Class NthPrimeUpperBounds
- java.lang.Object
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- de.tilman_neumann.jml.primes.bounds.NthPrimeUpperBounds
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public class NthPrimeUpperBounds extends Object
Bounds for the n.th prime p(n).- Author:
- Tilman Neumann
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Method Summary
All Methods Static Methods Concrete Methods 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.
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Method Detail
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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
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RosserSchoenfeld01
public static long RosserSchoenfeld01(long n)
Rosser/Schoenfeld 1961 for n >= 6.- Parameters:
n
-- Returns:
- upper bound for n.th prime
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RosserSchoenfeld02
public static long RosserSchoenfeld02(long n)
Rosser/Schoenfeld 1961 for n >= 20.- Parameters:
n
-- Returns:
- upper bound for n.th prime
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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
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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
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Dusart1999
public static long Dusart1999(long n)
Dusart 1999 page 14 for n >= 39017.- Parameters:
n
-- Returns:
- upper bound for n.th prime
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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"
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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"
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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
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