Welcome to CollatzNet!
The goal of this project is to reach and beat the current record for verification of the Collatz Conjecture by using the joint computing power of our users' personal computers. This project of grid computing (distributed computing network) was created by a group of students of the Collegio Superiore of the Alma Mater Studiorum of Bologna. The growing power of low price computers, combined with the ubiquity of Internet for domestic use, makes background computing the most natural choice as a solution to large computational problems: the idea is to divide the problem into "work units" easily transferable via the Internet and distributable on a large number of personal computers. In this way, they may process these "work units" through a simple client drawing on the idle resources of the computer, i.e. the unused computer time being daily wasted by computers left on inoperative, or being used for low-intensity tasks. Despite the large savings in terms of economic and environmental sustainability (no need of cooling large computer centers, no pollution by farms' backup generators), this solution is not widely practiced by business and government agencies. The development of this project is also aimed to show how close at hand is such technology, encouraging its diffusion. We are available for explanations on the technology used, and we share the source codes of our "Client CollatzNet" on demand.

The Collatz conjecture, also known as the "3x+1 conjecture" is a number theory conjecture still unproven. Often called "the simplest unsolved problem of mathematics" (simple in terms of formulation, undecidable in terms of formal proof) it lends itself very well to a "brute force" computerized test: it is possible to effect a large scale verification aiming to find a counterexample falsifying the conjecture, since it is not actually possible to realize a formal demonstration of it.

Avoiding the formalisms, the idea behind the conjecture is:

Pick any natural number n greater than 1. If it is odd, multiply it by 3 and add 1, if it is even divide it by 2. Reapply this procedure to the number obtained by this process, and so on.

The Collatz conjecture states that, continuing to apply this algorithm, sooner or later you will arrive at 1; the set of numbers obtained is called the "Chain of Collatz starting with n".

For example:
n = 3. 3 is odd--> 3 x 3 + 1 = 10. 10 is even--> 10/2 = 5  -->  5 x 3 + 1 = 16/2 = 8  ---> 8/2 = 4  ---> 4/2 = 2  ---> 2/2 = 1
Obviously this is a very simple chain, but as soon as you reach 27, you find a quite long chain:
27-->82-->41-->124-->62-->31-->94-->47-->142-->71-->214-->107-->322-->161-->484-->242-->121-->364-->182 [...] -> 16 --> 8 --> 4 --> 2 --> 1

There are many algorithms to test whether a number respects the Collatz Conjecture, specifically developed and optimized to run faster and faster on computers. We have personally developed an algorithm for the verification of the conjecture which is faster than many others in the literature. Based on results from the first benchmark we believe we can manage to beat the current record of numbers checked ( by the "Instituto de Engenharia Electronica e Telematica de Aveiro ", which has verified all numbers up to 5 x 2⁶⁰) thanks to the computing power of a large number of computers, all in a matter of days. Here's the role of the users: you just have to download a program that weights less than 10 megabytes and install it: it will process in the background, without overloading your machine (it runs automatically at lowest priority). Anyone can participate in the project: despite the lack of economic resources, we'll personally award the user who computes the most work units with a plate, and the five best computing users with the project's t-shirt.

We are available for questions, clarifications, help offers and requests for the source code: enjoy your computing!