Phase transition in a stochastic prime number generator

Details Phase transition in a stochastic prime number generator Phase transition in a stochastic prime number generator

2007-07-13

arxiv.org/abs/0707.1990v1

Physical Review E 76, 010103 (R) (2007)

Physics

Computational Physics

accepted in PRE (Rapid Comm.)

Scientific paper

10.1103/PhysRevE.76.010103

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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