An Algorithmic Random-Integer Generator based on the Distribution of Prime Numbers

Bertrand Teguia Tabuguia

doi:10.28933/rjmcs-2019-06-1705

Abstract

The prevalencWe talk about random when it is not possible to determine a pattern on the observed out-comes. A computer follows a sequence of ﬁxed instructions to give any of its output, hence the diﬃculty of choosing numbers randomly from algorithmic approaches. However, some algorithms like the Linear Congruential algorithm and the Lagged Fibonacci generator appear to produce “true” random sequences to anyone who does not know the secret initial input [1]. Up to now, we cannot rigorously answer the question on the randomness of prime numbers [2, page 1] and this highlights a connection between random number generator and the distribution of primes. From [3] and [4] one sees that it is quite naive to expect good random reproduction with prime numbers. We are, however, interested in the properties underlying the distribution of prime numbers, which emerge as suﬃcient or insuﬃcient arguments to conclude a proof by contradiction which tends to show that prime numbers are not randomly distributed. To achieve this end, we use prime gap sequence variation. Our algorithm makes possible to deduce, in a binary choice case, a uniform behavior in the individual consecutive occurrence of primes, and no uniformity trait when the occurrences are taken collectively.

Highlights

The use of randomness is needed in almost all areas, including cryptography [5] and bioinformatics [6]
PRNGs are periodic, and larger periods give better random imitation; that is why a major consideration in the choice of a pseudo random number generator is the size of its period, because this directly affects the frequency that a generator can be used
A good seeding may result from the aim of the random implementation; for example, in P&C Game [7], the author uses the first click of the player to seed the generator

Summary

Introduction

The use of randomness is needed in almost all areas, including cryptography [5] and bioinformatics [6]. PRNGs are periodic, and larger periods give better random imitation; that is why a major consideration in the choice of a pseudo random number generator is the size of its period, because this directly affects the frequency that a generator can be used Another common issue with PRNG algorithms is the seeding or the initialization, since this is the construction of a sequence following states, two sequences having the same initial state must be identical. Our algorithm for random integer generator uses the variation of the prime gap sequence. Zhang result does not prove the twin prime conjecture [10], these works ensure altogether the consistency of an algorithm to produce "random" behavior relying on the variation of the prime gap sequence.

Structure of Pseudo Random Integer Generator

Definition of Our Pseudo Random Integer Generator

Application and Tests

Probability variation of the prime gap sequence

Findings

Conclusion