# University professor discovers largest prime number to date

##### February 6, 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: The sum of digits of prime numbers is evenly distributed

## Related Stories

#### The sum of digits of prime numbers is evenly distributed

May 12, 2010

(PhysOrg.com) -- On average, there are as many prime numbers for which the sum of decimal digits is even as prime numbers for which it is odd. This hypothesis, first made in 1968, has recently been proven by French researchers ...

#### Freezing liquids help to predict properties of prime numbers

May 3, 2012

(Phys.org) -- The same freezing which is responsible for transforming liquids into glasses can help to predict some patterns observed in prime numbers, according to a team of scientists from Queen Mary, University of London ...

#### Z-prime search may hurdle Higgs hunt

August 25, 2011

If you're bummed about humanity's biggest accelerator not producing a Higgs particle yet, maybe the latest effort to find a Z-prime will make you feel better.

#### Physicists demonstrate that 15=3x5 about half of the time

August 19, 2012

Computing prime factors may sound like an elementary math problem, but try it with a large number, say one that contains more than 600 digits, and the task becomes enormously challenging and impossibly time-consuming. Now, ...

#### Mathematician wins Shaw Prize for prime numbers, symmetry unification

September 12, 2007

Herchel Smith Professor of Mathematics Richard Taylor has been awarded the Shaw Prize in Mathematical Sciences for work that unified the diverse fields of prime numbers and symmetry.

#### Mathematician announces that he's proved the ABC conjecture

September 12, 2012

(Phys.org)—In all of history there are very few names that stand out in the field of mathematics, at least among those not in the field: Euclid, Newton, Pythagoras, etc. This is likely due to several reasons, chief among ...

## Recommended for you

#### Sexual harassment common among middle school children, study finds

December 9, 2016

The recent suicide of Brandy Vela, a teen in Texas City, Texas, was a potent reminder of the sometimes tragic consequences of bullying. According to Vela's parents, the teen fatally shot herself Nov. 29 following months of ...

#### Digitally reconstructed skull and face may reveal Robert the Bruce, king-hero of the Scots

December 9, 2016

Could this be the face of Robert the Bruce, as it has never been seen before?

#### Archeologist claims to have found proof that Hebrew was the first written alphabet

December 8, 2016

(Phys.org)—Douglas Petrovich, an archaeologist with Ontario's Wilfrid-Laurier University in Canada has sparked controversy in the ancient history scholarly community by making claims that he has found proof that Hebrew ...

#### Mobile money access lifted two percent of Kenyan households out of poverty: study

December 8, 2016

Since 2008, MIT economist Tavneet Suri has studied the financial and social impacts of Kenyan mobile-money services, which allow users to store and exchange monetary values via mobile phone. Her work has shown that these ...

#### Amber specimen offers rare glimpse of feathered dinosaur tail

December 8, 2016

Researchers have discovered a dinosaur tail complete with its feathers trapped in a piece of amber. The finding reported in Current Biology on December 8 helps to fill in details of the dinosaurs' feather structure and evolution, ...

#### Fossilized evidence of a tumor in a 255-million-year-old mammal forerunner

December 8, 2016

When paleontologists at the University of Washington cut into the fossilized jaw of a distant mammal relative, they got more than they bargained for—more teeth, to be specific.

##### 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.

"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