Primality, Fractality, and Image Analysis

On the analysis tools of traffic fractality

The deep changes recently undergone by network traffic have strongly impacted its statistical characterization. The traditional assumptions on traffic characteristics have been proven to be obsolete and a new formalism has been brought about to properly take into account traffic new properties. Accordingly, newly designed analysis tools have been proposed. Our work is focused on the presentatio...

Randomness and Apparent Fractality

We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically relevant cutoffs. This range, spanning between one and two decades for densities of 0.1 and lower, is in good agreement with the typical range observed in experime...

Measuring Fractality

WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. Fi...

Distributed Primality Proving and the Primality of (23539+1)/3

We explain how the Elliptic Curve Primality Proving algorithm can be implemented in a distributed way. Applications are given to the certiication of large primes (more than 500 digits). As a result, we describe the successful attempt at proving the primality of the 1065-digit (2 3539 +1)=3, the rst ordinary Titanic prime.

Primality testing