A small world network of prime numbers

Anjan Kumar Chandra and Subinay Dasgupta

Physica A: Statistical Mechanics and its Applications, 2005, vol. 357, issue 3, 436-446

Abstract: According to Goldbach conjecture, any even number can be broken up as the sum of two prime numbers: n=p+q. We construct a network where each node is a prime number and corresponding to every even number n, we put a link between the component primes p and q. In most cases, an even number can be broken up in many ways, and then we chose one decomposition with a probability |p-q|α. Through computation of average shortest distance and clustering coefficient, we conclude that for α>-1.8 the network is of small world type and for α<-1.8 it is of regular type. We also present a theoretical justification for such behaviour.

Date: 2005
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:357:y:2005:i:3:p:436-446

DOI: 10.1016/j.physa.2005.02.089

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