[rc5] Mersenne primes, what good are they?

Ryan Dumperth woodie at indy.net
Wed Oct 1 02:43:38 EDT 1997


This text is stolen from
<http://reality.sgi.com/csp/ioccc/noll/prime/prime_press.html>


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 Silicon Graphics's Cray Research unit 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 T90 series
supercomputer test in which this prime number was discovered would run for
over 6 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.

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