Exhaustively analyzed gaps

The upper bound of exhaustive analysis of gaps has been extended successively, as follows.

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 16000e15 were carried out by Thomas Ritschel.

Upper bound Attained by Date Link
2**64PGS (Mersenne Forum)25 Sep 2018Prime Gap Search (Mersenne Forum)
18446.744e15PGS (Mersenne Forum)13 Aug 2018
17000e15PGS (Mersenne Forum)25 June 2018
16000e15PGS (Mersenne Forum)29 Apr 2018
15200e15PGS (Mersenne Forum)10 Apr 2018
14000e15PGS (Mersenne Forum)10 Mar 2018
13000e15PGS (Mersenne Forum)25 Feb 2018
12000e15PGS (Mersenne Forum)17 Jan 2018
10000e15PGS (Mersenne Forum)23 Nov 2017
9250e15PGS (Mersenne Forum)03 Nov 2017
7000e15PGS (Mersenne Forum)21 Sept 2017
6000e15PGS (Mersenne Forum)16 Aug 2017
5500e15PGS (Mersenne Forum)02 Aug 2017
5000e15PGS (Mersenne Forum)18 July 2017
4500e15PGS (Mersenne Forum)05 July 2017
4000e15Silva & Herzog & Pardi04 Apr 2012
3600e15Silva & Herzog & Pardi30 Mar 2012
3400e15Silva & Herzog & Silvio Pardi06 Feb 2012
2608e15Silva & Herzog13 Sept 2011
2222e15Silva & Herzog27 June 2011
2200e15Silva & Herzog24 May 2011
2188e15Silva & Herzog09 May 2011
2168e15Silva & Herzog09 Apr 2011
2133e15Silva & Herzog14 Feb 2011
2020e15Silva & Herzog06 Nov 2010
1610e15Silva & Herzog30 Aug 2010
1609e15Silva & Herzog05 Jan 2010
1600e15Silva & Herzog23 Dec 2009
1500e15Silva & Herzog24 July 2009
1e18Silva & Herzog26 Apr 2007
524e15Silva & Herzog01 Mar 2007
520e15Silva19 Feb 2007
425e15Donald E. Knuth22 Oct 2006
400e15Silva05 June 2006
300e15Silva & Herzog26 Dec 2005
200e15Siegfried "Zig" Herzog02 Feb 2005
150e15Silva17 Dec 2004
110e15Nyman20 Jan 2004 (27 Oct 2003)
100e15Silva & Herzog20 Jan 2004
64.7e15James Fry17 Sep 2003
60e15Tomás Oliveira e Silva21 Feb 2003
50.003e15Bertil Nyman22 Oct 2002
1.5e15Thomas R. NicelyJuly 1999New maximal prime gaps and first occurrences
72.63512e12Young & Potler1989
4.444e12Richard P. Brent1980The first occurrence of certain large prime gaps
2.6e12Richard P. Brent1973The First Occurrence of Large Gaps Between Successive Primes
1.46e9Lander & Parkin1967On first appearance of prime differences
104395289Gruenberger & Armerding & Baker1961Statistics on the First Six Million Prime Numbers
37e6D. H. Lehmer1957DOI:10.2307/2002199
10e6A. E. Western1934
3e6J. W. L. Glaisher1878

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.