| k | Digits | Early discovery with at least 1,000 digits to given pattern | Who | When | |
| 1 | 1332 | 24432 − 1 | Alexander Hurwitz | 3 Nov 1961 | |
| 2 | 1040 | 256200945 • 23426 ± 1 | Arthur Oliver Lonsdale Atkin & Neil W. Rickert | Dec 1980 | |
| 3 | 1041 | 23456 + 5661177712051 + d | d = 0, 2, 6 | Tony Forbes (PRP); François Morain (proven primes) | 1995 - 1998 |
| 3 | 1083 | 437850590 • (23567 − 21189) − 6 • 21189 − 5 + d | d = 0, 4, 6 | Tony Forbes | 04 Dec 1996 |
| 4 | 1004 | 76912895956636885 • (23279 − 21093) − 6 • 21093 − 7 + d | d = 0, 2, 6, 8 | Tony Forbes | 16 Sep 1998 |
| 5 | 1034 | 31969211688 • 2399# + 16061 + d | d = 0, 2, 6, 8, 12 | Norman Luhn | 30 Jul 2002 |
| 5 | 1107 | 424232794973 • 2593# + 43777 + d | d = 0, 4, 6, 10, 12 | Norman Luhn | 24 Mar 2009 |
| 6 | 1037 | 28993093368077 • 2399# + 19417 + d | d = 0, 4, 6, 10, 12, 16 | Norman Luhn | 14 Mar 2016 |
| 7 | 1002 | 113225039190926127209 • 2339# / 57057 + 1 + d | d = 0, 2, 6, 8, 12, 18, 20 | Peter Kaiser | 27 Jan 2021 |
| 7 | Not yet found ! | d = 0, 2, 8, 12, 14, 18, 20 | |||
| k | Digits | Early discovery with at least 2,000 digits to given pattern | Who | When | |
| 1 | 2917 | 29689 − 1 | Donald Bruce Gillies | 11 May 1963 | |
| 2 | 2003 | 260497545 • 26625 ± 1 | Arthur Oliver Lonsdale Atkin | Dec 1984 | |
| 3 | 2129 | 205702716 • 4973# / 35 − 1 + d | d = 0, 2, 6 | Rosenthal, Jobling | 17 Dec 2000 |
| 3 | 2049 | 102048 + 418590204063 + d | d = 0, 4, 6 | Norman Luhn | 11 Jan 2001 |
| 4 | 2058 | 4104082046 • 4799# + 5651 + d | d = 0, 2, 6, 8 | Norman Luhn | 29 Apr 2005 |
| 5 | 2002 | 126831252923413 • 4657# / 273 + 1 + d | d = 0, 2, 6, 8, 12 | Peter Kaiser | 8 Nov 2020 |
| 5 | 2034 | 566761969187 • 4733# / 2 − 8 + d | d = 0, 4, 6, 10, 12 | Serge Batalov | 7 Dec 2020 |
| k | Digits | Early discovery with at least 3,000 digits to given pattern | Who | When | |
| 1 | 3376 | 211213 − 1 | Donald Bruce Gillies | 2 Jun 1963 | |
| 2 | 3389 | 1706595 • 211235 ± 1 John Brown, Landon Curt Noll, Bruce K. Parady, Gene Ward Smith, Joel F. Smith, Sergio E. Zarantonello | The Amdahl 6 | 7 Jun 1989 | |
| 3 | 3153 | 813529138 • 1939938500 − 1 + d | d = 0, 2, 6 | Norman Luhn | 13 Jul 2002 |
| 3 | 4134 | (18599651274 • 4436 • 3251# • (4436 • 3251# + 1) + 210) • (4436 • 3251# − 1) / 35 + 7 + d | d = 0, 4, 6 | David Broadhurst | 28 Sep 2002 |
| 4 | 3024 | 43697976428649 • 29999 − 1 + d | d = 0, 2, 6, 8 | Peter Kaiser | 26 Mar 2012 |
| 5 | 3344 | 585150568069684836 • 7757# / 85085 + 5 + d | d = 0, 2, 6, 8, 12 | Peter Kaiser | 06 Mar 2022 |
| 5 | Not yet found ! | d = 0, 4, 6, 10, 12 | |||
| k | Digits | Early discovery with at least 4,000 digits to given pattern | Who | When | |
| 1 | 6002 | 219937 − 1 | Bryant Tuckerman | 4 Mar 1971 | |
| 2 | 4030 | 1692923232 • 104020 ± 1 | Harvey Dubner | Jul 1993 | |
| 3 | 4019 | (61504372896 • 5119 • 3163# • (5119 • 3163# + 1) + 210) • (5119 • 3163# − 1) / 35 + 5 + d | d = 0, 2, 6 | David Broadhurst | 10 Aug 2002 |
| 3 | 4134 | (18599651274 • 4436 • 3251# • (4436 • 3251# + 1) + 210) • (4436 • 3251# − 1) / 35 + 7 + d | d = 0, 4, 6 | David Broadhurst | 28 Sep 2002 |
| 4 | 5003 | 4122429552750669 • 216567 − 1 + d | d = 0, 2, 6, 8 | Peter Kaiser | 10 Mar 2016 |
| k | Digits | Early discovery with at least 5,000 digits to given pattern | Who | When | |
| 1 | 6002 | 219937 − 1 | Bryant Tuckerman | 4 Mar 1971 | |
| 2 | 5129 | 570918348 • 105120 ± 1 | Harvey Dubner | Oct 1995 | |
| 3 | 5132 | (91456744909 • 205881 • 4001# • (205881 • 4001# + 1) + 210) • (205881 • 4001# − 1) / 35 + 5 + d | d = 0, 2, 6 | Ken Davis | 4 May 2006 |
| 3 | 5132 | (63095588824 • 205881 • 4001# • (205881 • 4001# + 1) + 210) • (205881 • 4001# − 1) / 35 + 7 + d | d = 0, 4, 6 | Ken Davis | 7 Oct 2005 |
| 4 | 5003 | 4122429552750669 • 216567 − 1 + d | d = 0, 2, 6, 8 | Peter Kaiser | 10 Mar 2016 |
| k | Digits | Early discovery with at least 6,000 digits to given pattern | Who | When | |
| 1 | 6002 | 219937 − 1 | Bryant Tuckerman | 4 Mar 1971 | |
| 2 | 11713 | 242206083 • 238880 ± 1 | Karl-Heinz Indlekofer, Antal Járai | Nov 1995 | |
| 3 | 6223 | 5612052289 • 14489# / 5 − 1 + d | d = 0, 2, 6 | Norman Luhn | 3 Jan 2008 |
| 3 | 16737 | 6521953289619 • 255555 − 5 + d | d = 0, 4, 6 | Peter Kaiser | 30 Apr 2013 |
| 4 | 10132 | 667674063382677 • 233608 − 1 + d | d = 0, 2, 6, 8 | Peter Kaiser | 27 Feb 2019 |
| k | Digits | Early discovery with at least 7,000 ... 9,000 digits to given pattern | Who | When | |
| 1 | 13395 | 244497 − 1 | Harry Lewis Nelson, David Slowinski | 8 Apr 1979 | |
| 2 | 11713 | 242206083 • 238880 ± 1 | Karl-Heinz Indlekofer, Antal Járai | Nov 1995 | |
| 3 | 10047 | 2072644824759 • 233333 − 1 + d | d = 0, 2, 6 | Norman Luhn, François Morain | 17 Nov 2008 |
| 3 | 16737 | 6521953289619 • 255555 − 5 + d | d = 0, 4, 6 | Peter Kaiser | 30 Apr 2013 |
| 4 | 10132 | 667674063382677 • 233608 − 1 + d | d = 0, 2, 6, 8 | Peter Kaiser | 27 Feb 2019 |