[ExI] 2^57885161-1

[Dave Sill]

http://www.foxnews.com/science/2013/02/05/worlds-largest-prime-number-discovered/

If diamonds are a girl’s best friend, prime numbers are a mathematician’s.

And Curtis Cooper at the University of Central Missouri in Warrensburg
has just found the biggest, shiniest diamond of them all.

As part of the Great Internet Mersenne Prime Search (GIMPS), a
computer program that networks PCs worldwide to collectively hunt for
a special type of prime number, Cooper discovered the largest prime
number yet late last month: a beast with 17,425,170 digits.

The number -- 2 multiplied by itself 57,885,161 times, written
mathematically as 257,885,161-1 -- is the first prime discovered in
four years.

Though there is little mathematical value to finding a single new
prime, these rare numbers are prized in their own right by some. "It's
sort of like finding a diamond," Caldwell told New Scientist. "For
some reason people decide they like diamonds and so they have a value.
People like these large primes and so they also have a value."

You can see an abbreviated version of the new prime number, or
download all 17,425,170 digits in a massive, 22MB text file.

Prime numbers, which are divisible only by themselves and one, have
little mathematical importance. Yet the oddities have long fascinated
amateur and professional mathematicians.

The first prime numbers are 2, 3, 5, 7, 11, and so on. The number 10
is not prime because it is divisible by 2 and 5, for example. There
are an infinite number of primes: The curious or numerologically
inclined can peruse a list of the first 50 million primes online.

Mersenne primes like Cooper’s were named for the French monk Marin
Mersenne, who studied these numbers more than 350 years ago. The GIMPS
project has discovered all 14 of the largest known Mersenne primes.

A Mersenne prime is of the form 2P-1, where the variable P is itself a
prime -- making the Mersenne an elite sort of prime, a James Bond
among spies. The first Mersenne primes are 3, 7, 31, and 127
corresponding to P = 2, 3, 5, and 7, respectively, the GIMPS website
explains.

There are only 48 known Mersenne primes.