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arXiv · 0707.1990

Phase transition in a stochastic prime number generator

Bartolo Luque·Lucas Lacasa·Octavio Miramontes
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Abstract

We introduce a stochastic algorithm that acts as a prime number generator. The dynamics of such algorithm gives rise to a continuous phase transition which separates a phase where the algorithm is able to reduce a whole set of integers into primes and a phase where the system reaches a frozen state with low prime density. We present both numerical simulations and an analytical approach in terms of an annealed approximation, by means of which the data are collapsed. A critical slowing down phenomenon is also outlined.

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Bartolo Luque, Lucas Lacasa, Octavio Miramontes. 2007-07-13. Phase transition in a stochastic prime number generator. https://doi.org/10.1103/physreve.76.010103

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