ABC@Home Project

From Unofficial BOINC Wiki

ABC@home - http://abcathome.com/ - ABC@home is a mathematical project searching for abc-triples. An abc-triple consists of 3 numbers satisfying certain conditions. These triples might be helpful in proving the ABC-conjecture, one of the holy grails of mathematics, because of its interesting consequences.

[edit] General

The goal of this project is to find sets of three numbers a, b, and c, also called an ABC triple, that satisfies the following conditions:

• a + b = c
• a < b < c
• a, b, and c have no common divisors
• c > rad(a * b * c) (where rad() is the radical of an integer)

The ABC conjecture is an open problem in mathematics that theorizes the existence of only a finite number of ABC triples where log(c) / log(rad(a * b * c)) > h where h is a real number greater than one.

A lot of open questions can be answered if this conjecture is proved to be true. Right now there is a very complicated proof of Fermat's Last Theorem, but it follows easily from the ABC-conjecture. Also the existence of infinitely many non-Wieferich primes follows from the conjecture.

The project is run by the Leiden University.

[edit] Project information

• Science:
  • Results are publicly available/not-for-profit
• Credits:
  • Credit is heavily artificially inflated
  • Credit is granted statically
  • Credit is granted instantly
• Project size:
  • The project has over 3,500 active participants

[edit] Also see

• ABC presentation (PDF)
• Homepage