Steve Conway, 612/683-7133 LARGEST KNOWN PRIME NUMBER DISCOVERED ON CRAY RESEARCH SUPERCOMPUTER EAGAN, Minn., Jan. 10, 1994 -- Computer scientists at Cray Research, Inc. have discovered the largest-known prime number while conducting tests on a CRAY C90 series supercomputer. The new prime number has 258,716 digits. Printed in newspaper-sized type, the number would fill approximately 8 newspaper pages. In mathematical notation, the new prime number is expressed as 2^859433-1, which denotes two, multiplied by itself 859,433 times, minus one. Numbers expressed in this form are called "Mersenne" prime numbers after Father Marin Mersenne, a 17th century French monk who spent years searching for prime numbers of this type. The largest Mersenne prime known previously was discovered in February 1992 at AEA Technology's Harwell Laboratory in England by computer scientists who were also conducting a test of a Cray Research supercomputer. It had 227,832 digits. Six of the last seven Mersenne primes were discovered on Cray Research supercomputers. Prime numbers can be divided evenly only by themselves and one. Examples include 2, 3, 5, 7, 11 and so on. The Greek mathematician Euclid proved that there are an infinite number of prime numbers. But these numbers do not occur in a regular sequence and there is no formula for generating them. Therefore, the discovery of new primes requires randomly generating and testing millions of numbers. "Finding these special numbers is a true 'needle-in-a-haystack' exercise, but we improve our odds by using a tremendously fast computer and a clever program," said David Slowinski, a Cray Research computer scientist. Slowinski and fellow Cray Research computer scientist Paul Gage developed the program that found the new prime number. Mathematician Richard Crandall, Ph.D., independently verified that the number Slowinski and Gage found is prime and will note the discovery in a textbook to be published shortly. Prime numbers have applications in cryptography and computer systems security. Huge prime numbers like those discovered most recently are principally mathematical curiosities, but the process of searching for prime numbers does have several practical benefits. For instance, the "prime finder" program developed by Slowinski and Gage is used by Cray Research as a quality assurance test on all new supercomputer systems. A core element of this program is a routine that involves squaring a number repeatedly. As this process continues, it eventually involves multiplying immense numbers -- numbers of hundreds of thousands of digits -- by themselves. "This acts as a real 'torture test' for a computer," said Slowinski. "The prime finder program rigorously tests all elements of a system -- from the logic of the processors, to the memory, the compiler and the operating and multitasking systems. For high performance systems with multiple processors, this is an excellent test of the system's ability to keep track of where all the data is." Slowinski said the recent CRAY C90 test in which the new prime number was discovered would run for over 7 hours on one central processing unit of the system. "If a machine can complete this exhaustive run-through, we can be confident everything is working as it should," said Slowinski. In addition, Slowinski said, techniques used to speed up the performance of the prime finder can also be used to enhance the performance of programs customers use on real-world problems such as forecasting the weather and searching for oil. "Through our work on the prime finder program, we learn new techniques for speeding up certain kinds of mathematical operations. These operations are often key elements of the most computation-intensive portions of software programs our customers run on their systems," said Slowinski. Slowinski compared running the prime finder on supercomputers and continually "tuning" the program to building and racing exotic cars. "There aren't many practical uses for dragsters or Formula 1 race cars. But some things engineers do to make those cars perform better eventually find their way into cars you and I drive," said Slowinski. Slowinski noted that with the discovery of the new prime number, a new "perfect" number can also be generated. A perfect number is equal to the sum of its factors. For example, 6 is perfect because its factors -- 1, 2 and 3 -- when added together, equal 6. Mathematicians don't know how many perfect numbers exist. They do know, however, that all perfect numbers have a direct relationship to Mersenne primes. The new perfect number generated with the new Mersenne prime is the 33rd known perfect number and has 517,430 digits. The 32nd perfect number had 455,663 digits. Cray Research creates the most powerful, highest quality computational tools for solving the world's most challenging scientific and industrial problems. ### 