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Rice University Summer Institute of Statistics

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Study of the distances and increments between prime numbers by modular ... Conjectures A Weibull or exponential distribution models the distances and increments ... – PowerPoint PPT presentation

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Title: Rice University Summer Institute of Statistics


1
Rice University Summer Institute of Statistics
  • Study of the distances and increments between
    prime numbers by modular segregation and extreme
    value theory

Research group Jenny M. Fries Brandon M.
Perpich Matthew E. Pragel Tahira N. Saleem
Project Advisor Dr. Javier Rojo
2
Conjectures
  • A Weibull or exponential distribution models the
    distances and increments between consecutive
    primes when separated modulo six.
  • The extreme values over a certain threshold
    follow a generalized pareto distribution.
  • The number of distances congruent to two and four
    modulo six approach a limit.
  • The waiting times between extreme values follow a
    Poisson process.

3
Previous Studies
  • Information Entropy and Correlations in Prime
    Numbers
  • --Kumar, Ivanov, Stanley (2003)
  • Primes 2 3 5 7 11 13
    17
  • Distance 1 2 2 4 2
    4
  • Increment 1 0 2 -2 2
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