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New Record Prime Found
An anonymous reader writes, "The GIMPS project has found a new record prime. 2 ^ 32,582,657 - 1, clocking in at over 9 million digits, is a Mersenne prime, as were the last few record primes. Here is the 9-megabyte decimal expansion."
...Please move along."
/. said when I first clicked the story, anyway. I immediately assumed it had been commandeered for use in US military codes...
That's what
</tinfoil hat>
Meta will eat itself
They say that they are on a winning streak and that lightening strikes twice etc, well I just say they are continuing running a program which can handle large numbers.
The longer they run it the more they will find.
They are getting all the records because noone else is "trying" as hard.
Good luck that they get the 10million digits, but its just a pissing competition as far as I can see.
They win 100,000 from the EFF for breaking it, but the computational power and time wasted has to be getting close to that itself.
liqbase
2 ^ 32,582,657 - 1th post. Eventually...
Theory and practice are the same in theory, but different in practice.
I have the same combination on my luggage!
So what's the biggest known prime number that's not a Mersenne number? Wikipedia's "Prime number" article states that it's a prime Proth number, but what about the biggest prime that's not of any special form? Or is that illegal to discuss on Slashdot, a server on US soil?
I ca... Oh crap.
"If you make people think they're thinking, they'll love you; But if you really make them think, they'll hate you." - DM
Or when converted to binary, it turned out to be an mp3 of the latest song from [insert-RIAA-label], and so they banned distribution of it :-p
The revolution will not be televised... but it will have a page on Wikipedia
Mersenne primes are simply primes that have this form, but not all numbers that have this form are prime. For example, 15 = 2^4 -1 and is not prime.
Also, for a number to be a Mersenne prime, the 'n' from 2^n-1 must be prime (according to Mathworld).
If you want to expand the number on your machine, run this:
perl -Mbignum -e 'print 2**32582657 - 1'
If it takes too long for you, you can also have perl print an approximation:
perl -e 'print 2**32582657 - 1'
If a divides n, then 2^a-1 divides 2^n-1.
.... 2^((n/a)*a) == 1.
So for 2^n-1 to be prime, n itself must be prime.
Quick proof - consider the values of 2^i modulo (2^a-1) for i=0..n,
You'll notice that 2^0 == 2^a == 2^(2a) ==
i.e. 2^n-1 == 0 (mod 2^a-1)
Note, however, that it's a necessary condition, but is not sufficient.
There are plenty of prime p such that 2^p-1 is not prime.
See http://www.primepages.org/
FatPhil
Also FatPhil on SoylentNews, id 863
I know that was a joke, but this gives the impression that this number in binary is a long stream of 1's and 0's.
Seeing as 2^n is [1 followed by n 0's] in binary, and [1 followed by n 0's] minus 1 is [(n-1) 1's], this number in binary will just be 32,582,656 1's, which isn't decodeable as an MP3.
// MD_Update(&m,buf,j);
Doesn't stand a chance against the one true prime...
OPTIMUS PRIME!
Let the commencement BEGINULATE!
View it here in it's 12mb text form!!!!!!!!
Could be Bjork...
5*7-2 = 33 = 3*11
Trust me. If it was this easy, we'd have heard of it long ago.
Folding@Home is still pretty neat though - the whole "use your spare CPU cycles to (potentially) find cures for various nasty things"
I think you should have said:
Folding@Home is still pretty neat though - the whole "use your spare CPU cycles to (potentially) find cures for various nasty things and enrich the patent portfolios of drug manufacturers"
HTH HAND
-R
The Master (Angelo Rossitto) in Mad Max Beyond Thunderdome, "Not shit, energy!"
5, for example, is a solution to the general formula A(x^C)+D, sum(x)+C, Cx+D, and so on. (Because A, C and D are constants, they would need to be the same constants for all primes you apply the expression to. Otherwise, you've not really generalized or simplified anything.) It is easy to show this has an infinite number of special solutions - pick any value of C and for any equation with D in it, simply subtract/add the necessary value to give you the prime you want.
The original question, then, is whether there is any prime number (other than the three special cases listed) for which {E}
Let us define something else, which is #({E}
(It is easy to prove that there exist two primes which have no general form in common, as that is simply the same as the proof that no general equation for primes exists.)
This leads to interesting possibilities - "islands" of primes that are totally disconnected from all other primes, "peninsulas" where you almost have an island but some perfect subset of the cloud does have a general form in common with other primes, "mountains" where you have a massive number of general forms totally in common with a large number of primes, and so on.
If you were to draw out the interrelationships between primes as a topology, what do you see? A random blob? A sea of islands? Multiple large masses that are otherwise disconnected? If islands, or multiple disconnected continents, exist in prime number space, does this mean that prime numbers aren't a single, definable set of numbers at all, but multiple concepts that should (in general) not be treated as the same at all? Will the map indicate that we can generalize the definition of prime number in a useful way, that the concept can be usefully extended and meaningfully applied outside of the natural numbers?
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)