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(Mostly) Confirmed: New Mersenne Prime Found
A reader writes "Distributed computing seems once more to be succesful. The combined effort of many pc's joining Primenet in search for a new Mersenne prime may have found there fifth result. Among them many belonging to /. readers. There is an unconfirmed claim for Mersenne prime #39 of over 3,500,000 digits, for which a considerable amount of money has been awarded. SETI looks for ET's messages, but found none sofar. Mersenne primes are used to tell ET about us. A previous found Mersenne number was used to show the advance of science on our planet in a message send into outer space. " The Primenet list has confirmed that while they still need to totally test it out (which should be done by the 24th), they believe that the number found today is the 39th positive.
Does anyone have an envelope with this stamp on it?
Andrew Wiles
a**n + b**n != c**n for n > 2
I really wish that more folks would look over at Stanford's Folding@Home Project . I personally think it is the single most important and fascinating distributed computing project available. Just think, instead of searching for obscure numbers, or aliens, or trying to break the latest RSA key, you could be curing cancer with your spare CPU cycles!!!
Cancer drug research
Gene research
Protein folding
All of these distributed projects reach into medical research and are as such a bit more useful than searching for ET or cracking RC-5.
Remember, there are no stupid questions. But there are a lot of inquisitive idiots.
With these two projects you can help find cures for diseases like Alzheimers, Mad Cow even cancer!
:)
http://members.ud.com/projects/cancer/
big project sponsored by university of oxford, NFCR and Intel
http://folding.stanford.edu/
Protein Folding@Home - basically the same, much smaller in scale though
I run the one from UD on my windows desktop, and I run the folding@home client on my linux box
Any technology distinguishable from magic, is insufficiently advanced.
The EFF webpage says that the big prize ($100,000) is to be awarded for a 10,000,000+ digit prime, so the $100,000 is probably still up for grabs (if you should feel so lucky).
Granted, "greater than 3,500,000" could mean 10,000,000+ digits, but I don't think so...
Actually, it turns out that negative numbers are prime, mathematically. It works like this. Anytime you have a "ring" of objects (think of ring as set of objects where you've defined addition and multiplication), there are special elements of that set called "units". These are the elements in the ring which you can divide by, and stay in the set. For example, for the regular integers, the units are 1 and -1. In particular, 2 in not a unit because if you divide by 2, you don't get integers any more.
The way primes are defined in mathematics is that you say that a number is prime if it can only be divided by a unit, or, equivalently, p is prime if, whenever p divides ab, then p must divide either a or b. It is an easy theorem to show that a unit multiplied by a prime is also a prime. Thus, whenever n is prime, then so is (-n).
So, mathematically, it is more appropriate to say that -5 is prime just like 5 is. Of course, it is taught differently in elementary schools, where we say that a prime is positive integer which only has factors one and itself, but this is actually not quite correct.
Now, of course, a reasonable question is why would we consider primes of sets other than the integers? First, it turns out that the definitions, and most of the theorems, of number theory hold in any ring, i.e. any set with both an addition and a multiplication. It's a nice generalization to deal with other sets. Second, it is also practically useful if you're trying to prove things for regular integers also. Unfortunately, the examples for this are a bit too complicated, but trust me, this notion is useful.
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Come on, give it up, that's
It's pretty easy. Believe it or not, the method to check whether they are primes or not involves FFT's. This means that integers are turned to floats to make use of the newest instructions available to processors today. Then, they are turned back to ints at the end of each iteration. Some checking is done to verify that nothing was lost in the rounding.
If something is lost in the rounding, the next person who does the check will find it. When they start the first iteration, a random seed is picked. At the end, the seed is "subtracted" from the residue. The residue will exactly match the residue from the first person who ran the primality test.
The float-to-int rounding error would cause the two testers to have entirely different residues. Also, there is no way to create the residue except to run the full primality test.
Of course, I should be referring you to the official FAQ's. But they're crappy.
If you want a good faq about the math of the system, read the mailing list FAQ's. These are much more interesting.
Free unix account: freeshell.org
The Great Internet Mersenne Prime Search keeps all the large milestones here:
http://mersenne.org/status.htm
They haven't added #39 yet, but they probably will by the end of the day!!!
Free unix account: freeshell.org