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arXiv · 1708.06953

Using Dynamical Systems to Construct Infinitely Many Primes

Andrew Granville
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Abstract

Euclid's proof can be reworked to construct infinitely many primes, in many different ways, using ideas from arithmetic dynamics. After acceptance Soundararajan noted the beautiful and fast converging formula: $$ \tau = a^{1/(d-1)} x_0 \cdot \lim_{n\to \infty} \prod_{m=1}^n \left(\frac{x_m}{ax_{m-1}^d} \right)^{1/d^m} $$

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Andrew Granville. 2017-08-23. Using Dynamical Systems to Construct Infinitely Many Primes. https://arxiv.org/abs/1708.06953

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