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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

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