Collatz Conjecture

The Collatz conjecture -- also known as the 3x + 1, HOTPO (half or triple plus one), or Syracuse problem -- is a famous unsolved problem in number theory. First proposed by Lothar Collatz in 1937, it is easy to explain: Take any natural number. If it is even, divide it by 2; if it is odd, multiply it by 3 and add 1 (3x +1). Repeat the process indefinitely. The conjecture says that no matter what number you start with, the sequence of numbers generated will always eventually reach 1.

With the help of computers, mathematicians have checked the conjecture with ever-bigger starting numbers. This experimental evidence suggests the conjecture is true, but sometimes a conjecture's only counterexamples are found when using very large numbers. However, as the numbers get bigger, more and more CPU time is needed to make any progress. The Collatz Conjecture research project uses the power of grid-connected computers to process larger and larger calculations, searching for counterexamples that would disprove the conjecture. This project continues the work of the 3x+1@home BOINC project, which ended in 2008. It can run on an nVidia GPU, ATI GPU, or CPU.

Start date: July 11, 2009

Project website