47th Mersenne Prime Confirmed

radiot88 writes to let us know that he heard a confirmation of the discovery of the 47th known Mersenne Prime on NPR's Science Friday (audio here). The new prime, 2^42,643,801 - 1, is actually smaller than the one discovered previously. It was "found by Odd Magnar Strindmo from Melhus, Norway. This prime is the second largest known prime number, a 'mere' 141,125 digits smaller than the Mersenne prime found last August. Odd is an IT professional whose computers have been working with GIMPS since 1996 testing over 1,400 candidates. This calculation took 29 days on a 3.0 GHz Intel Core2 processor. The prime was independently verified June 12th by Tony Reix of Bull SAS in Grenoble, France..."

Why is this useful?

[Abreu]

The answer is not in the summary, nor in the first page of the FA...

Buried somewhere in the linked site is this FAQ:

http://primes.utm.edu/notes/faq/why.html [utm.edu]

However all the answers are a bit unsatisfactory, IMHO...

So, I ask the great Slashdot hive-mind... What are the practical applications of Mersenne Primes and why are people paying money to find them?

Re:Cool processor

[rbarreira]

Do they realize that they can put eight quad-core xeons in a machine and finish the calculation in a single shift instead of waiting a month?

Do you realize that that's less efficient than using those 32 cores to calculate 32 independent numbers?

Re:Cool processor

[Anonymous Coward]

*hands you the key to the city*

Re:Mersenne Primes correspond to Perfect Numbers

[Anenome]

Well, they may be unsolved problems, but again, they look like they have no relevance to anything, no application, other than being unanswered questions. But, like so many things, knowledge is valuable for its own sake, and who knows what revolution may result from what is now just a mathematical curiosity. Stealth-flight technology was originally harvested from a little known paper on radar written by an obscure Russian scientist. Kind of ironic that we were the ones to develop it. What you're really talking about is finding a proof for why there could or could not be any odd perfect numbers, and a proof for whether there are infinite perfect numbers or not. Typically, proofs like this that elude us lead into new forms, new paradigms of mathematics--which themselves result in great leaps forward in other areas once those proofs have been realized. That is certainly a story that has been repeated time and time again, most notably with calculus which is virtually the foundation of the modern world.

Even the concept of 'perfect numbers' is not familiar to me. Off to the Wiki!:

http://en.wikipedia.org/wiki/Perfect_number [wikipedia.org]
"In mathematics, a perfect number is defined as a positive integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors excluding the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself), or (n) = 2n.

The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6.

The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. This is followed by the perfect numbers 496 and 8128 (sequence A000396 in OEIS).

These first four perfect numbers were the only ones known to early Greek mathematics."

Re:Mersenne Primes correspond to Perfect Numbers

[JoshuaZ]

Well, this does actually fit some of the patterns we are beginning to see. For example, there are reasons to expect that for most Mersenne primes 2^p-1 one will have p-1 having many small prime factors (this has to do with Fermat's Little Theorem). We in fact see that again in this case we see that since p-1 factors as 2^3 * 3^3 * 5^2 * 53 * 149. Also, the discoveries are are enough to be noteworthy in the same way that discovery of new elements is noteworthy. We likely won't find out much by itself from the discovery of element 117 when it occurs but it will be a big enough deal to get on Slashdot. Discoveries like these are sort of like summiting mountains. And for all we know, each one may be in fact be the last, since we can't prove there are infinitely many primes. Furthermore, primes in general are a fundamental building block of the integers. So finding very large ones is intrinsically cool.

Re:Cool processor

[ceoyoyo]

You don't get the $100k by searching for one prime though. You've got to be the lucky one that does the month long calculation on the number that actually happens to be prime.

It's like the lottery. You can't make a profit at it unless you're lucky. Otherwise, some big company would come in, invest a few million in number crunching, and take home all the bounties.

Re:Why is this useful?

[Rockoon]

Well, for one thing if you need a prime divisor, 2^n-1 primes have some good properties...

Modulus or Division by such numbers can be accomplished with a few fast operations (bitwise Shift/And, a comparison, and maybe a subtraction) instead of a single very slow one (an actual division.)