Analytic number theory has seen many important breakthroughs in recent years, as documented by the Fields medals by Bourgain, Tao, Venkatesh, and most recently by Maynard (2022). Often, random and deterministic phenomena play an important role in problems in analytic number theory, and fruitful interactions with the area of dynamical system can be observed. One of the most striking open conjectures in the area of “arithmetic randomness” is Sarnak’s conjecture. It states that the Möbius function is orthogonal to any sequence that is realized in a deterministic dynamical system and resembles the behaviour of a random sequence. While still open in its full generality, considerable progress has been obtained with respect to special classes of sequences. We mention the solution of the conjecture by Müllner for automatic sequences which, informally speaking, are sequences that relate the value of its terms to the digits of its base-q representation. Sarnak’s conjecture is closely related to Chowla’s conjecture that, in turn, studies the correlations of the Möbius function. In recent years, various breakthroughs have been obtained in these areas. We mention the results by Green and Tao concerning the orthogonality of nilsequences, by Frantzikinakis and Host on the logarithmic Sarnak conjecture for zero entropy topological systems with only countably many ergodic measures, by Green and Bourgain concerning the computational complexity of the Möbius function, and many more. Bourgain and Swaenepoel considered the number of prime numbers and squares with preassigned digits, and Maynard obtained the count of prime numbers with restricted digits. The proofs often rely on a variety of tools ranging from analytic number theory, probability theory, Diophantine considerations, and dynamical systems.

The major aim of the conference is to gather people working on “randomness” properties of prime numbers, including both international and French mathematicians, and to provide an environment for scientific exchanges to foster new collaborations, especially with the younger participants. The conference has an overlap with the French–Austrian joint project ArithRand supported by the ANR and the FWF. It is a thematic broadening of the conference “Prime numbers, determinism and pseudorandomness” that was held at CIRM (4–8 November, 2019).