First known occurrence prime gaps (1000000 to 999999998)

First known occurrence prime gaps
(1000000 to 999999998)
Dr. Thomas R. Nicely

http://www.trnicely.net
Current e-mail address

Last updated 0600 GMT 12 August 2019. Additional lists of prime gaps are maintained on this site.

For detailed explanatory notes, a complete bibliography, and a list of the discoverers and their associated abbreviations, see the document First occurrence prime gaps.

FORMAT

Gaps of 1000000 or greater would overflow the standard format, which is described in the principal explanatory notes and employed in the other lists of prime gaps at this site. Consequently, a special format is employed for such gaps. A fictional example is shown below:

999999999  C?P WCFields 2004 113.7447 9999999  1234567890123456789

Submissions of such gaps may be in the above format (explained in detail below), or in the simpler format

ggggggggg  pppppppppp

where ggggggggg is the gap measure and ppppppppp is the initiating prime, specified as a literal integer, or in formula form. In either format, line continuation (as specified below) is optional in gap submissions.

The precise format specifications for "megagaps" are similar to those provided in the principal explanatory notes, with exceptions as follows (see the principal notes for further explanation of terms and concepts).

The measure of the gap is shown in positions 1-9, right justified using leading blanks.
The classifications of the gaps are shown in positions 10-14. Position 10 is an asterisk for maximal gaps, otherwise a blank. Position 11 is always blank. Position 12 is (in this table) always a "C", indicating an ordinary or common prime gap. Position 13 is ordinarily a "?", indicating that the gap is a first known occurrence, but that it is not known whether or not it is a true first occurrence. This character would be an "F" if the gap had been proven a first occurrence, or an "N" if it had been proven not a first occurrence. Position 14 is a "P" if the bounding primes are probabilistic, or a "C" if the bounding primes have been certified deterministically.
If position 14 is a "?" (classification code "C??"), the bounding integers are probable primes (primes or strong base-2 pseudoprimes), but the interior integers of the gap have not been verified all composite to the satisfaction of Thomas R. Nicely; consequently, there remains a significant possibility that such a gap may in fact be smaller in measure than indicated, due to the as yet undetected presence of an interior prime.
Position 15 is blank.
Positions 16-23 carry an eight-character abbreviation indicating the discoverer(s) of the gap, as provided in the accompanying key. Position 24 is blank.
Positions 25-28 indicate the year of discovery. Position 29 is blank.
Positions 30-37 indicate the merit of the gap, to four decimal places. Position 38 is blank.
Positions 39-45 indicate the number of decimal digits in the initiating prime. Positions 46 and 47 are blank.
The value of the initiating prime begins in position 48. This value must be specified in full in submissions, but for primes exceeding 200 digits or characters, the value shown in the table is truncated (some of the initiating primes exceed 100,000 decimal digits). Abbreviated primes are shown in the form 123456789012345678901234567890..., with a few (usually 25 or more) of the most significant digits shown, followed by an ellipsis "...".
In gap submissions, the initiating prime must be specified in full. If a formula is available, it can presumably be expressed within the 200-character limit. If the prime is a literal integer, of course, it may contain many thousands of digits. In this event, it may all be written to a single record in the file, or it may be written using line continuation, with a trailing backslash "\" as the continuation character. The line continuation format used by the author employs 200 digits per line, occupying positions 48-247 inclusive, with the trailing backslash in position 248, and blanks in positions 1-47 of continuation lines (this matches the location of the prime's most significant 200 digits in the first line).
This format is also to be used for gaps whose measure is less than 1000000, but whose initiating primes contain more than 99999 digits.
The file allgaps.dat is available for download. This contains the complete (no truncation or abbreviation of primes) specification of each and every first known occurrence prime gap. It is a text file (WinDOS format), with one line per gap in standard format. Note that this file is nearly 10 MB in size, and contains extremely long lines which will challenge most editors and file utilities (it is intended primarily for software input or output).
I have also made available the zipfile merits.zip, which contains a text file specifying the measure G and the merit M=G/ln(p_1) for all known first occurrence and first known occurrence prime gaps. This smaller file (less than 1 MB) should be of additional assistance in determining whether or not some newly discovered gap constitutes a new first known occurrence.

============================================================================
    Gap    Cls Discvrer Year   Merit   Digits  Following the prime
============================================================================
  1001548  C?P RosntlJA 2004  10.0157   43429  1913094464943476849014660...
  1002890  C?P Rosnthal 2017  20.1556   21610  1111111111111111111*49999#/(11#*4649) - 407228
  1004840  C?P Rosnthal 2017  20.1968   21608  1111111111111111111*49999#/(17#*3119) - 793542
  1004972  C?P Rosnthal 2017  20.1966   21611  1111111111111111111*49999#/(13#*41) - 682886
  1045498  C?P Rosnthal 2017  21.0130   21609  1111111111111111111*49999#/(13#*4751) - 863196
  1059838  C?P MrtnRaab 2017  11.6712   39438  91183#/510510 - 749374
  1069640  C?P Rosnthal 2017  21.4978   21609  1111111111111111111*49999#/(13#*1709) - 479714
  1075312  C?P MrtnRaab 2017  11.8386   39448  91199#/510510 - 326398
  1078180  C?P PierCami 2006  12.3203   38007  50491*(87811#)/6 - 657714
  1084830  C?P Rosnthal 2017  21.8035   21609  1111111111111111111*49999#/(13#*4049) - 763076
  1095368  C?P RobSmith 2016  10.9892   43290  11*99991#/46410 - 886674
  1113106  C?C MJPC&JKA 2013  25.9045   18662  587*43103#/2310 - 455704
  1113976  C?P Rosnthal 2017  22.3878   21610  1111111111111111111*49999#/(11#*1987) - 389212
  1117820  C?P RobSmith 2016  11.2141   43291  149*99991#/46410 - 813426
  1134502  C?P MrtnRaab 2017  12.5131   39376  91081#/223092870 - 266616
  1150108  C?P MrtnRaab 2017  12.6876   39369  91033#/510510 - 292500
  1151150  C?P Rosnthal 2017  23.1376   21608  1111111111111111111*49999#/(17#*3511) - 439532
  1158992  C?P MrtnRaab 2017  12.7816   39381  91097#/223092870 - 868638
  1162884  C?P RobSmith 2018   4.8229  104715  6119*241727#/46410 - 510266
  1176666  C?P MrtnRaab 2016  12.9561   39443  91199#/46473256830 - 629212
  1212942  C?P MrtnRaab 2017  13.3981   39318  90911#/9699690 - 578816
  1216548  C?P MrtnRaab 2017  13.3919   39453  91229#/510510 - 552182
  1217460  C?P MrtnRaab 2015  13.4036   39448  91229#/46093437390 - 495038
  1224222  C?P RobSmith 2016  12.2811   43293  8263*99991#/46410 - 600164
  1260182  C?P Rosnthal 2017  25.3279   21609  1111111111111111111*49999#/(13#*4903) - 519438
  1284234  C?P MrtnRaab 2017  14.1659   39372  91079#/9699690 - 502828
  1286500  C?P Rosnthal 2016  25.8571   21608  1111111111111111111*49999#/(510510*499) - 525318
  1289022  C?P MrtnRaab 2017  14.1924   39445  91199#/223092870 - 589586
  1289448  C?P MrtnRaab 2017  14.2096   39411  91141#/223092870 - 486524
  1321710  C?P MrtnRaab 2017  14.6129   39282  90833#/223092870 - 666794
  1358012  C?P RobSmith 2018   5.6322  104715  2087*241727#/46410 - 995132
  1386416  C?P MrtnRaab 2017  15.3176   39309  90901#/510510 - 617466
  1390164  C?P MrtnRaab 2017  15.3242   39398  91127#/510510 - 572762
  1398354  C?P RobSmith 2018  13.3957   45336  887*104729#/46410 - 1162948
  1417014  C?P MrtnRaab 2017  15.6246   39387  91099#/9699690 - 762506
  1419558  C?P MrtnRaab 2017  15.6620   39364  91019#/510510 - 607058
  1452592  C?P RobSmith 2016  14.5724   43291  451*99991#/46410 - 1136946
  1462522  C?P MrtnRaab 2015  16.1016   39448  91229#/46056680670 - 853776
  1471730  C?P MrtnRaab 2017  16.2111   39428  91159#/510510 - 804872
  1521800  C?P MrtnRaab 2017  16.7563   39443  91193#/510510 - 371324
  1569660  C?P M.Jansen 2012   7.0001   97384  224737#/510510 - 1054198
  1575828  C?P M.Jansen 2012  15.0964   45334  104729#/2310 - 1282742
  1926858  C?P RobSmith 2018   7.9915  104715  2819*241727#/46410 - 1043012
  1975746  C?P RobSmith 2018   6.8964  124422  893*287117#/46410 - 1160164
  2028240  C?P RobSmith 2018   6.5068  135376  953*312583#/46410 - 1053466
  2055816  C?P PierCami 2010  15.6743   56962  6887*(131591#)/2730 - 1381994
  2079500  C?P MrtnRaab 2017  22.9895   39284  90833#/510510 - 1177176
  2218822  C?P RobSmith 2018   7.1182  135374  41*312583#/46410 - 1634758
  2254930  C?P RosntlJA 2004  11.2755   86853  1122483511942968776411893...
  2332764  C?P MrtnRaab 2017  25.7927   39279  90823#/510510 - 1065962
  2435476  C?P MrtnRaab 2016  10.6037   99750  230077#/2226961526790 - 994222
  2493532  C?P MrtnRaab 2016  10.8564   99750  230077#/2227349514390 - 1441218
  2559528  C?P MrtnRaab 2016  11.1438   99750  230077#/2228280684630 - 961364
  2586246  C?P MrtnRaab 2016  11.2601   99750  230077#/2226554139810 - 1616044
  2724214  C?P MJandJKA 2013  11.8311  100000  230563#/2310 - 44352
  2765878  C?P MJPC&JKA 2013  12.0114  100006  230567#/2310 - 939244
  2945060  C?P MrtnRaab 2016  12.8223   99750  230077#/2227174919970 - 1072622
  3006474  C?P RobSmith 2018  10.4941  124422  613*287117#/46410 - 1686788
  3081120  C?P RobSmith 2018  10.7547  124422  389*287117#/46410 - 1640854
  3101868  C?P RobSmith 2018  12.8648  104714  523*241727#/46410 - 1839562
  3130254  C?P RobSmith 2018  10.9262  124422  967*287117#/46410 - 1916282
  3186150  C?P RobSmith 2018  13.2143  104715  1067*241727#/46410 - 1433258
  3190146  C?P RobSmith 2018  11.1353  124421  71*287117#/46410 - 1867414
  3311852  C?P MJandJKA 2012  14.6838   97953  226007#/2310 - 2305218
  3370374  C?P MrtnRaab 2017  11.2705  129873  300007#/9699690 - 2004098
  3377768  C?P RobSmith 2018  11.7902  124421  181*287117#/46410 - 1546166
  3870360  C?P RobSmith 2018  12.4164  135376  2267*312583#/46410 - 1157722
  4680156  C?P MrtnRaab 2016  20.3767   99750  230077#/2229464046810 - 3131794
  5103138  C?P RobSmith 2016  10.2203  216849  281*499979#/46410 - 2702372
  6582144  C?P MrtnRaab 2017  13.1829  216841  499973#/30030 - 4509212
============================================================================