Ibercivis

Citizen Science

Primalidad

What are prime numbers?

A prime number is a natural number that is only divisible by 1 and itself.

Around the year 300 B. C., Euclides demonstrated that an infinitude of prime numbers exists. The prime numbers are the opposite of composite numbers which are those numbers with some natural divisor rather than itself or the unit. By definition, the number 1 is not a prime nor a composite number.

The distribution of the prime numbers is a recurrent subject of investigation in the Theory of Numbers: if considered individually the prime number seem to be randomly distributed, however its "global" distribution follows well-defined laws.

In the figure: The Sieve of Eratosthenes was created by Eratosthenes of Cyrene, a greek mathematician from the 3rd century B. C. It is a simple algorithm to find all prime numbers up to a specified integer.

Primalidad Project

There is a great number of open conjectures about the prime numbers like for instance the Riemann Hypothesis and the Goldbach's Conjecture.

En la imagen: Riemann zeta function ζ(s) in the complex plane. The color of a point s encodes the value of ζ(s): dark colors denote values close to zero and hue encodes the value's argument. The white spot at s = 1 is the pole of the zeta function; the black spots on the negative real axis and on the critical line Re(s) = 1/2 are its zeros.

We propose to take advantage of Ibercivis calculus capability to know a little more on these numbers, about their distribution, and to try to find counterexamples to the conjectures.

In this project the software code is publicly available to allow any volunteer to read the code and possibly to incorporate improvements on it. It is also available a forum to the exchange of ideas on the project.

Wilson primes

Given a prime number "p", if (p - 1)! ≡ - 1 (mod p^2), p is name a Wilson prime, in honour of the mathematician John Wilson. Thus far, the only Wilson primes found are 5, 13 and 563. However, it is conjectured that the number of Wilson primes is infinite.

Mr. Wilson Application

Using Mr. Wilson application, we will try to find the next Wilson prime. It is shown that if it exists, it should be greater than 5x10^8.

Note that the main problem to test whether a prime number is or not a Wilson prime is the calculation of the factorial of p-1. Just to have an idea, we can tell that the factorial of 5x10^7 occupies about 350 MB in a ASCII file.

To facilitate the task, we grouped the prime number between 5x10^8 and 4x10^9 in blocks of 300. This way, each work unit analises each of these blocks, testing if the referred primes are or not Wilson primes.

The code is publicly available in github
git@github.com:Ibercivis/Wilson.git.

More information:
http://en.wikipedia.org/wiki/Wilson_prime

Participate in this new application through our forum:
http://forum.ibercivis.net/index.php