Abstract
Several ways of interleaving, as studied in theoretical computer science, and some subjects from mathematics can be modeled by length-preserving operations on strings, that only permute the symbol positions in strings. Each such operation X gives rise to a family {Xn}n≥2 of similar permutations. We call an integer nX-prime if Xn consists of a single cycle of length n (n≥2). For some instances of X–such as shuffle, twist, operations based on the Archimedes’ spiral and on the Josephus problem–we investigate the distribution of X-primes and of the associated (ordinary) prime numbers, which leads to variations of some well-known conjectures on the density of certain sets of prime numbers.
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