IntroductionThe computer labs in Temple University's College of Liberal Arts Educational Technology Center are participating in the Great Internet Mersenne Prime Search in the search for new Mersenne Prime numbers . The Great Internet Mersenne Prime Search (GIMPS) harnesses the power of tens of thousands of small computers around the world to solve the enormous task of finding huge prime numbers. The numbers currently being examined to determine if they are prime are over 2,000,000 digits long, and it takes an enormous amount of computational power to determine the primality of these numbers. Mersenne numbers are named after the French monk Marin Mersenne (1588-1648) who stated in the preface to his Cogitata Physica-Mathematica (1644) the definition of what would later be known as a Mersenne Prime Number. These numbers are of the form 2P-1, where P is a prime number.Mersenne Prime HistoryIn the seventeenth century Marin Mersenne
did all his computations by hand on paper. This was a very tedious and time consuming
process when it came to searching for primes because as the numbers being checked grew larger,
the time it took to do these calculations took longer and longer.
At the time of his death, there were only seven known numbers that conformed to the
definition that would later be named after Mersenne. A total of five Mersenne primes
would be found between the time of Mersenne's death and the 1950s when six more
Mersenne primes were found using computers, bringing the total to 18.
The use of computers to do the calculations needed to determine the primality of
a number greatly reduced the amount of time it took to do these calculations. The speed
that computers could do these calculations also increased the rate at which numbers
could be checked, and the size of the numbers increased substantially.
Sixteen more Mersenne primes were
found between 1951 and 1996, using early computers at first, and costly supercomputers
more recently. A typical supercomputer can cost upwards of
$10,000,000.00 and can be obsolete in just a couple of years. This makes getting
a supercomputer, or just time on a supercomputer quite difficult. With the advent
of the internet, a new way of
computing these numbers was developed called distributed processing. Numbers
are distributed either through e-mail or automatically from a
central server
through the internet to each computer participating in the
Great Internet Mersenne Prime Search (GIMPS).
Each client then works on the number that they were assigned, it determines if it is a
prime number or not, then sends the results back to the
central server, and requests another
number to process. Volunteers all over the world donate computer time to the effort
to find even more Mersenne Prime Numbers. Since it's inception in 1996, four numbers have
been found to be Mersenne Primes using the
GIMPS
internet based method of computation. The numbers found using
GIMPS
are the 35th, 36th, 37th, and 38th
known Mersenne Prime Numbers. The 37th, and 38th Mersenne Primes
were found using the PrimeNet central server
in conjunction with the GIMPS effort.
How GIMPS Works
Each computer participating in GIMPS
has a small freeware program running either as a service or in the system tray that
utilities unused CPU cycles to perform the calculations needed to determine
if a number is a Mersenne Prime. Almost all of the time that a computer is
turned on it is idle. The time when you are reading off the screen, and the time
in-between key strokes the computer is idle. This otherwise wasted idle
time is put to use for processing the complex algorithms to determine if a number
is a Mersenne Prime. To do this, a freeware program called
Prime95 runs in the background
of each computer, the only thing noticeable about the program is the tiny icon in
the lower right hand corner of the screen (called the system tray) next to the clock.
Other then this icon, the program runs completely unnoticed, it does not affect the
speed of the computer because it only does computations when the computer
is idle. The communication between the client computer and the central
PrimeNet Server
is only a few kilobytes per month, so it does not affect network bandwidth either.
The Prime95 software automatically
connects to the
PrimeNet Server
, downloads a set of numbers assigned to it by the server, determines the primality of the
number, returns the results to the
PrimeNet Server
, and does this all completely unattended.
Estimated PerformanceGIMPS measures the rate at which a computer is able to determine the primality of a number in Pentium 90 CPU hours per day. The Pentium 90 was chosen as the benchmark machine and all statistics calculated are based on this standard. Based on this, a Pentium 60 would calculate at 66% the rate of that of a Pentium 90, and conversely a Pentium II 300 would calculate at 400% of the rate of a Pentium 90. Below is a table listing each of our labs, and the estimated rate at which they compute primality individually and as a whole.
TempleU-DI Estimated Performance
These calculations are a best case scenario, they consider that all of the machines are turned on, working, and running Prime95 all of the time, and nothing else. This is not the case, our labs have heavy use for over 12 hours per day and even though it is our policy to keep the machines on at all times, they do get turned off by accident. A fair rate of error, taking in all of the circumstances, would be about 40 to 50 percent. Factors that lower the rate are: machines accidentally turned off, machines with very heavy use, and machines that somehow loose the number they are assigned. GIMPS CompetitionEach individual or organization participating in GIMPS has a unique account identification name assigned to them. Both their results of their computations and the total sum of all of their results are tracked. Each account can have as few and one, or up to hundreds of computers in it. When we initially started participating we were known as the college of Arts & Sciences in Temple University, hense the account ID of TempleU-CAS. We knew from the begining that we would be one of GIMPS' leading producers just by the sheer size of our labs. After we did the calculations and came up with the results listed in the table above it was clear that we would not only be one of the leading producers, but the highest producer of all time, and just in a matter of a few months.The link below is a page detailing the top producers who use the Entropia.com automated PrimeNet Server to be assigned work. Since it's inception in the spring of 1998, using this server has become the prefered way to participate in GIMPS. Previous to this server, all assignments and results were handled via e-mail, which can be very clumbersome when you have hundreds of computers. Look for the account ID labled TempleU-CAS to see our current ranking. This page lists all of the 5000+ GIMPS partipants in by the number of Pentium90 CPU years they have contributed to GIMPS. IPS Top Producers Awards, Updated Hourly Previous the the PrimeNet Server all work was distributed manually via e-mail. The cumulative all time top producer list is available from the link below. Look for my name, Marc Getty under the 'who' collum to check our current all time producer ranking. All Time Top Producer Awards, Updated Bi-Weekly. TempleU-CAS is in competition with other universities, corporations, research facilities and individuals not to see who can get the higest on the list, but rather to further the GIMPS cause. We are involved to promote distributed computing, and to find more Mersenne Prime Numbers. GIMPS CreditsThe two people who primarally deserve credit for GIMPS are George Woltman and Scott Kurowski. George Woltman is an Orlando computer programmer wrote the Prime95 software and established the Internet prime number search two years ago. Scott Kurowski is a San Jose software development manager who automated Woltman's search efforts and setup the PrimeNet Server at Entropia.com.GIMPS Links
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