PGpack Home Page


These are instructions for obtaining the software PGpack.m, a Mathematica package of functions which goes with "Bounded gaps between primes", by Kevin Broughan published by Cambridge University Press, 2021. There are more details concerning the package, its installation and functions in the "PGpack mini-manual", which is included in the book as Appendix I.

To use the software having Mathematica version 10.0 or later is recommended. Since the software is in the form of a standard Mathematica package, it should run under any common operating system (Windows, MacOS, or Unix/Linux).

Requests for assistance and advice are welcome, as are bug reports and suggestions for new software. If you find PGpack useful please let me know, and give references for any published work which references the software. The email address is given below.

The Functions of PGpack:

AdmissibleTupleQ, BesselZeroUpperBound, BombieriDavenportK, BrunsConstant, ComputeI, ComputeJ, ContractTuple, CountResidueClasses, DenseDivisibility, DenselyDivisibleQ, DenseTuple, EnlargeAdmissibleTuple, EnlargingElementQ, EnlargingElements, EratosthenesTuple, ExpandSignature, FeasibleKPolymathQ, GetPolymathTuple, GPYEH, GreedyTuple, HenselyRichardsTuple, HValues, InductiveTuple, InductiveTupleOffsets1000, IntegrateRk, KappaZhang, KrylovF, KrylovNewMonomial, KrylovWs, LargeSubsetQ, MonToPoly, NarrowestTuples, NarrowH, NarrowTuples, NextPrimeGapDist, OmegaZhang, OperatorL, PlotHValues, PlotTwins, PolyToMon, PolyMonDegrees, PrimeTuple, RayleighQuotientBogaert, RayleighQuotientFromWs, RayleighQuotientMaynard, RayleighQuotientPolymath, RhoStar, SchinzelTuple, ShiftedPrimeTuple, SignatureQ, SmallestKPolymath0, SmallestKPolymath1, SmallestKStar, SmallSubsetQ, SmoothIntegerQ, StabilizingElementQ, StabilizingElements, SymmetricPolynomialQ, TupleDiameter, TupleGaps, TupleMinimalCompanions, TwinPrimesConstant, VonMangoldtR.


Download the PGpack software (Mathematica package format with file name PGpack.m)

  • Kevin A. Broughan

    Last modified: 19th February 2021.