University professor discovers largest prime number to date

Feb 06, 2013 by Bob Yirka report

(Phys.org)—Curtis Cooper, professor of math and computer science at the University of Central Missouri, has discovered the largest prime number to date, it's 257,885,161 – 1. It has 17 million digits and is also a Mersenne prime (a prime number defined by the equation N=2n-1, where N and n are both prime numbers). The find was part of the Great Internet Mersenne Prime Search (GIMPS) project that uses a distributed approach to number crunching using volunteer computers.

Prime numbers, are of course, numbers that can only be divided by themselves and 1 (and are greater than 1). They were first discovered by the famous Greek over two thousand years ago. Since that time, amateurs and experts alike have sought to discover ever increasingly larger prime numbers, though mostly for sport, as prime numbers have very few practical purposes (in recent years they have been used in cryptography). The process is difficult as there is no formula for finding them. Thus, blunt force has typically been the only way—choosing a number at random and then attempting to divide it by every number that is smaller than it is (tossing out obvious ones of course). For this reason, it wasn't until people began building computers that really large prime numbers were discovered.

Mersenne Prime numbers are named after French monk Marin Mersenne, who was the first to detail the formula for the class of special prime numbers, over 350 years ago. This latest discovery is just the 48th ever discovered.

The GIMPS project has been exceptionally good at finding large prime numbers—it's been responsible for the discovery of the largest 14 over its seventeen year history. It's made up of 360,000 machines that together are able to calculate at peak times up to 150 trillion calculations per second. Cooper, clearly an avid member, has been credited with the discovery of two other large found by the group. For his efforts this time, he will receive $3000. Much bigger prizes (from the Electronic Frontier Foundation) are in store for anyone that discovers a prime with a hundred million or a billion digits ($150,000 and $250,000 respectively).

To make sure the number found by Cooper was indeed a prime, several other independent volunteer researchers verified it by testing it on their own computers.

Explore further: Ancient Greek well yields rare wooden statue

More information: www.mersenne.org/various/57885161.htm

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User comments : 14

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Sonhouse
5 / 5 (2) Feb 06, 2013
The title should be amended to 2^57,885,191 -1. It is now shown without the (2^) which is a slightly different number.
gmfr
3.5 / 5 (11) Feb 06, 2013
The Fox News write up of this story said that prime numbers are of little mathematical importance. I literally face-palmed.
grondilu
5 / 5 (5) Feb 06, 2013
The Fox News write up of this story said that prime numbers are of little mathematical importance. I literally face-palmed.


I guess they meant that this particular discovery (a large Mersenne prime) is of little importance. Which is quite true if the primality was proven only with brute force.
Noumenon
3.6 / 5 (20) Feb 06, 2013
The Fox News write up of this story said that prime numbers are of little mathematical importance. I literally face-palmed.


Because prime numbers are a socialist invention and are a means of tricking people into far leftist politics. // sarcasm
visualhawk
2.5 / 5 (11) Feb 06, 2013
The Fox News write up of this story said that prime numbers are of little mathematical importance. I literally face-palmed.


The combined IQ of the staff at Fox = 2^5 - 1
Silverhill
4.3 / 5 (3) Feb 06, 2013
choosing a number at random and then attempting to divide it by every number that is smaller than it is
Every number that is smaller than its square root, that is.
Sanescience
5 / 5 (5) Feb 06, 2013
Ok, I do not read FOX regularly but dismissing something that is a foundation to modern security in communications sounded like something I wanted to see for myself.

The offending segment(s) read:
"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"

and

"Finding a new prime number, a number divisible only by itself and one, has little mathematical importance, New Scientist said."

I agree FOX can (like any other media source) be idiotic. But just throwing out misleading agenda poop harms everybody.
TheWalrus
2.5 / 5 (4) Feb 06, 2013
Is this right? It's 2 to the power of 57 million , but it has only 17 million digits?
gwrede
5 / 5 (3) Feb 06, 2013
Is this right? It's 2 to the power of 57 million , but it has only 17 million digits?
Two to any power has roughly a third as many Decimal digits. When the word digits is used alone (as not like "binary digits"), then it means Decimal digits, which is a regular number. So this statement is right.

Shakescene21
5 / 5 (2) Feb 06, 2013
@Walrus -- I think it's right. If you raise 10 to the power of 57 million, it would have 57,000,001 digits.
NickFun
5 / 5 (3) Feb 06, 2013
Of course, there are an infinite number of prime numbers if you are willing to keep going higher. I'd rather spend my time doing other things ;)
VendicarE
5 / 5 (1) Feb 07, 2013
2**10 = 1024 = 3 decimal places approx
2**10 10 = 1024*1024 = 6 decimal places approx.
2**(10*n) = 3*n decimal places approx.

57,000,000/3 = 19,000,000
frajo
5 / 5 (2) Feb 07, 2013
First time I see superscript notation in a Phys.Org article. Congratulations.
pdalek
5 / 5 (1) Feb 07, 2013
17425170

1's:1743497, 2's:1739844, 3's:1745602, 4's:1743528, 5's:1739641,
6's:1742677, 7's:1743436, 8's:1743298, 9's:1743995, 0's:1739652