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 the k-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.
Cite this paper
Matsushita, R. and Silva, S. D. (2016). A Power Law Governing Prime Gaps. Open Access Library Journal, 3, e2989. doi: http://dx.doi.org/10.4236/oalib.1102989.
Hardy, G.H.
and
Littlewood, J.E. (1923) Some Problems of “Partitio Numerorum”.
III. On the Expression of a Number as a Sum of Primes. Acta Mathematica, 44, 1-70. http://dx.doi.org/10.1007/BF02403921