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Abstract: Negative correlations in the distribution of prime numbers are found todisplay a scale invariance. This occurs in conjunction with a nonstationarybehavior. We compare the prime number series to a type of fractional Brownianmotion which incorporates both the scale invariance and the nonstationarybehavior. Interesting discrepancies remain. The scale invariance also appearsto imply the Riemann hypothesis and we study the use of the former as a test ofthe latter.



Author: B. Holdom

Source: https://arxiv.org/



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