Quick, what's the biggest prime number you know?
OK, here's some help: A prime number is a number divisible only by 1 and itself. Most folks can recite a handful of prime numbers, usually the first few: 2, 3, 5, 7, 11 and so on.
According to the Greek mathematician Euclid, who invented geometry a few thousand years ago, there's actually no end to prime numbers. They just go on forever.
This week, two groups of mathematicians, including a San Diegan, announced they had discovered the two largest prime numbers yet. Neither goes on forever, but both numbers are too big to be printed in full here: One is 12,978,189 digits long; the other is 11,185,272 digits.
The discovery of the numbers – 24311269-1 and 237156667-1 in mathematical shorthand – concludes a decade-long research competition sponsored by the Electronic Frontier Foundation to find the first prime number exceeding 10 million digits. The winners receive $100,000 – a nice, if not prime, sum.
“The larger first number qualifies for the award,” said Scott Kurowski, a software technologist who works in Del Mar, “but the second number was found just two weeks later. After nearly a decade, that was hardly any time difference at all.”
Kurowski is credited with helping discover both numbers. Back in the mid-1990s, he helped George Woltman develop a global computing project called the Great Internet Mersenne Prime Search, or GIMPS. By downloading free software (mersenne.org), people could link thousands of personal, business and school computers around the world, each crunching numbers when not in use. The result was a sort of automated “grass-roots supercomputer” capable of performing 29 trillion calculations per second.
“Each individual computer doesn't have to be particularly powerful,” said Kurowski. “The real power comes from having 100,000 machines working together.”
Still, it took 12 years before the biggest prime number popped up on the screen of UCLA computer manager Edson Smith on Aug. 23. Two weeks later, another big prime appeared on the computer of Hans-Michael Elvenich, an electrical engineer in Langenfeld, Germany.
The numbers are the 45th and 46th primes found by the Mersenne project. The largest previous known prime, discovered in 2006, was 9,808,358 digits long.
So what do you do with very big prime numbers?
Well, not much, it turns out – at least not yet.
“Most new things, like the Internet, start in the abstract,” Kurowski said. “Ultimately, there could be some practical application from this knowledge, but the real benefit is knowing how to coordinate massive amounts of computer resources in a productive way.”
Kurowski and his colleagues Smith and Woltman say they'll donate half of their winnings to UCLA for its part in the discovery, give $25,000 to charity and split most of the rest with other GIMPS participants.
“Maybe we'll keep a few thousand for new computers,” Kurowski said.
He might need them. There's a $150,000 prize awaiting the first person to find a 100-million-digit prime number. The clock is counting down – or up.
