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|Quick! What do you call a number that can only be divided by itself and one?
bzzzzzztttttt! Time's up!
OK, that was an easy one. A prime number!
Now, do you know what a Mersenne prime is?
harumph. If you don't, you're not alone. In fact, the search for Mersenne prime numbers has become one of modern mathematics' greatest challenges. Finding primes among small numbers is pretty easy. But when you get into numbers with thousands of digits it becomes a lot more difficult. That's where a mathematician named Marin Mersenne comes in. In the 17th century he developed a formula that helped narrow the search for some large prime numbers. So far, 33 Mersenne primes has been discovered, the largest with the help of giant supercomputers. But now math buffs can join the search at home and all you need is a personal computer with access to the Internet. It's called The Great Internet Mersenne Prime Search and it's being led George Woltman in Orlando, Florida.
Mr. Woltman, how does the Great Prime Search work?
|GW||What I've done is I've written a program that ordinary personal computers can run, and, it takes a little longer but we use the Internet to attract a lot of personal computers and, in that way, we can compete effectively with the supercomputers.||So you're using the Internet like one, big supercomputer.||GW||It's a great communications medium. Right now we have 500 .... over 500 people using the program, to try and find Mersenne primes.||How long does it take a personal computer to find one?||GW||The largest Mersenne prime known right now is two to the one million two hundred fifty-seven thousand seven hundred and eighty-seven minus one.||(incredulous laughter) :-)||GW||It's about three hundred and sixty thousand digits, it's a real big number.||(still laughing)Really big ...?????? statement there!||GW||That's true. It's a bigger number than there are atoms in the universe.||Holy cow!||GW||It took a Cray computer -- supercomputer -- 6 hours to prove that that was a prime number. It takes an average personal computer, say a 150 MHz Pentium computer, home computer, it will take that computer about 2 days to run that test.||Wow. Does it take any special skill do to this? If I download your program, can a virtual math illiterate like me still do it?||GW||It's no problem to run the program. It's basically just a fun little project. You won't even notice it's on your computer. It runs in the background at very low priority, so it won't interfere with your word processing and your spreadsheets. Yes, you do not need to be a math-whiz to run the program, no.||So, how does it work, I mean do you, do you sort of, give, .... If I was to download your program, do you give me a number and then say "Here, search this", or how do I start?||GW||Also on the web pages, are not only the program that you download, but there's a web page telling which numbers are being testing and which ones are available for you to test. So you can take any range of exponents that somebody else isn't testing and start the program up and hopefully you'll get lucky.||How many numbers are you checking?||GW||My current program can only test exponents up to 2'630'000. That leaves about 50'000 exponents left to test.||Ah, so there's a few to chose from then, eh?||GW||Right.||How many Mersenne primes do you think are out there?||GW||If you go by past distributions, there are probably 36 below 2'630'000.||Really?||GW||Which mean that there's 2 left to find. (chuckle)||(laughing) 2 left to find? Out of all of those there's only two left!||GW||Yes, they each have one chance in 25'000.||So how long do you think it will take before you find them?||GW||They seem to be discovered at about a rate of about one every two years. I think that there was one -- there was one discovered this year, and there was one in '94 and one in '92. It's going to take about a thousand CPU years...||(laughs)||GW||...to test all those 50'000 exponents and if you have 500 people well that's, ..., we should be able cover that whole range in about 2 years.||Well, it sounds like a, a marvelous project and you've got all these people and you're using a lot of technology but I have to ask you, Mr. Woltman: Why are you doing this?||GW||I can't say that there's any great value in finding the next Mersenne prime. You'll get you name in the record book, the Guinness World Book of Records. It's more like climbing Mount Everest, the thrill of the conquest.||(laughs unbelievingly) That's it?||GW||That's it!||(laughs out loud)||GW||There's a lot of practical ideas that go into the theory behind the Mersenne primes and finding them and the program that you write to find these, but as far as just running it, there's no real practical use for finding these primes.||(laughs)The esoteric world of mathematics!||GW||A lot of people get interested in recreational mathematics at a young age. That's when I got interested. A lot of people follow-up with it in their later years.||Well, maybe with luck you'll get some more participants and get to your goal even sooner.||GW||That'd be great.||Mr. Woltman, thank you very much for speaking with us.||GW||Thank you, Bob!||George Woltman is head of Just For Fun Software in
Now, if you want to join the search for Mersenne primes and you've got some computer cycles to spare, all you have to do is visit our web site at www.radio.cbc.ca. Go to the Quirks page, click on this week, and follow the instructions from there.