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

Posted
by
timothy

from the sorry-won't-fit-on-vanity-plate dept.

from the sorry-won't-fit-on-vanity-plate dept.

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."*
## Re:Wrong (Score:3, Interesting)

I'm not trying to be inflammatory here... this is a genuine question.

Why? I mean... why bother with calculating this.. What has it added to study if prime numbers? And if it's added to the study of primes... then what use is that?

## Number of Digits (Score:5, Interesting)

"There are 10 kinds of people in the world. Those who understand binary, and those that don't."

This new number is 2^57,885,161 - 1, so naturally it has 57,885,161 digits, all of them 1. A simpler example: 2^5 - 1 is a Mersenne prime. Written in binary it's 100000 - 1 = 11111.

Oh! You meant that it has 17,425,170

decimaldigits. Booooooooring!## Re:They would have more primes to choose from ... (Score:4, Interesting)

Yes. The LL test only works on Mersenne numbers--numbers of the form 2^p-1 where p is prime. The LL test is not statistical. It can determine if a given mersenne number is prime or not without any doubt.

To protect against errors, GIMPS (Great Internet Mersenne Prime Search) uses a variety of double checks to ensure no number if mistested. Any number that passes the LL test is double (and sometimes triple checked) to verify that there wasn't a hardware or software error that caused a false positive. I had the honor of performing the double check of a record Mersenne prime some time ago.

## total energy consumed during the 17-year project? (Score:4, Interesting)

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

If the exponent is not prime, then the number will not be prime.

I don't do HTML, I'll use the symbol ^ for exponent (I don't do C either). Let's suppose c = a*b, then 2^c - 1 is divisible by both 2^a - 1 and 2^b - 1. (That's true with x instead of 2, the difference being 2^1 - 1 is 1 which is not prime.) Whether the definition requires primality or not, mathematics dictates that the exponent must be prime.

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

Actually, it's "worse" than that: the "proof" that most modern PKCS crypto works is: "It's hard to find the (prime) factors of the product of two primes".

Small correction, there is actually no proof that RSA reduces to factoring. It is true that if you can factor you can break RSA, but you may also be able to break RSA without factoring. http://en.wikipedia.org/wiki/RSA_problem [wikipedia.org]