## New Largest Known Prime Number: 2^57,885,161-1 254

An anonymous reader writes with news from Mersenne.org, home of the Great Internet Mersenne Prime Search:

*"On January 25th at 23:30:26 UTC, the largest known prime number, 257,885,161-1, was discovered on GIMPS volunteer Curtis Cooper's computer. The new prime number, 2 multiplied by itself 57,885,161 times, less one, has 17,425,170 digits. With 360,000 CPUs peaking at 150 trillion calculations per second, GIMPS — now in its 17th year — is the longest continuously-running global 'grassroots supercomputing' project in Internet history."*
## Wrong (Score:5, Informative)

## Re:Uhhh... (Score:5, Informative)

2^4-1 = 16-1 = 15.

5 * 3 = 15.

Go read it again.

## Re:Uhhh... (Score:3, Informative)

## Re:Uhhh... (Score:3, Informative)

It's really just a matter of semantics. If n is composite, then 2^n - 1 cannot be prime.

## Re:They would have more primes to choose from ... (Score:2, Informative)

There isn't a 100% correct primality proving method for general numbers that's anywhere near as efficient as the Lucas-Lehmer test for Mersenne numbers of the same size.

## Re:Uhhh... (Score:5, Informative)

lotof "disputed" definitions. Mathematics deal even with a lot of "disputed" logic and "disputed" interpretations. Read about the axiom of choice, set Theory in general, Constructivism (mathematics) and Finitism and you will understand that things get quite more complicated than you thought.## Re:Write the whole number (Score:3, Informative)

They're all right here: http://mersennewiki.org/index.php/List_of_known_Mersenne_primes [mersennewiki.org]

## A Little More Perfection (Score:5, Informative)

## Re:Why 2^n-1 (Score:5, Informative)

number of the form 2^n-1 are Mersenne numbers which are much more likely to be prime than a randomly chosen odd number. Also, we have "simple" test for these number to weed out many Mersenne numbers that are not prime. Once you have a Mersenne number that passed the "simple" primality test, there is a good chance that it will really be a prime number.

## Re:They would have more primes to choose from ... (Score:4, Informative)

Mersenne primes have a structure that makes it possible to test primality for very large numbers; there's no way to test whether unrestricted numbers of that size are prime (it's theoretically possible, but there aren't enough computing resources on the planet.)

I used to run the GIMPS search application back in the 90s; you really really don't want to run it on a laptop on batteries, especially with the battery technology of the time, and eventually I decided that my laptop didn't have enough horsepower to bother, compared to desktops that could run GPU-based calculations.

## Re:Why 2^n-1 (Score:4, Informative)

There is a very fast primality test for Mersenne numbers, the Lucas–Lehmer primality test. [wikipedia.org]

2^n+1 is prime only if it's a Fermat prime, n=2^k. None of these are known to be prime for k>4, and there probably aren't any more, whereas there are probably infinitely many Mersenne primes.

## Re:Uhhh... (Score:4, Informative)

If you could find new primes that easily then internet banking wouldn't be secure (well...as secure as it currently is, which is "enough for the insurance companies").

No, it relies on factoring being much more difficult than multiplication. That is, if I have two large primes p and q I can trivially calculate p*q = n, but you can not easily find p and q from n. Being able to generate primes quickly doesn't give you anything.

## Re:Wrong (Score:5, Informative)

As is well known, there is no direct mathematical benefit from finding these primes.

It is, however, a very useful "driving problem" to developing new algorithms, software, and distributed computing infrastructure which have wide ranging real-world applications.

Check out the Mersenne Forum [mersenneforum.org] where all types of interesting mathematical, software and computer issues are discussed.

## Re:CPUs? why not GPUs? (Score:4, Informative)

## Re:Wrong (Score:5, Informative)

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

## Re:CPUs? why not GPUs? (Score:5, Informative)

Yes. And both are used for GIMPS.

See the Mersenne Forum's GPU Computing sub-forum [mersenneforum.org] for details.

There are, however, many more CPUs than GPUs out there, so most of the work is still done by CPUs. Two different GPUs using different software (CUDALucas) were used to confirm that 2^57,885,161-1 was prime, in addition to two other CPUs (one using different software than the GIMPS standard Prime95/mprime).