A 12 million digit prime number, the largest such number ever discovered, has landed a voluntary math research group a $100,000 prize from the Electronic Frontier Foundation (EFF).
The number known as a Mersenne prime, is the 45th known Mersenne prime, written shorthand as 2 to the power of 43,112,609, minus 1 . A Mersenne number is a positive integer that is one less than a power of two, the group stated.
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The computing project called the Great Internet Mersenne Prime Search (GIMPS) made the discovery on a computer at the University of California, Los Angeles (UCLA) Mathematics Department. Computing manager Edson Smith installed and maintained the GIMPS software at UCLA, and thousands of other volunteers also participated in the computation.
According to the GIMP Web site the massive prime was first verified on June 12th by Tony Reix of Bull SAS in Grenoble, France using the Glucas program running on Bull NovaScale HPC servers, one featuring Itanium2 CPUs and another featuring Nehalem CPUs. The prime was later independently verified by Rob Giltrap of Sun Microsystems using Ernst Mayer's Mlucas program running on a Sun SPARC Enterprise M9000 Server.
The $100,000 prize will be awarded during EFF's Pioneer Awards ceremony on October 22nd in San Francisco.
EFF's first Cooperative Computing Award, given for a prime number of at least a million digits, was awarded nearly 10 years ago. Two Cooperative Computing Awards are still up for grabs: EFF will award $150,000 to the first individual or group who discovers a prime with at least 100 million digits, and $250,000 for a prime with at least a billion digits, EFF stated.
The huge prime number discovery comes close on the heels of another massive number finding. A group of researchers in September said they, through a technique for multiplying large numbers, have figured out congruent numbers up to a trillion. Apparently no one had taken them beyond a billion for some reason.
In case you were wondering, the first few congruent numbers are 5, 6, 7, 13, 14, 15, 20, and 21. Many congruent numbers were known prior to the new research. For example, every number in the sequence 5, 13, 21, 29, 37, ..., is a congruent number. But other similar looking sequences, like 3, 11, 19, 27, 35, ...., are more mysterious and each number has to be checked individually. The calculation found 3,148,379,694 of these more mysterious congruent numbers up to a trillion, the researchers said in a statement.
The problem, which was first posed more than a thousand years ago, concerns the areas of right-angled triangles. The difficult part is to determine which whole numbers can be the area of a right-angled triangle whose sides are whole numbers or fractions. The area of such a triangle is called a "congruent number." For example, the 3-4-5 right triangle which students see in geometry has area 1/2 × 3 × 4 = 6, so 6 is a congruent number. The smallest congruent number is 5, which is the area of the right triangle with sides 3/2, 20/3, and 41/6, researchers stated.
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