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This paper will illustrate two versions of an algorithm for finding prime number up to N, which give the first version complexity
where c1, c2 are constants, and N is the input dimension, and gives a better result for the second version. The method is based on an equation that expresses the behavior of not prime numbers. With this equation it is possible to construct a fast iteration to verify if the not prime number is generated by a prime and with which parameters. The second method differs because it does not pass other times over a number that has been previously evaluated as not prime. This is possible for a recurrence of not prime number that is (mod 3) = 0. The complexity in this case is better than the first. The comparison is made most with Mathematics than by computer calculation as the number N should be very big to appreciate the difference between the two versions. Anyway the second version results better. The algorithms have been
In this paper we will give an algorithm that in the worst case solve the question about the primality of a number in but that gives better result if the number is not prime (constant operation). Firstly, we will introduce an equation on which are based not prime numbers. With this equation it is possible to deduce the prime number that generates a not prime number and to establish an equation in which if exists a certain integer the number is not prime and therefore vice versa to deduce if it is prime.
This works aims to give an answer to the problem P = NP? The result is
positive with the criteria that solve the Traveling Salesman Problem in polynomial cost of the input size and a proof is given. This problem gets a solution because a polyhedron, with a cut
flower looking, is introduced instead of graph (e.g. tree).
Twenty years after
the last archaeological researches and surveys, a new investigation has been
carried out on the basement in the church of Santa Maria in Via Lata in Rome.
The study has employed three-dimensional surveys with laser scanning
methodology and has focused both on archaeological and architectural issues.
Indeed, the present layout of the basement derives from a XVII century
remodelling of early Christian and medieval spaces planned by Pietro da
Cortona. The architect gave a unique setting and composition to the underground
spaces, different in shapes and building materials, thanks to the refinement of
his baroque language. Though he worked in small spaces with static problems
connected to the foundations and to the loads of the church rising above, and
with poor lighting and extreme dampness, Pietro da Cortona put skilfully together
“modern” elements with ancient or historical pre-existences. The study focuses
on Berrettini’s design process through a three-dimensional analysis with CAD
systems, starting from the new XVII century fa?ade and from the articulated
distribution of routes that led to the intimate underground interiors. Metrical
processing gave the possibility to improve the knowledge about room geometry
and to confirm the interpretations put forward by major scholars such as Krautheimer