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. FriesBrandon M.

PerpichMatthew E.

PragelTahira N.

Saleem

Project Advisor: Dr. Javier Rojo

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.

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