Abstract
The highly irregular and rough fluctuations of the number of primes less or equal to a positive integer x for smaller values of x (x≤20,000) renders the approximations through the Prime Number Theorem quite unreliable. A fractal probability distribution more specifically, a multi-fractal fit to the density of primes less or equal to x for small values of x , is tried in this study. Results reveal that the multi-fractal fit to the density of primes in this situation outperforms the Prime Number Theorem approximation by almost 200% viz. the prediction error incurred by using the PNT approximation is double that of the multi-fractal fit to the density of primes. The study strongly suggests that a better multi-fractal distribution exists, even for large x, than the Prime Number approximation to the density of primes.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
