Hidden structure in the randomness of the prime number sequence?
arXiv:cond-mat/0310148 · doi:10.1016/j.physa.2005.06.066
Abstract
We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes, that would eventually appear in applications. Finally, our theory allows us to link with three different but important topics: the Hardy-Littlewood conjecture, the statistical mechanics of spin systems, and the celebrated Sierpinski fractal.
13 pages, 5 figures. New section establishing connection with the Hardy-Littlewood theory. Published in the journal where the solved problem was first described
References in corpus (1)
Cited by in corpus (12)
- Prime numbers and spontaneous neuron activity
- On a dynamical approach to some prime number sequences
- Predicting maximal gaps in sets of primes
- Pseudo Random test of prime numbers
- Fractal in the statistics of Goldbach partition
- Modeling the creative process of the mind by prime numbers and a simple proof of the Riemann Hypothesis
- Jacob's Ladder: Prime numbers in 2d
- Prime numbers and random walks in a square grid
- Jumping champions and prime gaps using information-theoretic tools
- Distance between natural numbers based on their prime signature
- Correlations between large prime numbers
- Prime numbers: periodicity, chaos, noise