Rice University Summer Institute of Statistics

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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
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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.

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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