# Primes in Short Intervals

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## Abstract

Contrary to what would be predicted on the basis of Cramér’s model concerning the distribution of prime numbers, we develop evidence that the distribution of *ψ*(*x*+*H*)−*ψ*(*x*), for 0≤*x*≤*N*, is approximately normal with mean ∼*H* and variance ∼*H* log *N*/*H*, when *N*^{ δ }≤*H*≤*N*^{1−}^{ δ }.

## Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Short Interval
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