Mathematics – Number Theory
Scientific paper
2006-07-24
Physica A 357 (2005) 436
Mathematics
Number Theory
6 pages, 10 figures
Scientific paper
10.1016/j.physa.2005.02.089
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 {\em one} decomposition with a probability $|p - q|^{\alpha}$. Through computation of average shortest distance and clustering coefficient, we conclude that for $\alpha > -1.8$ the network is of small world type and for $\alpha < -1.8$ it is of regular type. We also present a theoretical justification for such behaviour.
Chandra Anjan Kumar
Dasgupta Subinay
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