Displaying similar documents to “On the discrepancy of inversive congruential pseudorandom numbers with prime power modulus.”

Normal numbers and the middle prime factor of an integer

Jean-Marie De Koninck, Imre Kátai (2014)

Colloquium Mathematicae

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Let pₘ(n) stand for the middle prime factor of the integer n ≥ 2. We first establish that the size of log pₘ(n) is close to √(log n) for almost all n. We then show how one can use the successive values of pₘ(n) to generate a normal number in any given base D ≥ 2. Finally, we study the behavior of exponential sums involving the middle prime factor function.

The mantissa distribution of the primorial numbers

Bruno Massé, Dominique Schneider (2014)

Acta Arithmetica

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We show that the sequence of mantissas of the primorial numbers Pₙ, defined as the product of the first n prime numbers, is distributed following Benford's law. This is done by proving that the values of the first Chebyshev function at prime numbers are uniformly distributed modulo 1. We provide a convergence rate estimate. We also briefly treat some other sequences defined in the same way as Pₙ.