Computational Model of Prime Numbers by the Modified Chi-square Function
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 20, Issue 5
Abstract
An innovative approach that treats prime numbers as raw experimental data and as elements of larger and larger finite sequences {Pm}≡{P(mp)} is shown in the present report. The modified chi-square function Xk2(A,mp/xo) with its three parameters A, k and xo=xo(k) is the best-fit function of the finite sequences {ρm}≡{lgPm/lgmp} from the analytical viewpoint thus showing that the property of scale invariance does not hold for the finite sequences of this prime variable and so for primes themselves. In addition an injective map can be set between these {ρm} sequences and the {mα} progressions with domain N and co-domain R+ being α∈(–1,0)⊂R– through the parameter k=2+2α of their common fit function Xk2(A,mp/xo). All that leads to induction algorithms and to relationships of the kind Pm≈P(mp), though within the precisions of the calculations and holding locally.
Authors and Affiliations
Daniele Lattanzi
Keywords
Related Articles
- EP ID EP322586
- DOI 10.9734/BJMCS/2017/31589
- Views 77
- Downloads 0
Convergence Results of Two Step Iteration Procedure with Errors for a Pair of Asymptotically Non-Expansive Mappings in the Intermediate Sense
In this paper, we study strong and weak convergence results of a two step iterative process with errors for a pair of asymptotically non-expansive mapping in the intermediate sense.Our results generalize the correspondin...
Convergence Analysis of a Non-overlapping DDM for Optimal Absorbing Boundary Control Problems Governed by Wave Equations
A non-overlapping domain decomposition method (DDM) is described to solve optimal boundary control problems governed by wave equations with absorbing boundary condition. The whole domain is divided into non-overlapping s...
Analytic Approximation Solutions of Lyapunov Orbits around the Collinear Equilibrium Points for Binary -Centuari System: The Planar Case
A third order analytic approximation solution of Lyapunov orbits around the collinear equilibrium in the planar restricted three-body problem by utilizing the Lindstedt Poincaré method is presented. The primaries are obl...
Modeling Pulmonary Tuberculosis for Optimal Control Including Prevention
It is formulated and analyzed an optimal control problem for the transmission dynamics of the SEIS-like pulmonary tuberculosis (TB) including prevention by means of non-linear differential equations, which are linked to...
Experimental Study on Class Imbalance Problem Using an Oil Spill Training Data Set
There is a paucity of research on one of the key issues in oil spill detection: the imbalanced training set learning problem. This paper performs experiments to show the influence of the imbalanced learning problem (ILP)...