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Broward College professor builds supercomputer with video game cards to find new prime number
A homebuilt supercomputer assembled from garage sale parts and video game cards found the astronomically large prime number that put a Broward College professor on the mathematical map.
John Perretta, who teaches math and computer science, is the latest winner in the international hunt for ever-larger prime numbers. His number, which can't be printed here because it would require nearly 300,000 digits, was announced last week by Broward College and verified independently by academic databases devoted to large primes.
Prime numbers, which are those that can be divided only by 1 and by themselves, are actually found at a fast clip, with new ones rolling in at the rate of about one every two hours. But so-called titanic primes, huge numbers of at least 1,000 digits, are much rarer, with about 10 new ones announced a year.
Large prime numbers have uses in Internet encryption, but Perretta said his primary motivation was the desire for an intellectual adventure that he could share with his students.
"It was about discovering something new," he said in an interview in a classroom at Broward College's downtown Fort Lauderdale center. "It was a challenge and something that was difficult to do and required a great deal of work and effort. It's a personal passion. It's also because I want to give back to the students I teach and increase their interest."
The discovery and proof of new prime numbers dates at least to the fourth century BC, when the Greek mathematician Euclid was laying the foundation of mathematical science. In the centuries before computers, finding new primes required painstaking calculations.
"At first it was just a few people because the calculations were very difficult if you're doing it by hand," said Chris Caldwell, professor of mathematics at the University of Tennessee at Martin, who maintains a database on the world's largest prime numbers. "It's only with computers that it really took off."
The record prime number found in 1588, the year the Spanish Armada attempted to reach England, was just six digits long, discovered by the Italian mathematician Pietro Cataldi. Using increasingly complex calculations, mathematicians found bigger primes, but the discovery of really huge ones, in the thousands of digits, took place only after World War II with the introduction of the computer.
Today, thousands of mathematicians and amateurs hunt for primes, using university lab computers and desktops connected in networks to pool calculating power through web-based groups like Prime Grid, Seventeen or Bust and The Great Internet Mersenne Prime Search. Participants throw around terms like Kummer's proof, Goldbach's conjecture, the Riemann hypothesis and the Sieve of Eratosthenes as they try to make their own mark on the world of mathematics.
"Mostly it's just for the fun of it," Caldwell said. "It's a mountain to climb that you do in your study."
At the University of Central Missouri, where mathematicians found two primes of record-breaking size, more than 1,000 computers are working on discovering new ones, running the prime-finding programs in the background to avoid interfering with the computers' main work. It takes each machine about 40 days to test one potential prime, said Curtis Cooper, professor of mathematics and computer science, who was one of a team of two who found primes that broke the world records for size (since exceeded by bigger ones).
"The main reason I am searching for large prime numbers, on my own and as a volunteer in GIMPS [Great Internet Mersenne Prime Search], is mainly because of the intellectual challenge," Cooper said in an email. "I know of no practical use for these numbers. As byproducts of the search, there is new mathematics about prime numbers and their distribution and new algorithms to find primes which are discovered."
For Perretta, the challenge was less a problem of mathematics than one of computer science and engineering. Software exists to find prime numbers, but it requires computers of astonishing calculating power, and if Perretta wanted access to one, he would have to put it together himself.
As an adjunct professor, making a living by teaching at both Broward College and Keiser University, Perretta had to stick to a budget. He bought the basic hardware at garage sales. To obtain the brute calculating power required, he turned to video-game cards. Total cost: About $800.
"These video cards are probably the most sophisticated component of the computer," he said. "A lot of the video games today are these virtual reality games that require a lot of computing power."
After assembling the system and configuring it to handle the software, his biggest problem was preventing the computer from overheating as it conducted 5.4 trillion calculations per second. The heat blew out two central processing units, a mother board, RAM and a couple of video cards, but he replaced components as they went out and brought the computer back on line to continue the search.
Perretta set the computer to sound an alarm if it confirmed a new prime. The buzzer went off at 3 a.m. Getting out of bed, Perretta at first thought the sound was a warning for another overheating incident, but when he turned on the screen, he saw these words: Potential Prime Found.
"I was very, very excited," he said. "At first I thought it was an error. Then I was anxious for the next couple of days, until I got the verification response. I got the word, and I was like, wow!"
He isn't done. His next goal is lofty: To find the world's largest known prime number. The current record holder has nearly 13 million digits.