Open Access Library Journal

Volume 3, Issue 9 (September 2016)

ISSN Print: 2333-9705   ISSN Online: 2333-9721

Google-based Impact Factor: 0.47  Citations  

A Power Law Governing Prime Gaps

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DOI: 10.4236/oalib.1102989    1,319 Downloads   1,927 Views  Citations

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.

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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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