Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9727537 | Physica A: Statistical Mechanics and its Applications | 2005 | 11 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Anjan Kumar Chandra, Subinay Dasgupta,