The upper bound of exhaustive analysis of gaps has been extended successively, as follows. For the most recent results, see the Prime Gap Searches project at the Mersenne Forum (and see “PGS” in the Bibliography for a list of the participants). Most of the calculations beyond were carried out by Thomas Ritschel.
| Upper bound | Attained by | Date | Link |
|---|---|---|---|
| PGS (Mersenne Forum) | 25 Sep 2018 | Prime Gap Search (Mersenne Forum) | |
| PGS (Mersenne Forum) | 13 Aug 2018 | ||
| PGS (Mersenne Forum) | 25 June 2018 | ||
| PGS (Mersenne Forum) | 29 Apr 2018 | ||
| PGS (Mersenne Forum) | 10 Apr 2018 | ||
| PGS (Mersenne Forum) | 10 Mar 2018 | ||
| PGS (Mersenne Forum) | 25 Feb 2018 | ||
| PGS (Mersenne Forum) | 17 Jan 2018 | ||
| PGS (Mersenne Forum) | 23 Nov 2017 | ||
| PGS (Mersenne Forum) | 03 Nov 2017 | ||
| PGS (Mersenne Forum) | 21 Sept 2017 | ||
| PGS (Mersenne Forum) | 16 Aug 2017 | ||
| PGS (Mersenne Forum) | 02 Aug 2017 | ||
| PGS (Mersenne Forum) | 18 July 2017 | ||
| PGS (Mersenne Forum) | 05 July 2017 | ||
| Silva & Herzog & Pardi | 04 Apr 2012 | ||
| Silva & Herzog & Pardi | 30 Mar 2012 | ||
| Silva & Herzog & Silvio Pardi | 06 Feb 2012 | ||
| Silva & Herzog | 13 Sept 2011 | ||
| Silva & Herzog | 27 June 2011 | ||
| Silva & Herzog | 24 May 2011 | ||
| Silva & Herzog | 09 May 2011 | ||
| Silva & Herzog | 09 Apr 2011 | ||
| Silva & Herzog | 14 Feb 2011 | ||
| Silva & Herzog | 06 Nov 2010 | ||
| Silva & Herzog | 30 Aug 2010 | ||
| Silva & Herzog | 05 Jan 2010 | ||
| Silva & Herzog | 23 Dec 2009 | ||
| Silva & Herzog | 24 July 2009 | ||
| Silva & Herzog | 26 Apr 2007 | ||
| Silva & Herzog | 01 Mar 2007 | ||
| Silva | 19 Feb 2007 | ||
| Donald E. Knuth | 22 Oct 2006 | ||
| Silva | 05 June 2006 | ||
| Silva & Herzog | 26 Dec 2005 | ||
| Siegfried "Zig" Herzog | 02 Feb 2005 | ||
| Silva | 17 Dec 2004 | ||
| Nyman | 20 Jan 2004 (27 Oct 2003) | ||
| Silva & Herzog | 20 Jan 2004 | ||
| James Fry | 17 Sep 2003 | ||
| Tomás Oliveira e Silva | 21 Feb 2003 | ||
| Bertil Nyman | 22 Oct 2002 | ||
| Thomas R. Nicely | July 1999 | New maximal prime gaps and first occurrences | |
| Young & Potler | 1989 | ||
| Richard P. Brent | 1980 | The first occurrence of certain large prime gaps | |
| Richard P. Brent | 1973 | The First Occurrence of Large Gaps Between Successive Primes | |
| Lander & Parkin | 1967 | On first appearance of prime differences | |
| Gruenberger & Armerding & Baker | 1961 | Statistics on the First Six Million Prime Numbers | |
| D. H. Lehmer | 1957 | DOI:10.2307/2002199 | |
| A. E. Western | 1934 | ||
| J. W. L. Glaisher | 1878 |
Where two dates are given, the earlier one is the date of completion of computations for that interval; the later date is the point at which all other integers below that interval had also been exhaustively checked. See the bibliography for full names and attribution.