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Research Article Open access CC BY 4.0

Computer Simulation Model of Prime Numbers

Daniele Lattanzi

Journal of Advances in Mathematics and Computer Science · pp. 101–121 · Published 4 Jul 2023

10.9734/jamcs/2023/v38i81794

Abstract

Prime numbers represent one of the major open problems in number theory mostly in that at present it is not possible to state that the induction principle holds for them. The methodology of experimental mathematics has been little endeavored in this field thus the present report deals with an innovative approach to the problem of primes treated as raw experimental data and as elements of larger and larger finite sequences {Pn}. The modified Chi-square function in the form -1/X2k(A,n/μ) with the ad-hoc A, k and μ parameters is the best-fit function of the finite sequences of primes {Pn}, like the truncated progressions {Cαnα} with domain N and co-domain R+, being (α,k)≡(1+,0-) and k=2-2α and just like the function λn×n×ln(n), what leads to induction algorithms and to many fit relationships Pn≈P(n) though within the precisions of the calculations that is approximate. A bi-injective map can be set between the prime sequences and any of these three fit functions showing that the property of scale invariance does not hold for the fits of the finite sequences of prime numbers. Moreover an approximate inductive algorithm is shown capable of finding the approximate value of a prime Pn+1 starting from the value of the previous Pn. 

Prime number sequences scale variation numerical progressions data fits modified chi-square function experimental mathematics

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Cited by 1

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