arXiv subjects

Damian Gulich

Publications and source records attributed to Damian Gulich.

2 recordsLinked to original sources

arXiv2008

An algorithmic implementation of the Pi function based on a new sieve

In this paper we propose an algorithm that correctly discards a set of numbers (from a previously defined sieve) with an interval of integers. Leopoldo's Theorem states that the remaining integer numbers will generate and count the complete list of primes of absolute value greater than 3 in the interval of interest. This algorithm avoids the problem of generating large lists of numbers, and can be used to compute (even in parallel) the prime counting function $π(h)$.

math.GM↗

arXiv2007

An elementary sieve

In this paper we review the properties of families of numbers of the form $6n\pm1$, with $n$ integer (in which there are all prime numbers greater than 3 and other compound numbers with particular properties) to later use them in a new sieve that allows the separation of numbers $n$ that generate primes from those that only generate compounds. In principle, this can be used to find the amount of prime numbers up to a given number $h$; this means, $π(h)$.

math.GM↗