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The next meeting of the Algebra and Logic Seminar will be held in hybrid format (in Room 578 of IMI and online via Zoom) on October 20, 2023 (Friday) at 1:00 pm (UTC+3).

A talk on:

Prime numbers and random walks in a square grid

will be delivered by Alberto Fraile (Czech Technical University in Prague, Czech Republic).

Joint work with Osame Kinouchi, Prashant Dwivedi, Roberto Martínez, Theophanes E. Raptis, and Daniel Fernández

Abstract. One can argue that prime numbers present perplexing features, in a hybrid of local unpredictability and global regular behavior. It is this interplay between randomness and regularity that motivated searches for both local and global patterns that could potentially become signatures for certain underlying fundamental mathematical properties.In recent years, computer simulations are playing a fundamental role in unveiling some of the most intriguing features of prime numbers. In this work, we define an algorithm for a deterministic walk through a two-dimensional grid that we refer to as Prime Walk (PW). The walk is constructed from a sequence of steps dictated by and dependent on the sequence of last digits of the primes. Despite the apparent randomness of this generating sequence, the resulting structure – both in 2d and 3d – created by the algorithm presents remarkable properties and regularities in its pattern that we proceed to analyze in detail [1].

[1] A. Fraile, O. Kinouchi, P. Dwivedi, R. Martínez, T. E. Raptis, D. Fernández, Prime numbers and random walks in a square grid, Phys. Rev. E 104 (5), 054114-054120 (2021).

Link to the Zoom room:

Algebra and Logic Department, IMI – BAS
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