Class NthPrimeUpperBounds

java.lang.Object
de.tilman_neumann.jml.primes.bounds.NthPrimeUpperBounds

public class NthPrimeUpperBounds
extends java.lang.Object
Bounds for the n.th prime p(n).
  • Method Summary

    Modifier and Type Method Description
    static long Axler2013​(long n)
    Axler 2013 page viii Korollar G for n >= 8009824.
    static long combinedUpperBound​(long n)
    Computes an upper bound for p(n) given n.
    static long Dusart1999​(long n)
    Dusart 1999 page 14 for n >= 39017.
    static long Dusart2010p7​(long n)
    Dusart 2010 page 7, Lemma 6.5: Holds for n >= 178974.
    static long Dusart2010p8​(long n)
    Dusart 2010 page 8, Proposition 6.6: Holds for n >= 688383.
    static long Robin1983​(long n)
    Robin 1983 "for n >= 7022": My tests say it works for n >= 8601.
    static long RobinJacobsen​(long n)
    Robin 1983 modified by D.Jacobsen for n = 6...39016 _only_.
    static long RosserSchoenfeld01​(long n)
    Rosser/Schoenfeld 1961 for n >= 6.
    static long RosserSchoenfeld02​(long n)
    Rosser/Schoenfeld 1961 for n >= 20.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
  • Method Details

    • combinedUpperBound

      public static long combinedUpperBound​(long n)
      Computes an upper bound for p(n) given n.
      Parameters:
      n -
      Returns:
      upper bound for n.th prime
    • RosserSchoenfeld01

      public static long RosserSchoenfeld01​(long n)
      Rosser/Schoenfeld 1961 for n >= 6.
      Parameters:
      n -
      Returns:
      upper bound for n.th prime
    • RosserSchoenfeld02

      public static long RosserSchoenfeld02​(long n)
      Rosser/Schoenfeld 1961 for n >= 20.
      Parameters:
      n -
      Returns:
      upper bound for n.th prime
    • RobinJacobsen

      public static long RobinJacobsen​(long n)
      Robin 1983 modified by D.Jacobsen for n = 6...39016 _only_.
      Parameters:
      n -
      Returns:
      upper bound for n.th prime
    • Robin1983

      public static long Robin1983​(long n)
      Robin 1983 "for n >= 7022": My tests say it works for n >= 8601.
      Parameters:
      n -
      Returns:
      upper bound for n.th prime
    • Dusart1999

      public static long Dusart1999​(long n)
      Dusart 1999 page 14 for n >= 39017.
      Parameters:
      n -
      Returns:
      upper bound for n.th prime
    • Dusart2010p7

      public static long Dusart2010p7​(long n)
      Dusart 2010 page 7, Lemma 6.5: Holds for n >= 178974.
      Parameters:
      n -
      Returns:
      upper bound for n.th prime
      See Also:
      "https://arxiv.org/PS_cache/arxiv/pdf/1002/1002.0442v1.pdf"
    • Dusart2010p8

      public static long Dusart2010p8​(long n)
      Dusart 2010 page 8, Proposition 6.6: Holds for n >= 688383.
      Parameters:
      n -
      Returns:
      upper bound for n.th prime
      See Also:
      "https://arxiv.org/PS_cache/arxiv/pdf/1002/1002.0442v1.pdf"
    • Axler2013

      public static long Axler2013​(long n)
      Axler 2013 page viii Korollar G for n >= 8009824.
      Parameters:
      n -
      Returns:
      upper bound for n.th prime