SQL schema for representing the list of first known occurrence prime gaps

Details and rationale of schema creation

Dec 5, 2019 • Graham Higgins • projectdoc

Publication format

The list of first known occurrence gaps is published as a plaintext file of SQL statements allgaps.sql which, when read into a SQL-aware application, constructs two relational tables of data: gaps and credits.

The gaps table contains the data previously published by Dr Thomas Ray Nicely as a spatially-formatted plaintext file allgaps.dat. Archival versions of this data remain accessible as captures courtesy of archive.org’s “Wayback Machine”.

The credits table is taken from the one published by Dr. Nicely in a web page “First known occurrence of prime gaps”, similarly accessible as captured by the “Wayback Machine”. The credits table provides a mapping from the abbreviations of names of discoverers used in the gaps table to the full details.

Database schema for `gaps` table

CREATE TABLE gaps(
  "gapsize" INTEGER,
  "ismax" BOOLEAN,
  "primecat" TEXT,
  "isfirst" TEXT,
  "primecert" TEXT,
  "discoverer" TEXT,
  "year" INTEGER,
  "merit" REAL,
  "primedigits" INTEGER,
  "startprime" TEXT
);

The domain semantics of the data fields are described in a separate document

Database schema for `credits` table

CREATE TABLE credits(
  "abbreviation" TEXT,
  "name" TEXT,
  "ack" TEXT,
  "display" TEXT
);

In which abbreviation is a key to the abbreviations used in gaps for discoverers’ names and name is the indexed-to string originally published by Dr. Nicely (see below) with the credit acknowledgements (e.g. “(PGS)”, “Computer codes by Tomás Oliveira e Silva.”) separated out into the ack field. The display field is used for display purposes and is the discoverer’s name(s) plus a shortened form of the credit acknowledgement (e.g. “Robert W. Smith [Dana Jacobsen]”).

“Abbreviations for Discoverers” as last published by Dr. Thomas Ray Nicely

ANair_MF---Anand S. Nair (PGS).
APinhTOS---Armando Pinho. Computer codes by Tomás Oliveira e Silva.
A.Walker---Andrew John Walker.
AEWestrn---A. E. Western.
Andersen---Jens Kruse Andersen.
ApplRssr---Kenneth I. Appel and J. Barkley Rosser.
ATeixTOS---António Teixera. Computer codes by Tomás Oliveira e Silva.
Be.Nyman---Bertil Nyman.
Blnchtte---Gilles Blanchette.
CBastTOS---Carlos Bastos. Computer codes by Tomás Oliveira e Silva.
CKernTOS---Cristian Kern. Computer codes by Tomás Oliveira e Silva.
ColeStev---Steve Cole (PGS).
DanielH.---Daniel Hermle.
DBghFOH---D.; Baugh and F. O'Hara.
DHLehmer---Derrick Henry Lehmer.
DonKnuth---Donald Ervin Knuth.
Erickson---Eddie Erickson.
Euclid  ---Euclid.
Fougeron---Jim Fougeron.
GABandAR---F. J. Gruenberger, G. Armerding, and C. L. Baker (1959, 1961),
       and independently, Kenneth I. Appel and J. Barkley Rosser (1961).
Gapcoin----The Gapcoin network,
       a Bitcoin derivative, employs a hashing algorithm which searches
       for prime gaps of high merit. Jonnie Frey, developer.
Glaisher---J. W. L. Glaisher.
H.Dubner---Harvey Dubner.
HrzogTOS---Siegfried "Zig" Herzog. Computer codes by Tomás Oliveira e Silva.
Jacobsen---Dana Jacobsen, running code using C and Perl.
JamesFry---James Fry.
JdeGroot---Jeroen de Groot.
JFNSTOeS---John Fettig and Nahil Sobh, NCSA. Computer codes by Tomás Oliveira e Silva.
JLGPardo---Jose Luis Gomez Pardo.
JRdrgTOS---João Manuel Rodrigues. Computer codes by Tomás Oliveira e Silva.
K.Conrow---Kenneth Conrow.
KOGrndln---Kjell-Olav Grøndalen.
_Kokales---David Kokales. Also contributed deterministic primality proofs.
LLnhardy---Leif Leonhardy.
LMorelli---Luigi Morelli (PGS).
LndrPrkn---L. J. Lander and Thomas R. Parkin.
M.Jansen---Michiel Jansen.
MJandJKA---Michiel Jansen and Jens Kruse Andersen.
MJPCJKA---Michiel; Jansen, Pierre Cami, and Jens Kruse Andersen.
ML.Brown---Milton L. Brown.
MrtnRaab---Martin Raab.
NicelyHD---Thomas R. Nicely. Computer codes inspired by Harvey Dubner's work.
NoAttrib---Anonymous contributors who do not wish attribution.
NuuKuosa---Nuutti Kuosa.
PardiTOS---Silvio Pardi. Computer codes by Tomás Oliveira e Silva.
PDeGeest---Patrick De Geest.
PierCami---Pierre Cami.
Pinho_MF---Carlos Eduardo Leal de Pinho (PGS).
R.Athale---Rahul Ramesh Athale.
RFischer---Richard Fischer.
Ritschel---Thomas Ritschel (PGS).
RobSmith---Robert W. Smith. Some of Smith's results after 2014 employ
       Perl code written by Dana Jacobsen. Coordinator, PGS.
Rosnthal---Hans Rosenthal.
RosntlJA---Hans Rosenthal. Computer codes by Jens Kruse Andersen.
RosntlJF---Hans Rosenthal. Computer codes by Jim Fougeron.
RP.Brent---Richard P. Brent.
Shepherd---Rick L. Shepherd.
Spielaur---Helmut Spielauer.
TAlmFMJA---Torbjörn Alm. Computer codes by Jens Kruse Andersen.
           Deterministic primality proofs by François Morain.
T.Hadley---Thomas Hadley.
TOeSilva---Tomás Oliveira e Silva.
Toni_Key---Antonio Key, using Perl codes developed by Dana Jacobsen.
TorAlmJA---Torbjörn Alm. Computer codes by Jens Kruse Andersen.
TRNicely---Thomas R. Nicely.
Weslwski---Arkadiusz Wesołowski.
Yng&Ptlr---Jeff; Young and Aaron Potler.
YPPauloR---Jeff Young and Aaron Potler, as reported by Paulo Ribenboim.

This list of discoverers was hand-formatted as SQL statements.

A relational database representation of the list of known first occurrence prime gaps

A SQLite database is a single disk file. The file format is cross-platform. A database that is created on one machine can be copied and used on a different machine with a different architecture. SQLite databases are portable across 32-bit and 64-bit machines and between big-endian and little-endian architectures.

Each value stored in an SQLite database (or manipulated by the database engine) has one of the following storage classes:

NULL. The value is a NULL value.

INTEGER. The value is a signed integer, stored in 1, 2, 3, 4, 6, or 8
         bytes depending on the magnitude of the value.

REAL. The value is a floating point value, stored as an 8-byte
      IEEE floating point number.

TEXT. The value is a text string, stored using the database
      encoding (UTF-8, UTF-16BE or UTF-16LE).

BLOB. The value is a blob of data, stored exactly as it was input.

Create schema for gaps and credits tables

(Lines split for presentation, so not copy’n’pastable as displayed, needs collapsing into one line)

printf 'CREATE TABLE gaps (
    gapsize INTEGER,
    ismax BOOLEAN,
    primecat TEXT,
    isfirst TEXT,
    primecert TEXT,
    discoverer TEXT,
    year INTEGER,
    merit REAL,
    primedigits INTEGER,
    startprime BLOB
    );\n
    CREATE TABLE credits (
        abbreviation TEXT,
        name TEXT,
        ack TEXT,
        display TEXT
    );\n
    .save allgaps.db\n' | sqlite3

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