What has 17,425,170 digits, has sparked a positive flurry of excitement and has little practical value?

The largest known prime number, of course - and it's like finding a diamond

A Missouri professor has discovered the largest prime number known to man, a 17-million digit integer which dwarfs the previous record-holder.

Mathematicians gazed in awe at the number, which is 17,425,170 digits long and most easily expressed as 2 raised to the 57,885,161 power minus 1.

The number would stretch 30 miles if printed in standard font. It can be downloaded in its entirety but that requires a 22.45 megabyte text file.

However the birth of 257885161-1, discovered by Curtis Cooper, a professor at the University of Central Missouri using hundreds of computers networked on the campus, provoked a debate within the scientific community.

Ever since Euclid found that there must be an infinite number of primes - numbers that can only be divided by themselves and 1 – mathematicians have competed to discover the largest statistical incarnation.

Almost 100,000 volunteers have joined Cooper in the Great Internet Mersenne Prime Search (GIMPS) project, tapping into a network of 730,562 processors, performing about 129 trillion calculations per second.

While the competition to uncover ever larger primes may produce an intellectual, and even aesthetic thrill for its practitioners, its real-life applications are limited.

Prime numbers inform the algorithmic encryptions used to keep web commerce transactions secure. But a 22 Mb number would be too unwieldy to have much practical use.

“It’s like finding a diamond,” Chris Caldwell at the University of Tennessee at Martin, who keeps a record of the largest known primes, 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.”

The latest “diamond” is the 48th “Mersenne prime” to be discovered and eclipses the previous largest figure, a mere 12,978,189 digits, which was found by UCLA in 2008.

It took 39 days of non-stop computing on one of the University of Central Missouri’s PCs to verify Cooper’s result.

In 1640, French monk Marin Mersenne came up with a formula of 2p-1, with p being itself a prime number, which he said would produce large primes. Although it doesn’t work with every number, it gives a starting point for finding large primes and the GIMPS project tests likely candidates for Mersenne’s formula.

Cooper, who previously found record primes in 2005 and 2006, is one of 98,980 people and 574 teams involved in the GIMPS project, which has cornered the market in primes, discovering the last 11 largest numbers through its giant network of computers devoted to number-crunching.

A less cerebral attraction for prime number seekers is a cash reward. The Electronic Frontier Foundation will give $150,000 to the discoverer of the first prime number with at least 100 million digits. A $250,000 prize is on offer for the motherlode - a billion-digit prime. Cooper received $3,000 for his latest discovery.

Prime number observers defended their latest find. A Fox News report claiming that the new prime had “little mathematical value” was condemned on Twitter.

However the online magazine Slate encouraged readers to be excited by the discovery. “Just finding one large prime number is a fun puzzle to have solved, but it doesn’t say anything basic about how the world works,” wrote Konstantin Kakaes.  “The patterns behind the primes, however, both proven patterns and ones only suspected, are the lens through which humanity can apprehend deep and unfamiliar truths about how reality is structured.”

George Woltman, a retired scientist who created the GIMPS network, argued that finding a new prime number was “analogous to climbing Mt Everest.” He said: “People enjoy it for the challenge of the discovery of finding something that's never been known before.”

History of Prime Numbers

Ancient Egyptians stumble upon the prime number principle with the Rhynd mathematical papyrus, four thousand years ago, through their calculation of unit fractions.

It took the ancient Greeks to demonstrate the existence of an infinite number of primes thanks to Euclid’s Theorem. 2,3,5,7,11…Prime numbers can only be divided by themselves and 1. 

For every finite list of prime numbers, there is a prime number not on the list. Euclid concluded that there must then be infinitely many prime numbers, lighting the touch-paper on the race to find ever higher primes.

Euclid also proved the relationship between perfect numbers and Mersenne primes, a prime number which is one less than a power of two, later named after the French monk Marin Mersenne who studied them in the early 17th century.

Mersenne’s produced a formula of 2p-1 with p being itself a prime number, which would result in a larger prime. Mersenne primes are rare but the 10 largest-known primes are Mersenne’s.

Proving Pierre de Fermat’s Last Theorem, devised in the 1630s, eluded the mathematical community’s smartest minds for 350 years.  He died in the belief that he had found a relation which every prime number must satisfy.

Euler, Legendre and Gauss challenged and built upon Fermat’s Theorem. By the end of the 19th century the study of prime numbers threw out insights into how integers behave but was heading into abstract, number theory.

Relief for mathematicians as by the 1950s computer programmes are used to calculate those all-important largest-known Mersenne Primes.  The Great Internet Mersenne Prime Search (GIMPS), set up in 1996 using large-scale computer distribution, has calculated the 11 most recently-discovered largest-known primes. 

Prime numbers found a real world utility from the 1970s in the algorithms used in credit card and, later, web commerce security. The product of the two prime numbers can be used as a “public key”, while the primes themselves are stored as a private key. Even the most powerful computers struggle to work out the factors of a large prime number.

PROMOTED VIDEO
Life and Style
ebookNow available in paperback
ebooks
ebookPart of The Independent’s new eBook series The Great Composers
Arts and Entertainment
Frank Turner performing at 93 Feet East
musicReview: 93 Feet East, London
News
Toronto tops the charts across a range of indexes
news

World cities ranked in terms of safety, food security and 'liveability'

Extras
indybest
Voices
A mother and her child
voices
Voices
The veterans Mark Hayward, Hugh Thompson and Sean Staines (back) with Grayson Perry (front left) and Evgeny Lebedev
charity appealMaverick artist Grayson Perry backs our campaign
Latest stories from i100
Have you tried new the Independent Digital Edition apps?
Independent Dating
and  

By clicking 'Search' you
are agreeing to our
Terms of Use.

ES Rentals

    iJobs Job Widget
    iJobs Gadgets & Tech

    Recruitment Genius: Senior .Net Application Developer

    £40000 - £60000 per annum: Recruitment Genius: This is a fantastic opportunity...

    Recruitment Genius: .Net / SQL Developer

    £25000 - £35000 per annum: Recruitment Genius: A skilled .NET developer with e...

    Recruitment Genius: IT Technical Support Engineer - PC/Mac

    £25000 - £30000 per annum: Recruitment Genius: This IT support company are cur...

    Ashdown Group: IT Support Analyst - London - £43,000

    £35000 - £43000 per annum + Benefits: Ashdown Group: Senior IT Support Analyst...

    Day In a Page

    Isis hostage crisis: The prisoner swap has only one purpose for the militants - recognition its Islamic State exists and that foreign nations acknowledge its power

    Isis hostage crisis

    The prisoner swap has only one purpose for the militants - recognition its Islamic State exists and that foreign nations acknowledge its power, says Robert Fisk
    Missing salvage expert who found $50m of sunken treasure before disappearing, tracked down at last

    The runaway buccaneers and the ship full of gold

    Salvage expert Tommy Thompson found sunken treasure worth millions. Then he vanished... until now
    Homeless Veterans appeal: ‘If you’re hard on the world you are hard on yourself’

    Homeless Veterans appeal: ‘If you’re hard on the world you are hard on yourself’

    Maverick artist Grayson Perry backs our campaign
    Assisted Dying Bill: I want to be able to decide about my own death - I want to have control of my life

    Assisted Dying Bill: 'I want control of my life'

    This week the Assisted Dying Bill is debated in the Lords. Virginia Ironside, who has already made plans for her own self-deliverance, argues that it's time we allowed people a humane, compassionate death
    Move over, kale - cabbage is the new rising star

    Cabbage is king again

    Sophie Morris banishes thoughts of soggy school dinners and turns over a new leaf
    11 best winter skin treats

    Give your moisturiser a helping hand: 11 best winter skin treats

    Get an extra boost of nourishment from one of these hard-working products
    Paul Scholes column: The more Jose Mourinho attempts to influence match officials, the more they are likely to ignore him

    Paul Scholes column

    The more Jose Mourinho attempts to influence match officials, the more they are likely to ignore him
    Frank Warren column: No cigar, but pots of money: here come the Cubans

    Frank Warren's Ringside

    No cigar, but pots of money: here come the Cubans
    Isis hostage crisis: Militant group stands strong as its numerous enemies fail to find a common plan to defeat it

    Isis stands strong as its numerous enemies fail to find a common plan to defeat it

    The jihadis are being squeezed militarily and economically, but there is no sign of an implosion, says Patrick Cockburn
    Virtual reality thrusts viewers into the frontline of global events - and puts film-goers at the heart of the action

    Virtual reality: Seeing is believing

    Virtual reality thrusts viewers into the frontline of global events - and puts film-goers at the heart of the action
    Homeless Veterans appeal: MP says Coalition ‘not doing enough’

    Homeless Veterans appeal

    MP says Coalition ‘not doing enough’ to help
    Larry David, Steve Coogan and other comedians share stories of depression in new documentary

    Comedians share stories of depression

    The director of the new documentary, Kevin Pollak, tells Jessica Barrett how he got them to talk
    Has The Archers lost the plot with it's spicy storylines?

    Has The Archers lost the plot?

    A growing number of listeners are voicing their discontent over the rural soap's spicy storylines; so loudly that even the BBC's director-general seems worried, says Simon Kelner
    English Heritage adds 14 post-war office buildings to its protected lists

    14 office buildings added to protected lists

    Christopher Beanland explores the underrated appeal of these palaces of pen-pushing
    Human skull discovery in Israel proves humans lived side-by-side with Neanderthals

    Human skull discovery in Israel proves humans lived side-by-side with Neanderthals

    Scientists unearthed the cranial fragments from Manot Cave in West Galilee