====== ABC Lattices @Home ====== {{http://boinc2.cs.hs-rm.de/abclll/img/logo.png|ABC Lattices @Home}} ===== Project Description ===== ABC Lattices @HOME is a research project that uses Internet-connected computers for searching for good abc-triples. Unlike ABC@Home, this project is not aiming for a thorough search of a certain range of numbers. Instead, we are trying to find good triples with the help of a specialized algorithm and educated guesses in areas beyond 2^100. You can participate by downloading and running a free program on your computer. === The long version === == What the heck am I calculating? == The application //ABC Eval// runs an algorithm which aims to find good abc-triples. == What are abc-triples? == abc-triples are three integers (a, b and c) which satisfies the following conditions: a + b = c (now //that// looks easy, right?) The greatest common divisor of a and b is 1 (that's the tricky part) But it's getting trickier: Ask me what good abc-triples are! == Okay, what are good abc-triples? == First, you need to know, that the //radical//, rad(x), of a number is the product of distinct prime numbers of x. Then, the //quality// of an abc-triple is defined as q(abc) = log( c ) / rad( a*b*c ) A //good// abc-triple has a quality greater than 1.4 == All right, and what is all this good for? == It's part of my masters thesis to evaluate an algorithm for finding good abc-triples. Good abc-triples are very rare, yet it's unknown if there are infinitely many of them. Studying the nature of abc-triples and their distribution helps solving this so-called [[http://en.wikipedia.org/wiki/Abc_conjecture|abc-conjecture]]. == I want to learn more about that topic! == Great! The [[http://www.math.leidenuniv.nl/~desmit/abc/|Websites of the mathematical faculity of the University of Leiden]] are a great point to start. == Wait a minute! There is this long-time running project ABC@home, whats the difference to yours? == The goal of [[en:projects_abc_at_home|ABC@home]] is a thorough and complete list of every abc-triple within certain bounds. At the moment, their list goes roughly up to triples with c less than 2^63. Other searches already found many good triples within c < 10^30. ABC lattices @ Home strives to find as many good abc-triples as efficient as possible, outside of anybody elses numerical ranges (as we know them). We are not affiliated with [[en:projects_abc_at_home|ABC@home]] in any way, but we share the same passion for the topic. ==== Author(s) ==== ABC Lattices @HOME is based at [[http://www.cs.hs-rm.de/|Hochschule RheinMain - University of Applied Sciences]] It is as part of my (Jan Gampe) masters thesis 'Parallel algorithms and the abc-conjecture' ==== Credentials ==== * Website: **http://boinc2.cs.hs-rm.de/abclll/** * Join to team: **[[http://boinc2.cs.hs-rm.de/abclll/team_display.php?teamid=32|Ukraine]]** ==== Significant dates ==== * First seen on: **29 Apr 2013** * Date of completion: Project's Under Construction ===== Features ===== ==== Hardware requirements ==== The applications provided are designed for Pentium 3 machines or better, and have been tested under the following OS'ses: * GNU/Linux 2.6 or newer (32/64 bit) * Windows XP, Vista, 7 (8 is untested yet) * OS X (any 64bit Apple machine should handle it) ==== OSes & Applications ==== ^ ^ {{:uk:win.png|}} ^ {{:uk:linux.png|}} ^ {{:uk:macos.gif|}}{{:uk:amd64.jpg|}} | ^ABC Eval Tool | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} | {{:ru:yes.gif|}} |