Cycles and Patterns in the Sieve of Eratosthenes

George Grob; Matthias Schmitt

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arXiv · 1905.03117

Cycles and Patterns in the Sieve of Eratosthenes

George Grob·Matthias Schmitt

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Abstract

We describe recurring patterns of numbers that survive each wave of the Sieve of Eratosthenes, including symmetries, uniform subdivisions, and quantifiable, predictive cycles that characterize their distribution across the number line. We generalize these results to numbers that are relatively prime to arbitrary sets of prime numbers and derive additional insights about the distribution of integers counted by Euler's phi-function.

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George Grob, Matthias Schmitt. 2019-05-03. Cycles and Patterns in the Sieve of Eratosthenes. https://arxiv.org/abs/1905.03117

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