In their proof, Green and Tao considered how the primes
relate to a larger set of numbers that the pair calls almost-primes
--numbers that are a product of at most 10 primes
Lucas, Chairman of Command stated, "The acquisition of Prime
Source is a significant part of the company's overall strategy to expand its financial services business to include health care and medical services.
However, mathematicians have had some success in considering the more general case of primes
that are closer together than predicted by the average-spacing formula.
Therefore, the discovery of new primes
requires randomly generating and testing millions of numbers.
Previous Mersenne primes
discovered by GIMPS participants have been recognized as the world's largest in The Guinness Book of World Records.
The absence of any readily discernible pattern in their distribution makes identifying primes
a tricky proposition.
themselves are of interest to computational number theorists, who pursue such basic questions as the distribution of primes
among all whole numbers.
A fascination with gargantuan numbers, especially those that are primes
, has played a central role in the rise of collective computing.
Whether there are infinitely many twin primes
remains one of the major unsolved questions in number theory.
As participants in the Great Internet Mersenne Prime
Search (GIMPS), more than 4,000 people worldwide are chasing after the record for the largest known prime
The sequence of primes
goes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,37, 41, and so on.
Because a program for testing primes
constantly uses key parts of a microprocessor and stores and retrieves huge amounts of data, the chips can generate a greater than normal amount of heat, which sometimes causes failures.