Class NthPrimeUpperBounds


  • public class NthPrimeUpperBounds
    extends Object
    Bounds for the n.th prime p(n).
    Author:
    Tilman Neumann
    • Method Detail

      • 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