New Largest Prime Found: Over 7 Million Digits 305
Gilchrist continues "If you want to see the number in written in decimal, Perfectly Scientific, Dr. Crandall's company which developed the FFT algorithm used by GIMPS, makes a poster you can order containing the entire number. It is kind of pricey because accurately printing an over-sized poster in 1-point font is not easy! Makes a cool present for the serious math nut in your family.
For more information, the press release is available.
Congratulations to Josh and every GIMPS contributor for their part in this remarkable find. You can download the client for your chance at finding the next world record prime! A forum for newcomers is available to answer any questions you may have.
GIMPS is closing in on the $100,000 Electronic Frontier Foundation award for the first 10-million-digit prime. The new prime is 72% of the size needed, however an award-winning prime could be mere weeks or as much as few years away - that's the fun of math discoveries, said GIMPS founder George Woltman. The GIMPS participant who discovers the prime will receive $50,000. Charity will get $25,000. The rest will be used primarily to fund more prime discoveries. In May 2000, a previous participant won the foundation's $50,000 award for discovering the first million-digit prime."
Legit uses for Mersenne Primes (Score:5, Funny)
But Pseudoprimes? Probability of primeness? Hah! You people cut corners!
Re:Legit uses for Mersenne Primes (Score:2, Interesting)
Don't use one that's based on factoring, then. Go for a discrete-logarithm based cryptosystem, like ElGamal. Mmmm... 23-megabit asymmetric key... (Now we just need a 3-megabit hash function to make the signatures worthwhile. Oh, and some serious silicon to push the electrons required for a digital signature with a key that size. Ooog.)
Re:Legit uses for Mersenne Primes (Score:4, Funny)
I hate to be a pushover... (Score:5, Interesting)
Re:I hate to be a pushover... (Score:5, Interesting)
Every Mersenne prime gives rise to a perfect number [wolfram.com].
To answer your question a little more seriously the number is not much use in itself but like many peices of research the route to the goal often turns out more interesting information than the goal. GIMPS pushes back the bounds on many levels such as highly optimised coding and mathematical DC.
Re:I hate to be a pushover... (Score:4, Informative)
In the end, what does this get us?
Please elaborate for those of us who need a reason to care about primes, perfect numbers & the like.
Re:I hate to be a pushover... (Score:3, Insightful)
Re:I hate to be a pushover... (Score:2, Informative)
Oh, and more specifically (correct me if I'm wrong, I probably am) using mersenne primes (ie primes of the form 2^p-1) prevent certain factorization algorithms from succeeding. And if you manage to fa
Re:I hate to be a pushover... (Score:4, Insightful)
Re:I hate to be a pushover... (Score:5, Informative)
Re:I hate to be a pushover... (Score:4, Funny)
Kinda kicks you in the ass when people say "ok, what good is it?"
I know what good it is. It's a way of keeping 'scientists' employed (scientific welfare) so they don't pollute the job and gene pools.
I'm considering doin research on the 'how', 'why', and 'classification' of belly button lint. I'm sure there's a government funded grant in it. We REALLY NEED TO KNOW THESE THINGS 'just in case' they are usefull in the future.
Yeah, let's keep the scientists out of the gene pool, maybe even replace them with Christian Scientists(tm). I mean, why would we want people to have even the slightest hint of intellegence, I mean, the public, dear lord. You should let the current administration know you have devised such an excellect scheme for them...
Not that I'm saying this guy is a scientist, but whatever... Oh yeah, and you're a troll, but I couldn't help myself.
Re:I hate to be a pushover... (Score:2, Funny)
Sadly, you've been beaten to it. [abc.net.au]
Re:I hate to be a pushover... (Score:4, Insightful)
Re:I hate to be a pushover... (Score:5, Funny)
Notice I said it's an attempt, I didn't say it would work;)
Re:I hate to be a pushover... (Score:4, Funny)
In other words, it's not the size of your prime number, it's how you use it that counts.
Re:I hate to be a pushover... (Score:2, Interesting)
I consider it an extremely good way to attempt to impress chicks, since chicks who are impressed by this kind of thing are more likely to be chicks.
Re:I hate to be a pushover... (Score:2)
Re:I hate to be a pushover... (Score:2, Funny)
Re:I hate to be a pushover... (Score:5, Funny)
Wait, I didn't tell that right.
Re:I hate to be a pushover... (Score:5, Informative)
So right now, this is the largest proven prime number at this point in time. It is 1,000,000 digits larger than the next largest known prime number, (which is also a mersenne prime).
There very well may be a day where primes this large will be used for encryption purposes. But this may be a long way off.
Keep in mind, that so much of the underpinnings of today is based on mathematics from the 1600's to the early 1900's. The math we pursue today will most likely reach a practical application point next century.
Re:I hate to be a pushover... (Score:5, Funny)
Teacher: Ok class, your homework for tomorrow is to find a Mersenne prime longer than 1,000,000 digits. *By hand*. I don't want to see any computer printouts.
Class: *Groan*
Re:I hate to be a pushover... (Score:2)
Re:I hate to be a pushover... (Score:5, Informative)
Yes, because of the Lucas Lehmer primality test, which you can google if you want to see the details.
The standard proof of primality involves factoring the number one less than or one greater than the prime. Obviously, the number one greater than 2^p-1 is easily factored, which is the basis of the test.
Re:I hate to be a pushover... (Score:3, Interesting)
Re:I hate to be a pushover... (Score:4, Interesting)
Re:Persuit of uselessness != profit (Score:3, Insightful)
I ask because your tirade, although vigorous and interesting, is entirely unrelated to my post.
Since you seem to be articulate and well read I'm giving you the benefit of the doubt and assuming that you have some sort of agenda...
What is it exactly?
In case you missed it (Score:5, Informative)
Thought I would drive the point home as this is a great DC project that doesn't receive half the attention of some of the more dubious DC projects...
Re:In case you missed it (Score:3, Funny)
Phew, crisis averted. Good job!
Re:In case you missed it (Score:2, Funny)
Moderators, please tell me what is going on in your little heads. I really want to know. It's not hard to moderate properly, you know... You have the opportunity to motivate
Even primes (Score:4, Funny)
Re:Even primes (Score:3, Funny)
Re:Even primes (Score:3, Funny)
Proof of that will require a recalled grey market Pentium 1 with an FDIV "feature" added to it.
All math people wishing to prove / find your number must also "upgrade"
Re:Even primes (Score:5, Funny)
Re:Even primes (Score:3, Funny)
Start checking at 2**1FaE2D1h (Score:2)
Distributed Computing? (Score:3, Interesting)
Re:Distributed Computing? (Score:2, Interesting)
So... (Score:3, Funny)
Not in this case... (Score:3, Insightful)
Re:Not in this case... (Score:5, Insightful)
Theorem For any positive odd integer n, 3 divides 2^n+1
Proof We will use the Principal of Mathematical Induction.
Basis When n=1, we have 2^n+1=2^1+1=3. Furthermore, when n=3, we have 2^n+1=2^3+1=9.
Induction Now suppose n is a positive odd integer, and that 3 divides 2^n+1. We will now show that 3 divides 2^(n+2)+1.
Since 3 divides 2^n+1, there exists an integer q such that 2^n+1=3*q
2^(n+2)+1=2^(n+2)+4-3
=2^2*2^n+4-3
=4*(2^n+1)-3
=4*3*q-3
=3*(4*q-1)
=3*r, r=4*q-1
Where r is an integer by the closure properties of multiplication and subtraction.
QED
Re:Not in this case... (Score:5, Insightful)
if T = 2^(2p+1) + 1:
T = 2^(2p+1) - 2 [mod 3]
T = 2(2^2p - 1) [3]
T = 2(4^p - 1) [3]
T = 2(1^p - 1) [3]
T = 0 [3]
qed
Want a simple proof? (Score:5, Insightful)
= (-1)^(odd number)+1 [mod 3]
= -1 + 1 [mod 3]
= 0 [mod 3]
Re:Not in this case... (Score:2)
Re:Not in this case... (Score:2)
harrumph (Score:5, Funny)
Say all you will, but Optimus is still the ultimate prime.
Re:harrumph (Score:2)
Re:harrumph (Score:2)
-jim
My Hashtable (Score:5, Funny)
Re:My Hashtable (Score:2)
I think Microsoft has use for you and your hash table in longhorn
As a corollary, (Score:5, Interesting)
Hey, this is very important....... (Score:5, Funny)
Oblig. (Score:2)
Re:Hey, this is very important....... (Score:2)
I knew it (Score:5, Funny)
What happen ? (Score:2, Funny)
Somebody set up us the prime.
Re:What happen ? (Score:2)
That poster is a scam! (Score:4, Funny)
History of Prime #s (Score:2, Informative)
hmmm (Score:2, Insightful)
Personally I think someone should work this out on paper. Any volunteers/nominations?
Picture Frame (Score:3, Interesting)
Without frame: $77.00
With frame: $247.00
SCO's claim that their code has been stolen sounds more logical than this!
Here is the whole number! (Score:5, Funny)
Your comment violated the "postercomment" compression filter. Try less whitespace and/or less repetition. Comment aborted.
Sorry
fermat was here (Score:5, Funny)
I will verfiy on my 66mhz running windows 3.11 (Score:5, Funny)
Re:I will verfiy on my 66mhz running windows 3.11 (Score:2)
Re:I will verfiy on my 66mhz running windows 3.11 (Score:2)
Call me Fermat (Score:3, Funny)
-
Last digit is a 7 (Score:5, Interesting)
#include <stdio.h>
int main()
{
int i;
int p = 1;
int m = 1000000000;
for (i = 0; i < 24036583; i++)
p = p*2 % m;
p = (p+m-1) % m;
printf("%d\n", p);
}
Wow... (Score:3, Funny)
That primate must have big hands...
Primality is in P (Score:2)
Recall that primality testing is now in polytime. It's currently impractical, since the polynomial is order 12 or thereabouts. But expect the search for the largest known prime to get much more boring once someone figures out how to get this algorithm down to a reasonable running time.
Re:Primality is in P (Score:3, Informative)
BTW wasn't the polynomial order 6 whenever a unproved-but-likely hypothesis was true?
Re:Primality is in P (Score:4, Informative)
http://primepages.org/
'proving'
YAW.
I'm feeling funny! (Score:2)
But this makes me want to go out and buy cheap computers and have a "server farm" at home to try to find primes.
I'm serious.
One day I'll be able to understand myself (yeah right, and the day after that I'll understand women).
Bullshit! (Score:2)
6 years (Score:4, Informative)
Started with a p120 laptop, at times had a dozen computers teamed up.
In that time
What a good OS X client for this? (Score:2)
Don't trust the poster (Score:2)
Perfectly Scientific Homepage (they sell the poster): We have a physical poster of all (over) 7.2 million decimal digits available.
Poster Caption: The largest known (November 2003) explicit prime number 2^20996011-1, having more than 6.3 million decimal digits
We really don't know how many digits it has... But it's lots! (Seems to me it would be =20996011/(LN(10)/LN(2)), which is 6.320429 Million Digits, not 7 Million!)
So is someone going to post the number? (Score:2)
Intel (Score:2)
When it is found.. (Score:3, Funny)
When it is found that computer will be wondering: 1 $100.000 hookerbot or 100.000 $1 hookerbots?
Verification (Score:3, Insightful)
Re:Verification (Score:3, Informative)
Slashdot Earns It's Name (Score:3, Insightful)
I love it!
Want to see the number? (Score:2, Informative)
so why arent more people doing this? (Score:2)
Why do we care? (Score:2)
This is posted to the list like a new technical breakthrough that more than 1-2 people will be able to make use of this; like we should all go home and reset our prime number machine.
Why is so much technology pointed at this?
This reminds me of the long-running trickle of IRC bots, image viewers and 'light and fast browsers' that keep getting posted to Sourceforge and/or Freshmeat. We only need so many of these, ya know?
heheh (Score:3, Funny)
What? (Score:3, Funny)
Not even the slightly more tame Prime Number Pooping Bear? [surfeu.fi]
Re:The real question (Score:2)
Re:The real question (Score:2)
Re:The real question (Score:2)
What did they distribute? 16 byte hashes which could be used to validate copyrighted works.
Re:The real question (Score:2)
45484815978915948954345978940045648971501560 8 79456
045089704504897089074045604891501210804898097001 05
123048604876156048907456045601540890489079456015 04
894089078970450156040789079801560487890790456048 97
090890456049807980789078907897980789045604501231 56
048907890159189459041597987089459105901980159454 84
984090494089048979078978910012318048907406459789 07
456048907090419504987009410704895640104816240816 20 48974801041560489489079056047
Re:The real question (Score:2)
Imagine, a piece of music represented in digital form carries a copyright. That can be represented as a very long number (millions of digits?)
Is this long number, therefore, copyrighted?
Re:wow (Score:2, Funny)
What if (Score:2, Interesting)
Isn't it possible that some civilisation is so advanced that their 'bc' would give back the 50th mersenne prime just like our bc would return 3*5
Wouldn't it be cool to find out that the msg you've just now found on SETI isn't gibberish but a hi from another advanced civilisation
Re:Please! I have I higher prime. (Score:2, Funny)
3765761637264764023 divides it.
IAAM.
YAW
Re:So an Itanium GHz is worth less that a P4 GHz? (Score:4, Informative)
Not to mention that you can't expect the threading to scale perfectly. I'm surprised that there are any gains at all because the LL algorithm is so sequential. I remember hearing that Glucas could have done it in half the time on that machine if it had been optimized for NUMA, though.
Re:So an Itanium GHz is worth less that a P4 GHz? (Score:3, Informative)
No, it's not. Not for finding Mersenne primes anyway. You see, the relative performance of different CPU types depends on the kind of work being done.
The benchmark charts at mersenne.org show that a P4 1800 MHz beats the Athlon 64 3400+ running at 2200 MHz. Even my own old P4 1600 MHz comes in ahead of the AthlonXP 3200+ running at 2200 MHz.
So, my guess is that there is some kind of work where the Itanium beats the P4 and the Athl
Re:Yeah sure. (Score:2)
Re:fun with python! (Score:3, Funny)
>>> math.floor(math.log(2**24036583-1,2))
24036583.0
I assume you realize that any number of the form 2^n -1 is going to take n bits to represent.
Re:oye. it is not the largest prime ever (Score:2, Informative)
What kind of math background do you have?