** Research Article of Research Journal of Mathematics and Computer Science**

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

**Bertrand Teguia Tabuguia**

Ph.D. student, Computer Algebra, Mathematics and Natural Sciences, University of Kassel, Germany, Heinrich-Plett-Str.40, 34132 Kassel

We 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.

** Keywords: **Pseudo random-number generator, Prime numbers.

## Free Full-text PDF

**How to cite this article:**

Bertrand Teguia Tabuguia. An Algorithmic Random-Integer Generator based on the Distribution of Prime Numbers. Research Journal of Mathematics and Computer Science, 2019; 3:16. DOI: 10.28933/rjmcs-2019-06-1705

**References:**

1. David F DiCarlo. Random number generation: Types and techniques. Liberty Univer-sity, 2012.

2. Terence Tao. Structure and randomness in the prime numbers. In An Invitation to Mathematics, pages 1–7. Springer, 2011.

3. Robert J Lemke Oliver and Kannan Soundararajan. Unexpected biases in the dis-tribution of consecutive primes. Proceedings of the National Academy of Sciences, 113(31):E4446–E4454, 2016.

4. S Torquato, G Zhang, and M de Courcy-Ireland. Uncovering multiscale order in the prime numbers via scattering. Journal of Statistical Mechanics: Theory and Experiment, 2018(9):093401, sep 2018.

5. OF TRUE RANDOMNESS. The importance of true randomness in cryptography. Cite-seer.

6. David Jones. Good practice in (pseudo) random number generation for bioinformatics applications. URL http://www.cs.ucl.ac.uk/staﬀ/d.jones/GoodPracticeRNG.pdf, 2010.

7. Bertrand Teguia. P&C Game. ResearchGate, 2019

8. Yitang Zhang. Bounded gaps between primes. Annals of Mathematics, pages 1121–1174, 2014.

9. Eric W Weisstein. Twin primes. Wolfram Research, Inc., 2003

10. Tom Kennedy. Monte Carlo Methods – a special topics course. Spring, 2016

11. Python Software Foundation. Python 2.7.0 release. https://www.python.org/, 2019

12. John Renze and Eric W. Weisstein. Law of large numbers. Mathworld