rad(abc), where rad(n) is the product of the distinct prime factors of n. The ABC conjecture says that there are only finitely many a,b,c such that log(c)/log(rad(abc)) > h for any real h > 1. The ABC conjecture is currently one of the greatest open problems in mathematics. If it is proven to be true, a lot of other open problems can be answered directly from it.",
""
),
array(
"PrimeGrid",
"http://www.primegrid.com",
"Private",
"Cryptography",
"Primegrid is generating a public sequential prime number database, and is searching for large twin primes of the form k*2n+1 and k*2n-1",
"primegrid_logo.png"
),
array(
"SZTAKI Desktop Grid",
"http://szdg.lpds.sztaki.hu/szdg/",
"MTA-SZTAKI Laboratory of Parallel and Distributed Systems (Budapest)",
"Mathematics",
"Find all the generalized binary number systems (in which bases are matrices and digits are vectors) up to dimension 11.",
"szdg1_small.jpg"
),
array(
"Riesel Sieve",
"http://boinc.rieselsieve.com/",
"Riesel Sieve community",
"Mathematics",
"Find prime numbers of the form k*2n-1",
""
),
array(
"Rectilinear Crossing Number",
"http://dist.ist.tugraz.at/cape5/",
"Graz University of Technology (Austria)",
"Mathematics",
"What is the least number of crossings a straight-edge drawing of the complete graph on top of a set of n points in the plane obtains? From very recent (not even published yet) mathematical considerations the rectilinear crossing numbers for n=19 and n=21 are also known. So the most tantalizing problem now is to determine the true value for n=18, which is the main focus of this project.",
""
),
array(
"Chess960@home",
"http://www.chess960athome.org/alpha/",
"Chess-960.org",
"Game-playing",
"This project studies Chess 960, a variant of orthodox chess. In classical chess the starting position of the game never changes. In Chess 960, just before the start of every game, the initial configuration of the chess pieces is determined randomly.",
"chess960athome.jpg"
),
array(
"NQueens@home",
"http://nqueens.ing.udec.cl/",
"Universidad de Concepción, Chile",
"Game-playing",
"The eight queens problem consists of trying to place eight queens on a chessboard so that no queen attacks any other queen. I has long been known that there are 92 solutions, of which 12 are distinct. NQueens@home studies the generalization to N queens on an NxN board, for N=19 and greater.",
"NQueens-Logo1b.png"
),
),
);
$areas = array($biomed, $astro_phys_chem, $math, $earth);
?>