One small beep brings prime number glory to Missouri

Ian Sample, science correspondent
Thursday January 5, 2006
The Guardian


If it takes 700 computers nine years to find the answer, it must be one beast of a question. But for researchers in Missouri, on a quest to find the world's largest prime number, it was all worthwhile.
In mid-December, a reassuring beep signalled the end of the long search, and one of the computers came up with a prime number with the mysterious name of M30402457. Made up of 9.1m digits, it trounces all others discovered so far.


Prime numbers are positive numbers divisible only by themselves and the number one, such as 1, 2, 3, 5 and 7. The number discovered in Missouri falls into a special category called mersenne prime numbers. These are expressed as the number 2 raised to the power of "p" minus one, where "p" is also a prime number.

For Steven Boone and Curtis Cooper at Central Missouri State University, it was a moment to remember. "It's a huge achievement, we're really excited," said Dr Boone. "People ask why we do this. It's like going on a quest. We're looking for something incredibly rare," he said. "It's the icing on the cake."

And then there is the financial incentive. The person who finds the first mersenne prime number more than 10m digits long stands to win $100,000 (£58,000), the prize of the Great Internet Mersenne Prime Search competition.

http://www.guardian.co.uk/usa/story/0,12271,1678100,00.html

All I have to do is memorize it. I guess I should write it down somewhere, you know, just in case...

No you're not, Dr. Boone. There are an infinite number of prime numbers, and the last time I checked, an infinite number of anything means it's not rare. You're engaged in nerd masturbation; don't try to make it sound like a bigger deal than it is, okay?

Without mathematicians you wouldn't be wasting your time on a computer.

I took Dr. Boone to task for engaging in hyperbole about what his "accomplishment" was all about.

And what is the practical use of a prime number 9 million digits long? About the only thing I can think of is greater encryption of computer code, which will be reserved for use by powerful men to hide what they're doing from public view and gather greater control to themselves. Or am I missing something?

You look for something,and you find something completely different.

There's no practical use to climbing Everest, but some people get an enormous thrill from the challenge. Is that masturbation too?

A prime number of only about 100 digits would be more than enough to hide any secret from anybody. That includes hiding your secrets from the government.

And tried to tell me that this was some significant, life-changing, never-before-done accomplishment, then yes, I would call it masturbation as well. Read Dr. Boone's comments again. He seems to think that eight years and untold computer time spent coming up with a nine million digit prime is a "quest," and something rare. As I noted, there are infinite prime numbers, and infinite still doesn't quite qualify as "rare," even if you dedicate eight years to finding it.

But apparently I'm quite alone on this. I agree, it's the most signal achievement ever on the face of the planet, and Dr. Boone and his team should be acknowledged as the gods among mortals that they are, without question. Nothing in the realm of human endeavor even approaches this feat for its magnificence, and the extraordinary news that it was done in only eight years merely confirms the magnitude of the genius involved here.

All hail the nine million digit prime number! Hallelujah!

very rare in the sea of integers, so Dr. Boone is probably taking about that. Either way, he is definitely engaged in masturbation. He probably has a government grant to do it too.

just human brains and the electronic machines they build as their glorified abacus replacements that are finite.

So untimately, prime numbers could be as endless as the so-called boundaries of the cosmos.

There is a fairly elementary proof of this in the numbers theory. Other than that I do agree with you. There is no point trying to find larger and larger prime number, because we know this will never end.

I am impressed with what they have accomplished. However, a quest to find the largest prime number is a fool's errand. They didn't, and won't, find it.

Does this mean that the number is (2^30402457)-1 ? Just guessing about the notation.

2^(30402457...-1)

...or not

if every Mersenne number is a prime number than how hard is it to find a Mersenne prime with more than 10 million digits?
They get big pretty fast
2 - - 3
3 - - 5
5 - - 31
7 - - 127
11 - - 2047
13 - - 8191
17 - - 131071

Up to 6 digits before I am past 20. 2 to the 127th has 38 digits.

The prize does not seem worth it since it took 700 computers 9 years to find this number with a mere 9.1 million digits. You are using more than $100,000 worth of computer time to win that prize. :silly:

biggest prime - for 'use in cryptography'?

but not all. That's why it's necessary to use the computer to verify that a M number is a prime. Kind of silly really.

I would start trying to divide it by other prime numbers - 7, 11, 13, 17, 23 ... up to 65,535. (Since the computer cannot be expect to remember all the primes, it is probably easy just to divide by every odd number.) I am not sure how far I went on my list. In college I wrote a program that would print out prime numbers and printed out about thirty pages of primes. I was trying to find a pattern in their frequency. I did not get very far in that, but I think I still have the list. That makes me wonder how far that program would get if I had run it for seven years.

which is why they are valuable in encryption.

For example, in the first ten numbers there are 4 primes, in the 2nd ten there are 4, 3rd - 2, 4th - 3, 5th - 2, 6th -2, 7th - 3, 8th - 2, 9th - 1. It does not work for tens, but in the first hundred numbers there are 23 primes, and fewer in the 2nd hundred and so on. Of course, it was Asimov who got me started on that, in the same essay probably, that led me to re-discovering a formula for perfect numbers. One that he did not bother to mention.

a pattern for the numbers themselves would follow (keep narrowing the frequency "window"--hundreds, then tens, then ones).

Just a hunch.

Since sqrt(x)*sqrt(x)=x, there is no need to go to sqrt(x)+2.

The Republicans have their number now!

5.

Dan Quayle is reported to be feverishly scribbling in his composition book trying to find the next one.

:dunce: :dunce: :dunce: