%0 Journal Article
%T A Power Law Governing Prime Gaps
%A Raul Matsushita
%A Sergio Da Silva
%J Open Access Library Journal
%V 3
%N 9
%P 1-7
%@ 2333-9721
%D 2016
%I Open Access Library
%R 10.4236/oalib.1102989
%X <div style="text-align:justify;">
	<span style="line-height:1.5;">A prime gap is the difference between two successive
prime numbers. Prime gaps are casually thought to occur randomly. However, the
¡°</span><i style="line-height:1.5;">k</i><span style="line-height:1.5;">-tuple conjecture¡± suggests that prime
gaps are non-random by estimating how often pairs, triples and larger groupings
of primes will appear. The </span><i style="line-height:1.5;">k</i><span style="line-height:1.5;">-tuple
conjecture is yet to be proven, but a very recent work presents a result that
contributes to a confirmation of the </span><i style="line-height:1.5;">k</i><span style="line-height:1.5;">-tuple
conjecture by finding unexpected biases in the distribution of consecutive
primes. Here, we present another contribution to confirmation of the </span><i style="line-height:1.5;">k</i><span style="line-height:1.5;">-tuple conjecture based on statistical
physics. The pattern we find </span><span style="line-height:1.5;">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.</span>
</div>
%K Prime Numbers
%K Power Laws
%K Prime Gaps
%K k-Tuple Conjecture
%K Number Theory
%U http://www.oalib.com/paper/5272609