====== Collatz Conjecture ====== ===== Project Description ===== Collatz Conjecture is a research project that uses Internet-connected computers to do research in mathematics, specifically testing the Collatz Conjecture also known as 3x+1 or HOTPO (half or triple plus one). Collatz Conjecture is based in Wood Dale, Illinois, USA and continues the work of the previous 3x+1@home BOINC project which ended in 2008. It can run on an nVidia GPU, ATI GPU, or CPU. ==== Credentials ==== * Website: **http://boinc.thesonntags.com/collatz/** * Join to team: **[[http://boinc.thesonntags.com/collatz/team_display.php?teamid=578|Ukraine]]** ==== Subprojects ==== * collatz * mini_collatz * solo_collatz ==== Author(s) ==== * **Slicker** - project administrator/developer * **Bender Bending Rodriguez/Crunch3r** - optimization guru and supplier of various platform builds * **Gipsel/Cluster Physik** - ATI application guru without whom there would be no ATI app (or it would run at CPU speeds) ==== Introduction ==== The **Collatz conjecture** is a [[conjecture]] in [[mathematics]] named after [[Lothar Collatz]], who first proposed it in 1937. The conjecture is also known as the **3//n// + 1 conjecture**, the **Ulam conjecture** (after [[Stanisław Ulam]]), **Kakutani's problem** (after [[Shizuo Kakutani]]), the **Thwaites conjecture** (after Sir Bryan Thwaites), **Hasse's algorithm** (after [[Helmut Hasse]]), or the **Syracuse problem**; the sequence of numbers involved is referred to as the **hailstone sequence** or **hailstone numbers**, or as **wondrous numbers**. Take any [[natural number]] //n//. If //n// is even, divide it by 2 to get //n// / 2. If //n// is odd, multiply it by 3 and add 1 to obtain 3//n// + 1. Repeat the process (which has been called "Half Or Triple Plus One", or **HOTPO**) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called **oneness**. ==== Significant dates ==== * First seen on: **11 Jun 2009** * Date of completion: Project is Active ===== Features ===== ==== Hardware requirements ==== * Computer running Windows, Linux, or OS X * Catalyst 8.12 or later drivers for ATI GPU processing and a CAL 1.3 capable GPU * nVidia 190.38 or later drivers for nVida/CUDA GPU processing and a CUDA capable GPU * For ATI GPU processing, BOINC 6.10.10 or higher is recommended. * For MAC OS X CUDA processing, BOINC 6.10.29 is recommended with CUDA toolkit and drivers 2.2 or later. * For MAC OS X OpenCL processing, BOINC 7.0.25 or higher is recommended. ==== OSes & Applications ==== **collatz** | | cuda23 | cuda50 | ati | ati13amd | ati13ati | opencl_amd | cuda | opencl_osx | |Windows | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | |Windows 64-bit | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | |Linux 64-bit | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | |Mac OS X | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | |Mac OS X 64-bit | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | **mini_collatz** | | cuda23 | cuda50 | ati13amd | ati13ati | opencl_ati_100 | CPU | opencl_osx | |Windows | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | |Windows 64-bit | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | |Linux | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | |Linux 64-bit | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | |Mac OS X | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | |Mac OS X 64-bit | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:no.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | **solo_collatz** | | cuda50 | opencl_ati_100 | opencl_intel_gpu | |Windows | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:no.gif|}} | |Windows 64-bit | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} |