Largest Prime Number discovered

A scientist has used his computer to find the largest prime number found so far - written out, it would stretch for 25 kilometres.
Primes are important to encryption and could lead to uncrackable codes.

The new figure, identified by Josh Findley, contains 7,235,733 digits, and would take someone the best part of six weeks to write out longhand.

Mr Findley was taking part in a mass computer project known as the Great Internet Mersenne Prime Search (Gimps).

Longest Prime




now thats a long number!!

ah, very interesting Gryffen ,
I can't believe that it would take six weeks out the number

You can download this number here, it's 3.34 mb, and it's zipped txt

Or go directly here to view it in the browser.

BTW, I read somewhere that there is not enough ink in the whole universe to write the largest number ever used in math (Graham's number).

it's been a very long time since I've been in school and I was never much of a mathematician, soooo, would / could someone explain "prime" numbers and why it's a big deal to find this one, etc.

thanks

GIMPS really seems to be doing its job in November they announced the discoverer of the then largest prime number at 6.3 million digits.

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I take my hats off to them and another important fact of this find is that if the tests hold up it will be the 41st Mersenne Prime number

Prime #s are only divisible by 1 and themselves 1,2,3,5,7,11,13.... And happen less and less frequently as they get larger . Encryption programs use a sum o two prime #'s to make a code that can only be deciphered with the original #s . someone else could edxplain how a bit better , qnd I'd like to know myself .

wow very intresting post, I too would also like to know how this works with encription more....

Actually the BCC is a bit late. Mathworld had an article about it on the 1st of this month: [url=http://mathworld.wolfram.com/news/2004-06-01/mersenne/]. It provides some more mathematical information and links.

You chose two primes, p and q. You multiply them, and u get N (N=p*q).
then you chose another number: e
e has to be coprime to the number (q-1)*(p-1). (coprime means that the only devisor that they both share is 1)

N and e are now your Public Key, There is no risk in making it available to the public, and it's is the only thing that people must have access to in order to sent you encrypted messages.

To encrypt you turn letters (of the message you want to encrypt) to numbers (using ascii for example) and the whole message is now a number. We'll call it M.

Now you need another number, we'll call it C.
You calculate C=(M^e)*(mod N) (^ = in the power of...)

so now C=the encrypted message.

No one - besides the one who knows p and q (the primes we used at the beginning) - can decrypt it now.

The one who knows p and q recieves the message, and calculates another number (we'll call it d) by using the formula:

e*d=1(mod(p-1)*(q-1)

N and d are the Private Key, and you are supposed to keep them secret.

To decrypt an encrypted message (C) you do M=(c^d)*(mod N).

And you get M, which is the decrypted message.

Large primes are needed so it will be almost impossible to find out the values of q and p (if the N that is small, it's is easy to find out the values of p and q, because they are probably small primes and it is easy to find which).

This is called RSA, and it's good because of:
1. It's basically unbreakable when using huge primes.
2. Most important: it's public key cryptography, meaning you don't need to pass secretly the key to the people who will send you messages (which is very risky, because some one might intercept the key and decode all your messages)

Hope it helped.

[edit on 8/6/04 by Transc3ndent]

[edit on 8/6/04 by Transc3ndent]

Primo!

We were primed on the previous largest Mersenne prime a long prime ago.

With the increasing grunt available to obsessed Mersennians, I figure this record will stand about two months. Intervals between homo sapiens largest prime discoveries are an interesting piece of impure mathematical research.

thanks Trans... but I have to say WTF !!!

I have no clue, I hate math... always have always will, and guess what ?

I work in Finance actually collections, but lots of numbers to work with...

Originally posted by Transc3ndent
You can download this number here, it's 3.34 mb, and it's zipped txt

Or go directly here to view it in the browser.

BTW, I read somewhere that there is not enough ink in the whole universe to write the largest number ever used in math (Graham's number).

LOL!! Now......I gotta ask this...WHERE THE HELL ELSE ARE YOU GOING TO FIND INK, EXCEPT HERE??

Large prime Numbers are not the future of cryptography the future direction is Quantum cryptography. Which is using pattrens of photons to encrypt data.
www.cs.dartmouth.edu...