A Power Law Governing Prime Gaps - Open Access Library Journal

OALibJ > Vol.3 No.9, September 2016

A Power Law Governing Prime Gaps ()

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DOI: 10.4236/oalib.1102989 1,449 Downloads 2,820 Views Citations

Author(s)

Raul Matsushita¹, Sergio Da Silva²

Affiliation(s)

¹Department of Statistics, University of Brasilia, Brasilia, Brazil.
²Graduate Program in Economics, Federal University of Santa Catarina, Florianopolis, Brazil.

ABSTRACT

A prime gap is the difference between two successive prime numbers. Prime gaps are casually thought to occur randomly. However, the “k-tuple conjecture” suggests that prime gaps are non-random by estimating how often pairs, triples and larger groupings of primes will appear. The k-tuple conjecture is yet to be proven, but a very recent work presents a result that contributes to a confirmation of thek-tuple conjecture by finding unexpected biases in the distribution of consecutive primes. Here, we present another contribution to confirmation of the k-tuple conjecture based on statistical physics. The pattern we find comes in the form of a power law in the distribution of prime gaps. We find that prime gaps are proportional to the inverse of the chance of a number to be prime.

KEYWORDS

Prime Numbers, Power Laws, Prime Gaps, k-Tuple Conjecture, Number Theory

Share and Cite:

Matsushita, R. and Da Silva, S. (2016) A Power Law Governing Prime Gaps. Open Access Library Journal, 3, 1-6. doi: 10.4236/oalib.1102989.

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