682357 + 109393276·n)·607#+1 0..9 260 2006 Mike Oakes, NewPGen, PrimeForm
10 (501788528 + 12970338·n)·463#+1 0..9 202 2005 Jens Kruse Andersen
10 507618446770482 · 193# + x77 + 210n 0..9 93 1998 Manfred Toplic, Harvey Dubner, Tony Forbes, Nik Lygeros,
Michel Mizony, Paul Zimmermann

11 (16533786790 + 1114209832·n)·666#+1 0..10 289 2019 Norman Luhn
11 (3186700865 + 61959394·n)·653#+1 0..10 283 2010 Ken Davis, NewPGen, PrimeForm
11 (197477410 + 146636·n)·457#+1 0..10 196 2009 Jeff Anderson-Lee, NewPGen, PrimeForm
11 (631346030 + 151515939·n)·449#+1 0..10 195 2007 Jeff Anderson-Lee, NewPGen, PrimeForm
11 (1366899295 + 54290654·n)·401#+1 1..11 173 2006 Jeff Anderson-Lee, NewPGen, PrimeForm
11 (1405659596 + 55680004·n)·349#+1 0..10 150 2006 Jeff Anderson-Lee, NewPGen, PrimeForm
11 (1075032530 + 89982195·n)·283#+1 1..11 128 2006 Jeff Anderson-Lee, NewPGen, PrimeForm
11 (262779044 + 49839897·n)·281#+1 0..10 125 2005 Jens Kruse Andersen
11 17 + 11387819007325752·13#·n 6..16 22 2001 Phil Carmody

12 (15079159689 + 502608831·n)·420#+1 0..11 180 2019 Norman Luhn
12 (1366899295 + 54290654·n)·401#+1 0..11 173 2006 Jeff Anderson-Lee, NewPGen, PrimeForm
12 (1075032530 + 89982195·n)·283#+1 0..11 128 2006 Jeff Anderson-Lee, NewPGen, PrimeForm
12 (53660216 + 27243281·n)·229#+1 0..11 100 2006 Jens Kruse Andersen
12 (117531238 + 1064977·n)·199#+1 0..11 91 2006 Norman Luhn
12 (30150295 + 3538849·n)·173#+1 0..11 77 2006 Mike Oakes, PrimeForm
12 (8986417 + 30820926·n)·157#+1 0..11 71 2005 Jens Kruse Andersen
12 17 + 11387819007325752·13#·n 5..16 22 2001 Phil Carmody

13 (50448064213 + 4237116495·n)·229#+1 0..12 103
2019 Norman Luhn, NewPGen, PrimeForm
13 (58494782328 + 70321714·n)·229#+1 0..12 103
2019 Norman Luhn, NewPGen, PrimeForm
13(3107048086 + 2726206·n)·229#+10..12101
2019Norman Luhn, NewPGen, PrimeForm
13 (58814898610 + 1121191·n)·199#+1 0..12 93
2018 Norman Luhn, NewPGen, PrimeForm
13 (1296982250 + 14976848·n)·191#+1 0..12 85 2010 Mike Oakes, NewPGen, PrimeForm
13 (7967748420 + 340308346·n)·181#+1 0..12 83 2010 Ken Davis, NewPGen, PrimeForm
13 (1374042988 + 22886141·n)·173#+1 0..12 78 2006 Mike Oakes, NewPGen, PrimeForm
13 (208988611 + 32224644·n)·139#+1 0..12 64 2006 Jens Kruse Andersen
13 (11428680 + 6738753·n)·127#+1 0..12 57 2006 Norman Luhn
13 (539591312 + 45914254·n)·103#+1 0..12 50 2005 Jens Kruse Andersen
13 17 + 11387819007325752·13#·n 4..16 22 2001 Phil Carmody

14 (55507616633 + 670355577·n)·229#+1 0..13 103
2019 Norman Luhn, NewPGen, PrimeForm
14(2032207368 + 34268355·n)·163#+10..13742019Norman Luhn
14 (145978014 + 25313115·n)·157#+1 0..13 71 2009 Mike Oakes, NewPGen, PrimeForm
14 (1067385825 + 193936257·n)·151#+1 0..13 69 2007 Jens Kruse Andersen
14 (211370029 + 22263450·n)·131#+1 0..13 60 2006 Mike Oakes, NewPGen, PrimeForm
14 (358766428 + 17143877·n)·101#+1 1..14 48 2005 Jens Kruse Andersen
14 17 + 11387819007325752·13#·n 3..16 22 2001 Phil Carmody

15 (14512034548 + 87496195·n)·149#+1
0..14 68 2019 Norman Luhn
15 (829774854 + 61796110·n)·131#+1
0..14 60
2019 Mike Oakes
15(14563635080 + 9152216·n)·113#+10..14572019Norman Luhn
15 (237375311 + 118560155·n)·109#+1 0..14 54 2009 Mike Oakes, NewPGen, PrimeForm
15 (358766428 + 17143877·n)·101#+1 0..14 48 2005 Jens Kruse Andersen
15 17 + 11387819007325752·13#·n 2..16 22 2001 Phil Carmody

16 (9700128038 + 75782144·n)·83#+1 1..16 43 2019 Norman Luhn
16 442604220336549402080078796974991691613909 + 103#·n 1..16 42 2014 Jaroslaw Wroblewski
16 (263013824 + 18107251·n)·83#+1 1..16 42 2009 Mike Oakes, NewPGen, PrimeForm
16 (636435342 + 49408956·n)·73#+1 0..15 38 2008 Jeff Anderson-Lee, NewPGen, PrimeForm
16 (1723800454 + 529799·n)·71#+1 0..15 36 2006 Mike Oakes, NewPGen, PrimeForm
16 (253456539 + 13892183·n)·43#+1 1..16 25 2005 Jens Kruse Andersen
16 17 + 11387819007325752·13#·n 1..16 22 2001 Phil Carmody

17 (9700128038 + 75782144·n)·83#+1 0..16 43 2019 Norman Luhn
17 442604220336549402080078796974991691613909 + 103#·n 0..16 42 2014 Jaroslaw Wroblewski
17 (263013824 + 18107251·n)·83#+1 0..16 42 2009 Mike Oakes, NewPGen, PrimeForm
17 (1259891250 + 70154768·n)·53#+1 0..16 29 2007 Jens Kruse Andersen
17 62749659973280668140514103 + 107·61#·n 2..18 27 2007 Jaroslaw Wroblewski
17 (253456539 + 13892183·n)·43#+1 0..16 25 2005 Jens Kruse Andersen
17 17 + 11387819007325752·13#·n 0..16 22 2001 Phil Carmody

18 (33277396902 + 139569962·n)·53#+1 1..18 31 2019 Norman Luhn, NewPGen, PrimeForm
18 (16013322956 + 918494804·n)·53#+1 0..17 31 2019 Norman Luhn, NewPGen, PrimeForm
18 (19024732855 + 282152663·n)·53#+1 0..17 30 2019 Norman Luhn, NewPGen, PrimeForm
18(16682454839 + 24397524·n)·53#+10..17302019Norman Luhn, NewPGen, PrimeForm
18 1029+999 + 1806448944300798320195·19#·(n-2) 1..18 30 2014 Jaroslaw Wroblewski
18 (1051673535 + 32196596·n)·53#+1 0..17 29 2007 Jens Kruse Andersen
18 62749659973280668140514103 + 107·61#·n 1..18 27 2007 Jaroslaw Wroblewski
18 47 + 19622534420177523·17#·n 0..17 24 2007 Gennady Gusev
18 970080760458011996047 + 53#·n 0..17 22 2007 Jaroslaw Wroblewski
18 398182070391807316627 + 53#·n 0..17 21 2006 Jaroslaw Wroblewski
18 (273972449 + 25355830·n)·31#+1 1..18 21 2005 Jens Kruse Andersen
18 (1042322200 + 11598832·n)·23#+1 0..17 18 2002 Markus Frind

19 (33277396902 + 139569962·n)·53#+1 0..18 31 2019 Norman Luhn, NewPGen, PrimeForm
19 1029+999 + 1806448944300798320195·19#·(n-2) 0..18 30 2014 Jaroslaw Wroblewski
19 62749659973280668140514103 + 107·61#·n 0..18 27 2007 Jaroslaw Wroblewski
19 254215977184797362303 + 53#·n 0..18 21 2007 Jaroslaw Wroblewski
19 (273972449 + 25355830·n)·31#+1 0..18 21 2005 Jens Kruse Andersen
19 (669956329 + 7563194·n)·23#+1 1..19 18 2002 Markus Frind

2023 + 134181089232118748020·19#·n0..1929
2017Wojciech Izykowski
20 3533531731191494525351461 + 61#·n 0..19 25 2014 Jaroslaw Wroblewski
20 21816168581655686541377 + 59#·n 0..19 23 2014 Jaroslaw Wroblewski
20 178284683588844176017 + 53#·n 0..19 21 2007 Jaroslaw Wroblewski
20 1925228725347080393 + 47#·n 1..20 20 2007 Jaroslaw Wroblewski
20 2962411312104427 + 185·41#·n 0..19 19 2007 Jaroslaw Wroblewski
20 2036800114407689 + 66·41#·n 0..19 18 2007 Jaroslaw Wroblewski
20 11735227242889999 + 43#·n 0..19 18 2006 Jaroslaw Wroblewski
20 9372688136871853 + 43#·n 0..19 18 2006 Jaroslaw Wroblewski
20 (669956329 + 7563194·n)·23#+1 0..19 18 2002 Markus Frind

21 5547796991585989797641 + 29#·n 0..20 22 2014 Jaroslaw Wroblewski
21 24657656407921828441 + 47#·n 0..20 20 2014 Jaroslaw Wroblewski
21 23260414913723182141 + 47#·n 0..20 20 2014 Jaroslaw Wroblewski
21 28112131522731197609 + 19#·n 0..20 20 2008 Jaroslaw Wroblewski
21 1925228725347080393 + 47#·n 0..20 20 2007 Jaroslaw Wroblewski
21 25521343898340097 + 37·41#·n 0..20 18 2007 Jaroslaw Wroblewski
21 1245653020090313 + 384·37#·n 0..20 17 2007 Jaroslaw Wroblewski
21 3135462279378283 + 316·37#·n 1..21 17 2007 Jaroslaw Wroblewski
21 789337428437009 + 320·37#·n 1..21 17 2007 Jaroslaw Wroblewski
21 620353098196661 + 84·37#·n 0..20 17 2007 Jaroslaw Wroblewski
21 9358091177025961 + 11·37#·n 0..20 17 2007 Jaroslaw Wroblewski
21 556904117141899 + 1105111·23#·n 1..21 16 2006 Markus Frind
21 1291515762123569 + 947674·23#·n 0..20 16 2006 Markus Frind
21 56211383760397 + 199678·23#·n 2..22 16 2004 Markus Frind, Paul Jobling, Paul Underwood

22 22231637631603420833 + 8·41#·n 1..22 20 2014 Jaroslaw Wroblewski
22 1351906725737537399 + 43#·n 0..21 19 2008 Jaroslaw Wroblewski
22 117075039027693563 + 6548·37#·n 1..22 19 2008 Raanan Chermoni & Jaroslaw Wroblewski
22 110236462100072933 + 2422·37#·n 0..21 18 2008 Raanan Chermoni & Jaroslaw Wroblewski
22 39468294485409091 + 2416·37#·n 1..22 18 2008 Raanan Chermoni & Jaroslaw Wroblewski
22 89563668600668359 + 1840·37#·n 0..21 18 2008 Raanan Chermoni & Jaroslaw Wroblewski
22 5105850615934567 + 1788·37#·n 0..21 18 2008 Raanan Chermoni & Jaroslaw Wroblewski
22 126599504321565949 + 912·37#·n 0..21 18 2008 Raanan Chermoni & Jaroslaw Wroblewski
22 32392290909421589 + 905·37#·n 0..21 18 2008 Raanan Chermoni & Jaroslaw Wroblewski
22 950203555027421 + 892·37#·n 0..21 18 2007 Jaroslaw Wroblewski
22 3135462279378283 + 316·37#·n 0..21 17 2007 Jaroslaw Wroblewski
22 789337428437009 + 320·37#·n 0..21 17 2007 Jaroslaw Wroblewski
22 556904117141899 + 1105111·23#·n 0..21 16 2006 Markus Frind
22 1059297083391793 + 408270·23#·n 0..21 16 2006 Markus Frind
22 56211383760397 + 199678·23#·n 1..22 16 2004 Markus Frind, Paul Jobling, Paul Underwood

23 22231637631603420833 + 8·41#·n 0..22 20 2014 Jaroslaw Wroblewski
23 117075039027693563 + 6548·37#·n 0..22 19 2008 Raanan Chermoni & Jaroslaw Wroblewski
23 39468294485409091 + 2416·37#·n 0..22 18 2008 Raanan Chermoni & Jaroslaw Wroblewski
23 660593947782971 + 5414270·23#·n 0..22 17 2008 Raanan Chermoni & Jaroslaw Wroblewski
23 542440132260899 + 4560607·23#·n 0..22 17 2008 Raanan Chermoni & Jaroslaw Wroblewski
23 3465600168789197 + 3405459·23#·n 0..22 17 2008 Raanan Chermoni & Jaroslaw Wroblewski
23 489357377433019 + 2701556·23#·n 0..22 17 2008 Raanan Chermoni & Jaroslaw Wroblewski
23 43760869165417 + 2339805·23#·n 0..22 17 2008 Raanan Chermoni & Jaroslaw Wroblewski
23 1172380401690583 + 1675204·23#·n 0..22 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
23 1564588127269043 + 1249750·23#·n 1..23 16 2007 Raanan Chermoni & Jaroslaw Wroblewski
23 242354932628899 + 291535·23#·n 0..22 16 2007 Jaroslaw Wroblewski
23 468395662504823 + 205619·23#·n 1..23 16 2007 Jaroslaw Wroblewski
23 654737613204229 + 110135·23#·n 0..22 16 2007 Markus Frind
23 56211383760397 + 199678·23#·n 0..22 16 2004 Markus Frind, Paul Jobling, Paul Underwood

24 224584605939537911 + 81292139·23#·n 3..26 18 2019 Rob Gahan, PrimeGrid, AP26
24271702189272825977 + 67515487·23#·n2..25182018Syracuse University, PrimeGrid, AP26
24293037522812241983 + 42713298·23#·n1..24182017Bill Brandt-Gasuen, PrimeGrid, AP26
24320382581839925153 + 36759418·23#·n1..24182017David E. Miller, PrimeGrid, AP26
24296950539631234873 + 32252465·23#·n1..24182017 William Donovan, PrimeGrid, AP26
24 163578055942973267 + 54221892·23#·n 0..23 18 2016 Bryan Little, AP26
24 161004359399459161 + 47715109·23#·n 2..25 18 2015 Bryan Little, AP26
24 154915016996669203 + 46919728·23#·n 0..23 18 2014 Bryan Little, AP26
24 136926916457315893 + 44121555·23#·n 2..25 18 2014 Bryan Little, AP26
24 133959376918860781 + 45008483·23#·n 0..23 18 2014 Bryan Little, AP26
24 28806475189976381 + 36028618·23#·n 0..23 18 2010 John Petterson, PrimeGrid, AP26
24 4076845864885399 + 35779587·23#·n 0..23 18 2010 Edward Gordon, PrimeGrid, AP26
24 6450318626856161 + 30430175·23#·n 0..23 18 2009 Dave Mumper, PrimeGrid, AP26
24 7448460750808573 + 27806605·23#·n 0..23 18 2009 Jesper Kågefors, PrimeGrid, AP26
24 12353443596260323 + 23793841·23#·n 1..24 18 2009 Rune Nordbøe Skillingstad, PrimeGrid, AP26
24 4911007789148401 + 20273384·23#·n 0..23 18 2009 Piotr M. Zalewski, PrimeGrid, AP26
24 4891686128805269 + 19453568·23#·n 0..23 18 2009 Roald Solbjørg, PrimeGrid, AP26
24 4687877159107031 + 18203167·23#·n 0..23 17 2009 Marcus Rosario, PrimeGrid, AP26
24 1948053460212667 + 17745794·23#·n 0..23 17 2009 Chris Wingate, PrimeGrid, AP26
24 3634080452156039 + 16981607·23#·n 0..23 17 2009 Ian Dickinson, PrimeGrid, AP26
24 4187489431145893 + 15636117·23#·n 0..23 17 2009 Anonymous, PrimeGrid, AP26
24 3193781476385167 + 15609111·23#·n 0..23 17 2009 John S Morris III , PrimeGrid, AP26
24 10307159737232191 + 14120563·23#·n 0..23 17 2009 Kevin Erickson, PrimeGrid, AP26
24 13678065943093049 + 13223804·23#·n 0..23 17 2009 Bryan Little, PrimeGrid, AP26
24 10317962076055027 + 10241601·23#·n 0..23 17 2009 Jan-Cornelius Molnar, PrimeGrid, AP26
24 13432401425380607 + 9219580·23#·n 0..23 17 2009 Carsten Hartwig, PrimeGrid, AP26
24 14992521666441877 + 8832442·23#·n 0..23 17 2009 Anonymous, PrimeGrid, AP26
24 167806194923077 + 4935146·23#·n 0..23 17 2009 Andreas Kobara, PrimeGrid, AP26
24 7960592659339799 + 2326495·23#·n 0..23 17 2009 Pawel Stachowiak, PrimeGrid, AP26
24 1606021011322579 + 3490622·23#·n 0..23 17 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 1564588127269043 + 1249750·23#·n 0..23 16 2007 Raanan Chermoni & Jaroslaw Wroblewski
24 468395662504823 + 205619·23#·n 0..23 16 2007 Jaroslaw Wroblewski

25 224584605939537911 + 81292139·23#·n 2..26 18 2019 Rob Gahan, PrimeGrid, AP26
25271702189272825977 + 67515487·23#·n1..25182018Syracuse University, PrimeGrid, AP26
25
293037522812241983 + 42713298·23#·n0..24182017Bill Brandt-Gasuen, PrimeGrid, AP26
25 320382581839925153 + 36759418·23#·n0..24182017David E. Miller, PrimeGrid, AP26
25296950539631234873 + 32252465·23#·n0..24182017 William Donovan, PrimeGrid, AP26
25 161004359399459161 + 47715109·23#·n 1..25 18 2015 Bryan Little, AP26
25 136314114923771779 + 47064543·23#·n 0..24 18 2014 Bryan Little, AP26
25 136926916457315893 + 44121555·23#·n 1..25 18 2014 Bryan Little, AP26
25 65921086021334669 + 43905174·23#·n 0..24 18 2013 Bryan Little, AP26
25 18626565939034793 + 30821486·23#·n 0..24 18 2010 Chris Wingate, PrimeGrid, AP26
25 25300381597038677 + 28603610·23#·n 0..24 18 2010 Dave Sunderland, PrimeGrid, AP26
25 42592855872841649 + 19093314·23#·n 0..24 18 2010 Keith Pattenden, PrimeGrid, AP26
25 12353443596260323 + 23793841·23#·n 0..24 18 2009 Rune Nordbøe Skillingstad, PrimeGrid, AP26
25 46176957093163301 + 1109121·23#·n 0..24 17 2009 Ian Dickinson, PrimeGrid, AP26
25 18162964758258289 + 3755664·23#·n 0..24 17 2009 Keith Dale, PrimeGrid, AP26
25 20919497549238289 + 3155495·23#·n 0..24 17 2009 Jochen Beck, PrimeGrid, AP26
25 2960886048458003 + 2346233·23#·n 0..24 17 2009 BOINC@Poland , PrimeGrid, AP26
25 6171054912832631 + 366384·23#·n 0..24 16 2008 Raanan Chermoni & Jaroslaw Wroblewski

26 224584605939537911 + 81292139·23#·n 1..26 18 2019 Rob Gahan, PrimeGrid, AP26
26271702189272825977 + 67515487·23#·n0..25182018Syracuse University, PrimeGrid, AP26
26 161004359399459161 + 47715109·23#·n 0..25 18 2015 Bryan Little, AP26
26 136926916457315893 + 44121555·23#·n 0..25 18 2014 Bryan Little, AP26
26 43142746595714191 + 23681770·23#·n 0..25 18 2010 Benoãt Perichon, PrimeGrid, AP26

27 224584605939537911 + 81292139·23#·n 0..26 18 2019 Rob Gahan, PrimeGrid, AP26

xN is an N-digit number which was used in a CPAP record but has no simple expression.
x77 = 545382416838875826681897035 90110659057865934764604873840781923513421103495579
x87 = 2798725096345871863320391354140463307 28180994209092523040703520843811319320930380677867

The minimal possible difference in an AP-k is conjectured to be k# for all k > 7, proved for k ≤ 21 as of 2013. The smallest starting prime for the minimal difference is shown below. Finding an AP with a predetermined difference is much harder than an arbitrary difference. Red entries are the smallest known difference when the minimal has not been found.

Smallest AP-k with minimal difference
k Primes n's Digits Year Discoverer
3 3 + 2·n 0..2 1
4 5 + 6·n 0..3 2
5 5 + 6·n 0..4 2
6 7 + 30·n 0..5 3 1909 G. Lemaire
7 7 + 150·n 0..6 3 1909 G. Lemaire
8 199 + 210·n 0..7 4 1910 Edward B. Escott
9 199 + 210·n 0..8 4 1910 Edward B. Escott
10 199 + 210·n 0..9 4 1910 Edward B. Escott
11 60858179 + 11#·n 0..10  8 1999 David W. Wilson
12 147692845283 + 11#·n 0..11 12 1999 David W. Wilson
13 14933623 + 13#·n 0..12 8 1999 David W. Wilson
14 834172298383 + 13#·n 0..13 12 2004 Gennady Gusev
15 894476585908771 + 13#·n 0..14 15 2004 Jens Kruse Andersen
16 1275290173428391 + 13#·n 0..15 16 2004 Gennady Gusev & Jens Kruse Andersen
17 259268961766921 + 17#·n 0..16  15 2004 Gennady Gusev & Jens Kruse Andersen
18 1027994118833642281 + 17#·n 0..17 19 2005 Gennady Gusev & Jens Kruse Andersen
19 1424014323012131633 + 19#·n 0..18 19 2008 Jaroslaw Wroblewski
20 1424014323012131633 + 19#·n 0..19 19 2008 Jaroslaw Wroblewski
21 28112131522731197609 + 19#·n 0..20 20 2008 Jaroslaw Wroblewski
22 166537312120867 + 9959·19#·n 0..21 15 2006 Markus Frind
23 403185216600637 + 9523·23#·n 0..22 15 2006 Markus Frind
24 158209144596158501 + 65073·23#·n 0..23 18 2014 Bryan Little, AP26
25 6171054912832631 + 366384·23#·n 0..24 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
26 3486107472997423 + 1666981·23#·n 0..25 17 2012 James Fry
27 224584605939537911 + 81292139·23#·n 0..26 18 2019 Rob Gahan, PrimeGrid, AP26

Record history for smallest AP-k with minimal difference
The smallest existing has been found for k = 3 to 21 (see above table for k = 3 to 17).
k Primes n's Digits Year Discoverer
18 1027994118833642281 + 17#·n 0..17 19 2005 Gennady Gusev & Jens Kruse Andersen
18 24604783199 + 581·17#·n 0..17 11 2002 Gennady Gusev

19 1424014323012131633 + 19#·n 0..18 19 2008 Jaroslaw Wroblewski
19 20736372344841161 + 5·19#·n 0..18 17 2007 Jaroslaw Wroblewski
19 63734273908111 + 11·19#·n 0..18 14 2007 Jaroslaw Wroblewski
19 2773814832407 + 155·19#·n 0..18 13 1992 Paul Pritchard

20 1424014323012131633 + 19#·n 0..19 19 2008 Jaroslaw Wroblewski
20 20736372344841161 + 5·19#·n 0..19 17 2007 Jaroslaw Wroblewski
20 2773814832407 + 155·19#·n 0..19 13 1992 Paul Pritchard

21 28112131522731197609 + 19#·n 0..20 20 2008 Jaroslaw Wroblewski
21 809504830479349 + 208·19#·n 0..20 15 2007 Pawel Nowak & Jaroslaw Wroblewski
21 5749146449311 + 2681·19#·n 0..20 13 1992 Paul Pritchard

22 166537312120867 + 9959·19#·n 0..21 15 2006 Markus Frind
22 497003857949969 + 179998·19#·n 0..21 15 2004 Markus Frind

23 403185216600637 + 9523·23#·n 0..22 15 2006 Markus Frind
23 100308707032367 + 156722·23#·n 0..22 15 2006 Markus Frind
23 56211383760397 + 199678·23#·n 0..22 16 2004 Markus Frind, Paul Jobling, Paul Underwood

24 158209144596158501 + 65073·23#·n 0..23 18 2014 Bryan Little, AP26
24 515486946529943 + 136831·23#·n 0..23 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 468395662504823 + 205619·23#·n 0..23 16 2007 Jaroslaw Wroblewski

25 6171054912832631 + 366384·23#·n 0..24 16 2008 Raanan Chermoni & Jaroslaw Wroblewski

26 3486107472997423 + 1666981·23#·n 0..25 17 2012 James Fry
26 43142746595714191 + 23681770·23#·n 0..25 18 2010 Benoãt Perichon, PrimeGrid, AP26

27 224584605939537911 + 81292139·23#·n 0..26 18 2019 Rob Gahan, PrimeGrid, AP26

The minimal starting prime in an AP-k is conjectured to be the smallest prime ≥ k, proved for k ≤ 20 as of 2017. Smaller start primes would lead to a number with a factor ≤ k. The smallest difference for the minimal start is shown below. There may have been earlier discoverers in some cases. Red primes are the smallest known when the minimal is unknown.

Smallest AP-k with minimal start
k Primes n's Digits Year Discoverer
3 3 + 2·n 0..2 1
4 5 + 6·n 0..3 2
5 5 + 6·n 0..4 2
6 7 + 30·n 0..5 3 1909 G. Lemaire
7 7 + 150·n 0..6 3 1909 G. Lemaire
8 11 + 5763·7#·n 0..7 7
9 11 + 155577·7#·n 0..8 9 1993 Siemion Fajtlowicz
10 11 + 1069022·7#·n 0..9 10 1999 Gennady Gusev
11 11 + 7315048·7#·n 0..10 11 1986 Günter Löh
12 13 + 641865320·11#·n 0..11 14 1994 W. Holsztynski, Micha Hofri
13 13 + 4293861989·11#·n 0..12 15 1986 Günter Löh
14 17 + 8858801964·13#·n 0..13 16 2001 Gennady Gusev
15 17 + 8858801964·13#·n 0..14 16 2001 Gennady Gusev
16 17 + 378230305161714·13#·n 0..15 21 2005 Phil Carmody
17 17 + 11387819007325752·13#·n 0..16 22 2001 Phil Carmody
18 19 + 251988718036418903·17#·n 0..17 25 2012 Gennady Gusev
19 19 + 4244193265542951705·17#·n 0..18 26 2013 Wojciech Izykowski
20 23 + 134181089232118748020·19#·n 0..19 29
2017 Wojciech Izykowski
21 124701216737 + 9986827·19#·n 0..20 16 2009 Ryszard Walczak from BOINC@Poland, Jaroslaw Wroblewski
22 1322554958713 + 2861998·23#·n 0..21 17 2009 Jacek Kotnowski, PrimeGrid, AP26
23 20389023122473 + 5785546·23#·n 0..22 17 2009 Eric Markle, PrimeGrid, AP26
24 39421708111691 + 9740894·23#·n 0..23 17 2009 Mark Codding, PrimeGrid, AP26
25 2960886048458003 + 2346233·23#·n 0..24 17 2009 BOINC@Poland , PrimeGrid, AP26
26 3486107472997423 + 1666981·23#·n 0..25 17 2012 James Fry
27 224584605939537911 + 81292139·23#·n 0..26 18 2019 Rob Gahan, PrimeGrid, AP26

Record history for smallest AP-k with minimal start
The smallest existing has been found for k = 3 to 19 (see above table for k = 3 to 15).
k Primes n's Digits Year Discoverer
16 17 + 378230305161714·13#·n 0..15 21 2005 Phil Carmody
16 17 + 11387819007325752·13#·n 0..15 22 2001 Phil Carmody

17 17 + 11387819007325752·13#·n 0..16 22 2001 Phil Carmody

18 19 + 251988718036418903·17#·n 0..17 25 2012 Gennady Gusev
18 47 + 19622534420177523·17#·n 0..17 24 2007 Gennady Gusev
18 602521111 + 96575729250·n 0..17 13 2005 Gennady Gusev
18 1052724247 + 6549·17#·n 0..17 11 2002 Gennady Gusev

19 19 + 4244193265542951705·17#·n 0..18 26 2013 Wojciech Izykowski
19 19 + 13234551541698967679·17#·n 0..18 27 2013 Wojciech Izykowski
19 275525353 + 407133393·19#·n 0..18 17 2009 Mariusz Szafranski from BOINC@Poland, Jaroslaw Wroblewski
19 275955343 + 368042893·19#·n 0..18 17 2009 Mariusz Szafranski from BOINC@Poland, Jaroslaw Wroblewski
19 1358498353 + 16584560·19#·n 0..18 16 2009 Machloj from BOINC@Poland, Jaroslaw Wroblewski
19 2027663243 + 1002606·19#·n 0..18 15 2008 Jaroslaw Wroblewski
19 8297644387 + 431·19#·n 0..18 11 1984 Paul Pritchard

2023 + 134181089232118748020·19#·n0..1929
2017Wojciech Izykowski
20 566547019 + 846627559·19#·n 0..19 18 2009 Aleksander Parkitny from BOINC@Poland, Jaroslaw Wroblewski
20 24670154221 + 370766·19#·n 0..19 14 2009 Sebastian Jaworowicz from BOINC@Poland, Jaroslaw Wroblewski
20 68469367129 + 4926·19#·n 0..19 12 1992 Paul Pritchard

21 124701216737 + 9986827·19#·n 0..20 16 2009 Ryszard Walczak from BOINC@Poland, Jaroslaw Wroblewski
21 142072321123 + 146372·19#·n 0..20 14 1990 Paul Pritchard

22 1322554958713 + 2861998·23#·n 0..21 17 2009 Jacek Kotnowski, PrimeGrid, AP26
22 1365385579783 + 405927·23#·n 0..21 16 2007 Jaroslaw Wroblewski
22 11410337850553 + 475180·19#·n 0..21 15 1993 Paul Pritchard et al.

23 20389023122473 + 5785546·23#·n 0..22 17 2009 Eric Markle, PrimeGrid, AP26
23 43760869165417 + 2339805·23#·n 0..22 17 2008 Raanan Chermoni & Jaroslaw Wroblewski
23 56211383760397 + 199678·23#·n 0..22 16 2004 Markus Frind, Paul Jobling, Paul Underwood

24 39421708111691 + 9740894·23#·n 0..23 17 2009 Mark Codding, PrimeGrid, AP26
24 167806194923077 + 4935146·23#·n 0..23 17 2009 Andreas Kobara, PrimeGrid, AP26
24 401516288036293 + 608239·23#·n 0..23 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 468395662504823 + 205619·23#·n 0..23 16 2007 Jaroslaw Wroblewski

25 2960886048458003 + 2346233·23#·n 0..24 17 2009 BOINC@Poland , PrimeGrid, AP26
25 6171054912832631 + 366384·23#·n 0..24 16 2008 Raanan Chermoni & Jaroslaw Wroblewski

26 3486107472997423 + 1666981·23#·n 0..25 17 2012 James Fry
26 43142746595714191 + 23681770·23#·n 0..25 18 2010 Benoãt Perichon, PrimeGrid, AP26

27 224584605939537911 + 81292139·23#·n 0..26 18 2019 Rob Gahan, PrimeGrid, AP26

Unlike the minimal difference and starting prime, there is probably no system in the minimal ending prime (shown below in parentheses) in an AP-k. Red primes are the smallest known when the minimal is unknown. It appears unlikely there exists a value of k with two AP-k sharing the minimal end, so the table heading does not begin with "Smallest".

AP-k with minimal end
k Primes n's Digits Year Discoverer
3 3 + 2·n (7) 0..2 1
4 5 + 6·n (23) 0..3 2
5 5 + 6·n (29) 0..4 2
6 7 + 30·n (157) 0..5 3 1909 G. Lemaire
7 7 + 150·n (907) 0..6 3 1909 G. Lemaire
8 199 + 210·n (1669) 0..7 4 1910 Edward B. Escott
9 199 + 210·n (1879) 0..8 4 1910 Edward B. Escott
10 199 + 210·n (2089) 0..9 4 1910 Edward B. Escott
11 110437 + 6·11#·n (249037) 0..10 6 1967 Edgar Karst
12 110437 + 6·11#·n (262897) 0..11 6 1967 Edgar Karst
13 4943 + 2·13#·n (725663) 0..12 6 1963 V. N. Seredinskij
14 31385539 + 14·13#·n (36850999) 0..13 8 1983 Paul Pritchard
15 115453391 + 138·13#·n (173471351) 0..14 9 1983 Paul Pritchard
16 53297929 + 323·13#·n (198793279) 0..15 9 1976 Sol Weintraub
17 3430751869 + 171·17#·n (4827507229) 0..16 10 1977 Sol Weintraub
18 4808316343 + 1406·17#·n (17010526363) 0..17 11 1983 Paul Pritchard
19 8297644387 + 431·19#·n (83547839407) 0..18 11 1984 Paul Pritchard
20 214861583621 + 1943·19#·n (572945039351) 0..19 12 1987 Jeff Young & James Fry
21 5749146449311 + 2681·19#·n (6269243827111) 0..20 13 1992 Paul Pritchard
22 11410337850553 + 475180·19#·n (108201410428753) 0..21 15 1993 Paul Pritchard et al.
23 403185216600637 + 9523·23#·n (449924511422857) 0..22 15 2006 Markus Frind
24 515486946529943 + 136831·23#·n (1217585417914253) 0..23 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
25 6171054912832631 + 366384·23#·n (8132758706802551) 0..24 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
26 3486107472997423 + 1666981·23#·n (12783396861134173) 0..25 17 2012 James Fry
27 224584605939537911 + 81292139·23#·n (696112717486210091) 0..26 18 2019 Rob Gahan, PrimeGrid, AP26

Record history for AP-k with minimal end
The end is in parantheses. The smallest existing has been found for k = 3 to 21 (see above table).
k Primes n's Digits Year Discoverer
22 11410337850553 + 475180·19#·n (108201410428753) 0..21 15 1993 Paul Pritchard et al.

23 403185216600637 + 9523·23#·n (449924511422857) 0..22 15 2006 Markus Frind
23 100308707032367 + 156722·23#·n (869507044019447) 0..22 15 2006 Markus Frind
23 56211383760397 + 199678·23#·n (1036239621869317) 0..22 16 2004 Markus Frind, Paul Jobling, Paul Underwood

24 515486946529943 + 136831·23#·n (1217585417914253) 0..23 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 468395662504823 + 205619·23#·n (1523454717745013) 0..23 16 2007 Jaroslaw Wroblewski

25 6171054912832631 + 366384·23#·n (8132758706802551) 0..24 16 2008 Raanan Chermoni & Jaroslaw Wroblewski

26 3486107472997423 + 1666981·23#·n (12783396861134173) 0..25 17 2012 James Fry
26 43142746595714191 + 23681770·23#·n (175223597495211691) 0..25 18 2010 Benoãt Perichon, PrimeGrid, AP26

27 224584605939537911 + 81292139·23#·n (696112717486210091) 0..26 18 2019 Rob Gahan, PrimeGrid, AP26

All known AP24 to AP27
Listed in reverse order of discovery. Only included in news section if they set a record.
The first known of each length has green background.
AP24's are no longer added after the end of AP26 Search in April 2010 with the first known AP26.
AP25's are no longer added after 1 January 2018.
k Primes n's Digits Year Discoverer
27 224584605939537911 + 81292139·23#·n 0..26 18 2019 Rob Gahan, PrimeGrid, AP26
2689937610947392099 + 78413143·23#·n0..25182018Daniel Wimmer, PrimeGrid, AP26
26271702189272825977 + 67515487·23#·n0..25182018Syracuse University, PrimeGrid, AP26
26 55837783597462913 + 62121807·23#·n 0..25 18 2018 Tom Greer, PrimeGrid, AP26
AP25's are not added above here
25188705909233852867 + 44924692·23#·n0..24182017 Jeff Webster, PrimeGrid, AP26
2566147818970286411 + 43305462·23#·n0..24182017Tim Terry, PrimeGrid, AP26
25146492329344492673 + 42846350·23#·n0..24182017 Kyle Schwind, PrimeGrid, AP26
25293037522812241983 + 42713298·23#·n0..24182017Bill Brandt-Gasuen, PrimeGrid, AP26
25139819001440953661 + 39776662·23#·n0..24182017Steven Schapendonk, PrimeGrid, AP26
25282340243066022987 + 39699195·23#·n0..24182017 Wolfgang Schwieger, PrimeGrid, AP26
2648277590120607451 + 37835074·23#·n0..25182017 Bruce E. Slade, PrimeGrid, AP26
2596256695044976793 + 37286573·23#·n0..24182017Bryan Little, PrimeGrid, AP26
25 320382581839925153 + 36759418·23#·n0..24182017David E. Miller, PrimeGrid, AP26
25172620809233105201 + 35156983·23#·n0..24182017Wolfgang Schwieger, PrimeGrid, AP26
25161146967531777047 + 34071541·23#·n0..24182017 Gustav Nylinder, PrimeGrid, AP26
25 296950539631234873 + 32252465·23#·n 0..24 18 2017 William Donovan, PrimeGrid, AP26
25 228315362514429847 + 29165712·23#·n 0..24 18 2017 Tuna Ertemalp, PrimeGrid, AP26
25 211810229255864971 + 26698740·23#·n 0..24 18 2017 Erik Klein, PrimeGrid, AP26
25 264703230462051737 + 25208577·23#·n 0..24 18 2017 user Autumn_Beijing, PrimeGrid, AP26
25 73237102080888511 + 23647405·23#·n 0..24 18 2017 Vince Splain, PrimeGrid, AP26
25 233662486570847311 + 23473713·23#·n 0..24 18 2017 Anthony Ayiomamitis, PrimeGrid, AP26
25 92134030929661723 + 23073685·23#·n 0..24 18 2017 Patrik Eriksson, PrimeGrid, AP26
25 234934262624764103 + 22561202·23#·n 0..24 18 2017 Syracuse University, PrimeGrid, AP26
25 171104686521473149 + 19323763·23#·n 0..24 18 2017 Bryan Little, PrimeGrid, AP26
25 295363409604322229 + 17257904·23#·n 0..24 18 2016 Roland Klepel, PrimeGrid, AP26
25 269235074116077859 + 17010331·23#·n 0..24 18 2016 Eirik Lunner, PrimeGrid, AP26
26 142099325379199423 + 16549135·23#·n 0..25 18 2016 Koichi Soraku, PrimeGrid, AP26
25 148375001202532501 + 15439522·23#·n 0..24 18 2016 Eirik Lunner, PrimeGrid, AP26
25 298190132293964681 + 15023287·23#·n 0..24 18 2016 Evelyn Chew, PrimeGrid, AP26
25 117409484129625731 + 15143792·23#·n 0..24 18 2016 user "skgiven", PrimeGrid, AP26
25 240091225937752601 + 14964187·23#·n 0..24 18 2016 Stefan Hofacker, PrimeGrid, AP26
25 228744309021939859 + 14918987·23#·n 0..24 18 2016 David Walling, PrimeGrid, AP26
25 183800317923336901 + 10816541·23#·n 0..24 18 2016 James Krauss, PrimeGrid, AP26
25 290884103695102903 + 12444168·23#·n 0..24 18 2016 Mike Kinney, PrimeGrid, AP26
25 231349139005158193 + 12169920·23#·n 0..24 18 2016 Stefan Larsson, PrimeGrid, AP26
25 203563934890169353 + 11105961·23#·n 0..24 18 2016 Stephen Draycott, PrimeGrid, AP26
25 193513604089287343 + 10189009·23#·n 0..24 18 2016 John S Chambers, PrimeGrid, AP26
25 84314670428700353 + 9954590·23#·n 0..24 18 2016 Ross Goudie, PrimeGrid, AP26
25 327723838632911059 + 10176298·23#·n 0..24 18 2016 Josef Matousek, PrimeGrid, AP26
25 322477370185894411 + 9633039·23#·n 0..24 18 2016 Rafael Trigueiro, PrimeGrid, AP26
25 299460668118437929 + 9026994·23#·n 0..24 18 2016 Hiroyuki Okazaki, PrimeGrid, AP26
26 149836681069944461 + 7725290·23#·n 0..25 18 2016 Takeshi Nakamura, PrimeGrid, AP26
25 124464776168666173 + 2104383·23#·n 0..24 18 2016 Honza Cholt, PrimeGrid, AP26
25 235660731794099011 + 1949500·23#·n 0..24 18 2016 Magnus Karlsson, PrimeGrid, AP26
25 223696034591087459 + 1731112·23#·n 0..24 18 2016 Tom Greer, PrimeGrid, AP26
25 109968592612273693 + 56069187·23#·n 0..24 18 2016 Bryan Little, AP26
25 13124650646226187 + 39527888·23#·n 0..24 18 2016 Bryan Little, AP26
25 38485413788776093 + 34731706·23#·n 0..24 18 2016 Bryan Little, AP26
25 99571126548111473 + 645973·23#·n 0..24 18 2016 Bryan Little, AP26
26 161004359399459161 + 47715109·23#·n 0..25 18 2015 Bryan Little, AP26
25 136314114923771779 + 47064543·23#·n 0..24 18 2014 Bryan Little, AP26
25 18840719948982091 + 49903506·23#·n 0..24 18 2014 Bryan Little, AP26
26 136926916457315893 + 44121555·23#·n 0..25 18 2014 Bryan Little, AP26
25 65921086021334669 + 43905174·23#·n 0..24 18 2013 Bryan Little, AP26
26 3486107472997423 + 1666981·23#·n 0..25 17 2012 James Fry
AP24's are not added above here
24 35930857390358597 + 24335672·23#·n 0..23 18 2010 Ossi Mauno, PrimeGrid, AP26
24 76189875325979951 + 9176349·23#·n 0..23 18 2010 Oleg Tchij, PrimeGrid, AP26
26 43142746595714191 + 23681770·23#·n 0..25 18 2010 Benoãt Perichon, PrimeGrid, AP26
25 83386545459573043 + 1684949·23#·n 0..24 17 2010 Tigz Mordan, PrimeGrid, AP26
24 78604090316508061 + 8498518·23#·n 0..23 18 2010 Gerrit Slomma, PrimeGrid, AP26
25 18626565939034793 + 30821486·23#·n 0..24 18 2010 Chris Wingate, PrimeGrid, AP26
24 37706304556102387 + 21790711·23#·n 0..23 18 2010 John R. Bailey, PrimeGrid, AP26
24 16509022283270389 + 29463383·23#·n 0..23 18 2010 Gerrit Slomma, PrimeGrid, AP26
24 2687263842007609 + 38710532·23#·n 0..23 18 2010 Richard J. Konish, PrimeGrid, AP26
24 69067110822206929 + 6753086·23#·n 0..23 18 2010 Anonymous, PrimeGrid, AP26
24 35866756599356303 + 19359923·23#·n 0..23 18 2010 Ronald J. Littlefield, PrimeGrid, AP26
24 59742395397388433 + 12519529·23#·n 0..23 18 2010 Alessandro Ceriani, PrimeGrid, AP26
25 25300381597038677 + 28603610·23#·n 0..24 18 2010 Dave Sunderland, PrimeGrid, AP26
24 9029101367197477 + 37882313·23#·n 0..23 18 2010 Roald Solbjørg, PrimeGrid, AP26
24 1580853039814361 + 36803506·23#·n 0..23 18 2010 Anonymous, PrimeGrid, AP26
24 31884137812843999 + 26514806·23#·n 0..23 18 2010 Uros Vizintin, PrimeGrid, AP26
24 73423142215059841 + 4720552·23#·n 0..23 17 2010 Ulrich Hartel, PrimeGrid, AP26
24 57421089862716869 + 12188684·23#·n 0..23 18 2010 Jan Mihrmeister, PrimeGrid, AP26
24 68534294086445963 + 11549562·23#·n 0..23 18 2010 Dave and Antonia Domm, PrimeGrid, AP26
25 42592855872841649 + 19093314·23#·n 0..24 18 2010 Keith Pattenden, PrimeGrid, AP26
24 28806475189976381 + 36028618·23#·n 0..23 18 2010 John Petterson, PrimeGrid, AP26
25 58555890166091939 + 10416756·23#·n 0..24 18 2010 Bryan Little, PrimeGrid, AP26
24 28177336417360261 + 25675304·23#·n 0..23 18 2010 Paweł Kaczmarczyk, PrimeGrid, AP26
24 4076845864885399 + 35779587·23#·n 0..23 18 2010 Edward Gordon, PrimeGrid, AP26
24 24217435709571029 + 24938944·23#·n 0..23 18 2010 Jack England, PrimeGrid, AP26
24 37560025189846517 + 16380129·23#·n 0..23 18 2010 Anonymous, PrimeGrid, AP26
24 22972217245866943 + 23923567·23#·n 0..23 18 2010 Mathias Striecks, PrimeGrid, AP26
24 38156446254970321 + 16171100·23#·n 0..23 18 2010 Anonymous, PrimeGrid, AP26
24 36216875966560057 + 24123429·23#·n 0..23 18 2010 Jon Sonntag, PrimeGrid, AP26
25 49644063847333931 + 7851809·23#·n 0..24 17 2010 Jan Stenzel, PrimeGrid, AP26
24 69844511157803653 + 1408042·23#·n 0..23 17 2010 Geoffrey Leist, PrimeGrid, AP26
24 77964779011754827 + 1320946·23#·n 0..23 17 2010 Bryan Little, PrimeGrid, AP26
24 52284918375969179 + 5444625·23#·n 0..23 17 2010 Charlene Schaar, PrimeGrid, AP26
24 47559343191365491 + 12958707·23#·n 0..23 18 2010 Hubert Stickelberger, PrimeGrid, AP26
24 29578980078344351 + 23462565·23#·n 0..23 18 2010 Donald Hatland, PrimeGrid, AP26
25 46428033558097831 + 12893265·23#·n 0..24 18 2010 Gerrit Slomma, PrimeGrid, AP26
24 22894182607279507 + 19352116·23#·n 0..23 18 2010 Edward Gordon, PrimeGrid, AP26
24 22050598518962261 + 20896917·23#·n 0..23 18 2010 Klaus Bauer, PrimeGrid, AP26
24 36629598861376343 + 11370937·23#·n 0..23 17 2010 Edward Gordon, PrimeGrid, AP26
25 24715375237181843 + 19071018·23#·n 0..24 18 2010 Dan Swearingen, PrimeGrid, AP26
24 35061200218767479 + 10757586·23#·n 0..23 17 2010 Scott Henderson, PrimeGrid, AP26
24 47951620104244397 + 11867770·23#·n 0..23 18 2010 Junyi Guo, PrimeGrid, AP26
24 51098319563712361 + 3993145·23#·n 0..23 17 2009 Uwe Boll, PrimeGrid, AP26
24 29831273365663157 + 16680270·23#·n 0..23 18 2009 Jan Stenzel, PrimeGrid, AP26
24 63445575002484173 + 2307769·23#·n 0..23 17 2009 Robert Scullin, PrimeGrid, AP26
24 18418363373094851 + 16742739·23#·n 0..23 18 2009 Hal Wold, PrimeGrid, AP26
24 49161262681970809 + 10137725·23#·n 0..23 18 2009 Rune Fredriksen, PrimeGrid, AP26
25 29952203513013839 + 8769895·23#·n 0..24 17 2009 David Chevalier, PrimeGrid, AP26
24 61593273431157907 + 446068·23#·n 0..23 17 2009 SETI.USA Cluster, PrimeGrid, AP26
25 45013419998786779 + 9560248·23#·n 0..24 17 2009 Rune Fredriksen, PrimeGrid, AP26
24 4616206285589027 + 27245041·23#·n 0..23 18 2009 Anonymous, PrimeGrid, AP26
24 29051233904541803 + 18765591·23#·n 0..23 18 2009 Krzysztof Koczubik, PrimeGrid, AP26
24 17014421509997489 + 17580742·23#·n 0..23 18 2009 Fred Richard, PrimeGrid, AP26
24 6450318626856161 + 30430175·23#·n 0..23 18 2009 Dave Mumper, PrimeGrid, AP26
24 44265615051136733 + 7821972·23#·n 0..23 17 2009 Jörg Steinmetz, PrimeGrid, AP26
24 3694862982684983 + 28285375·23#·n 0..23 18 2009 Siegfried Niklas, PrimeGrid, AP26
24 22133406276301387 + 15744033·23#·n 0..23 18 2009 Rune Fredriksen, PrimeGrid, AP26
24 7448460750808573 + 27806605·23#·n 0..23 18 2009 Jesper Kågefors, PrimeGrid, AP26
24 28236790404122779 + 13068553·23#·n 0..23 17 2009 Rune Fredriksen, PrimeGrid, AP26
24 20813446029088183 + 11788369·23#·n 0..23 17 2009 Robert Szafrański, PrimeGrid, AP26
24 14698398021483853 + 24362735·23#·n 0..23 18 2009 Pawel Ferus, PrimeGrid, AP26
25 12353443596260323 + 23793841·23#·n 0..24 18 2009 Rune Nordbøe Skillingstad, PrimeGrid, AP26
24 4911007789148401 + 20273384·23#·n 0..23 18 2009 Piotr M. Zalewski, PrimeGrid, AP26
24 48306600448056229 + 1742643·23#·n 0..23 17 2009 Anonymous, PrimeGrid, AP26
24 36252687055565597 + 2173244·23#·n 0..23 17 2009 Pawel Ferus, PrimeGrid, AP26
24 35973377180183173 + 1622443·23#·n 0..23 17 2009 Jacek Kotnowski, PrimeGrid, AP26
25 46176957093163301 + 1109121·23#·n 0..24 17 2009 Ian Dickinson, PrimeGrid, AP26
24 17868447568925983 + 9564699·23#·n 0..23 17 2009 Senji Yamashita, PrimeGrid, AP26
24 26637789112428883 + 9196753·23#·n 0..23 17 2009 Tim Jungbluth, PrimeGrid, AP26
24 4891686128805269 + 19453568·23#·n 0..23 18 2009 Roald Solbjørg, PrimeGrid, AP26
24 4687877159107031 + 18203167·23#·n 0..23 17 2009 Marcus Rosario, PrimeGrid, AP26
24 1948053460212667 + 17745794·23#·n 0..23 17 2009 Chris Wingate, PrimeGrid, AP26
24 3634080452156039 + 16981607·23#·n 0..23 17 2009 Ian Dickinson, PrimeGrid, AP26
24 28453270488159667 + 6183387·23#·n 0..23 17 2009 Pietari Snow, PrimeGrid, AP26
24 26851278717686693 + 5551454·23#·n 0..23 17 2009 Anonymous, PrimeGrid, AP26
24 18567190093510343 + 5352686·23#·n 0..23 17 2009 Krzysztof Koczubik, PrimeGrid, AP26
24 4187489431145893 + 15636117·23#·n 0..23 17 2009 Anonymous, PrimeGrid, AP26
24 3193781476385167 + 15609111·23#·n 0..23 17 2009 John S Morris III, PrimeGrid, AP26
24 24676336785406967 + 5024493·23#·n 0..23 17 2009 Danial L Puckett, PrimeGrid, AP26
24 1220728403569963 + 14348016·23#·n 0..23 17 2009 Martin Siegrist, PrimeGrid, AP26
24 2635631384342027 + 14133381·23#·n 0..23 17 2009 Anonymous, PrimeGrid, AP26
24 10307159737232191 + 14120563·23#·n 0..23 17 2009 Kevin Erickson, PrimeGrid, AP26
24 18038585883263339 + 3679127·23#·n 0..23 17 2009 Karsten Hilbich, PrimeGrid, AP26
24 28263557466746377 + 3312503·23#·n 0..23 17 2009 Anonymous, PrimeGrid, AP26
25 18162964758258289 + 3755664·23#·n 0..24 17 2009 Keith Dale, PrimeGrid, AP26
25 20919497549238289 + 3155495·23#·n 0..24 17 2009 Jochen Beck, PrimeGrid, AP26
24 13678065943093049 + 13223804·23#·n 0..23 17 2009 Bryan Little, PrimeGrid, AP26
24 25545151920212759 + 1140241·23#·n 0..23 17 2009 Paolo Bassi, PrimeGrid, AP26
24 20187352211709911 + 1799216·23#·n 0..23 17 2009 Jeffrey D Sessler, PrimeGrid, AP26
24 20909681071069667 + 234797·23#·n 0..23 17 2009 Tina Kent, PrimeGrid, AP26
24 19471368812966089 + 410682·23#·n 0..23 17 2009 Andreas Mohr, PrimeGrid, AP26
24 10317962076055027 + 10241601·23#·n 0..23 17 2009 Jan-Cornelius Molnar, PrimeGrid, AP26
24 19516186145019209 + 313705·23#·n 0..23 17 2009 Carsten Hartwig, PrimeGrid, AP26
24 7979661543967237 + 9936237·23#·n 0..23 17 2009 Bryan Little, PrimeGrid, AP26
24 39421708111691 + 9740894·23#·n 0..23 17 2009 Mark Codding, PrimeGrid, AP26
24 5531900872160491 + 9383796·23#·n 0..23 17 2009 Paweł Feruś, PrimeGrid, AP26
24 13432401425380607 + 9219580·23#·n 0..23 17 2009 Carsten Hartwig, PrimeGrid, AP26
24 14992521666441877 + 8832442·23#·n 0..23 17 2009 Anonymous, PrimeGrid, AP26
24 167806194923077 + 4935146·23#·n 0..23 17 2009 Andreas Kobara, PrimeGrid, AP26
25 2960886048458003 + 2346233·23#·n 0..24 17 2009 BOINC@Poland, PrimeGrid, AP26
24 7960592659339799 + 2326495·23#·n 0..23 17 2009 Pawel Stachowiak, PrimeGrid, AP26
24 6274259724784693 + 2522655·23#·n 0..23 17 2009 Pawel Stachowiak, PrimeGrid, AP26
24 6872932294461509 + 2042703·23#·n 0..23 17 2009 Krzysztof Koczubik, PrimeGrid, AP26
24 2725131905640097 + 1342336·23#·n 0..23 16 2009 Stefan Smietanowski, PrimeGrid, AP26
24 13785500104035967 + 1004314·23#·n 0..23 17 2009 Krzysztof Koczubik, PrimeGrid, AP26
25 6171054912832631 + 366384·23#·n 0..24 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 6173646951801709 + 587522·23#·n 0..23 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 3120744164655323 + 851923·23#·n 0..23 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 1630799846252777 + 985151·23#·n 0..23 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 401516288036293 + 608239·23#·n 0..23 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 1368212299836997 + 148682·23#·n 0..23 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 515486946529943 + 136831·23#·n 0..23 16 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 1606021011322579 + 3490622·23#·n 0..23 17 2008 Raanan Chermoni & Jaroslaw Wroblewski
24 1564588127269043 + 1249750·23#·n 0..23 16 2007 Raanan Chermoni & Jaroslaw Wroblewski
24 468395662504823 + 205619·23#·n 0..23 16 2007 Jaroslaw Wroblewski

From Chris Caldwell's The Prime Pages:
The Top Twenty: Arithmetic Progressions of Primes (only primes with at least 1000 digits)
The Prime Glossary: arithmetic sequence
The Prime Database: Search on Arithmetic
Dirichlet's Theorem on Primes in Arithmetic Progressions

Records for special AP's:
Neil Sloane's On-Line Encyclopedia of Integer Sequences: A033189 (start of smallest AP-k with minimal difference), A061558 (smallest difference for AP-k with smallest start), A005115 (smallest end of an AP-k),
Carlos Rivera's The Prime Puzzles & Problems Connection: Puzzle 34. Prime Triplets in arithmetic progression (largest AP3 starting at 3), and Puzzle 269. 13 primes in A.P. (smallest AP-k starting at k)
Jens Kruse Andersen: The Largest Known CPAP's (consecutive primes in AP)