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Computing a prime champion.

Computing a prime champion

More than 2,000 years ago, the Greek geometer Euclid proved there is no largest prime number. But proving that a particular whole number is a prime -- that is, divisible evenly only by itself and the number one -- is a time-consuming task that limits the size of numbers that can be tested for primality. Last month, a team of six computer scientists at the Amdahl Corp.'s Key Computer Laboratories in Fremont, Calif., succeeded in showing that the number 391,581 x [2.sup.216,193] - 1 is a prime, setting a record for the largest known prime. The number has 65,087 digits -- 37 digits more than the previous record holder.

The researchers sifted through 350,000 huge candidate numbers before settling on 7,000 behemoths for final testing. Using an advanced version of the Lucas-Lehmer primarily test, they spent more than a year checking out the numbers whenever company computers were otherwise idele. By the time they had refined their testing algorithm, the group could test a candidate number in 33 minutes, using a program that took up only a small fraction of the computer's memory.

"The main benefit is the fine-tuning we did on the algorithm, primarily speeding up the multiplication of high-precision numbers," says team member Sergio Zarantonello. Weather forecasters and other researchers may find the improved multiplication techniques useful for speeding up their own computer models.
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Title Annotation:prime numbers
Publication:Science News
Date:Sep 16, 1989
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