Take one blackboard, one piece of chalk, 1,257,787 twos and work out a world record (don't forget to subtract one)

Yesterday was a bad day for (2859,433-1). Listed in the Guinness Book of Records as the largest-known prime number, it has been knocked into numerical obscurity by (21,257,787-1), a monster of 378,632 digits which has been proven prime by a computer at Cray Research, Wisconsin. It would take about 12 pages of this newspaper to print out the number in full. The old record-holder would have run out after about nine pages.

Prime numbers - those that can be divided without remainder by no whole numbers other than one and themselves - have fascinated mathematicians for more than 2,000 years. Euclid provided the first simple proof that there is an infinity of primes. (If not, just multiply them all together and add one. The resulting number is either itself prime or has a prime divisor different from those you started with. QED.)

For the last 100 years, we have even known roughly how many prime numbers there are below any given figure. (This is given by the so-called prime number theorem, first proved in 1896.) Yet despite knowing there is no largest prime, people have continued searching for ever larger ones.

In 1772, the record was held by a 10-digit number; by 1884, it had been raised to 20 digits, but the real acceleration began in the computer age. In 1971, months of computer calculations led to the discovery of a 6,002- digit prime, and in the 1980s and 90s Cray computers have been pushing the record higher almost every year.

A spokesman for Cray described prime testing as a "torture test" for supercomputers. Others might call it a waste of time. Recently, however, the task of factorising large numbers has had important applications in computer security.

We had intended to print the new top prime in full, but - perhaps for reasons of security - the people at Cray have not divulged all its digits. Of course, you can work it out yourself: just take 1,257,787 twos, multiply them together and subtract one from the answer.

Suggested Topics
News

election 2015
News

people
News

people
News

election 2015
ebooks

The Independent Voter’s Handbook 2015

ebooksA celebration of British elections
Arts and Entertainment

tv
News

news
News

election 2015
Environment

environment
News

news
News

news
Life and Style

fashion
Voices

'Sorry Britain, but nobody cares about your little election – try being relevant next time'

voicesEmanuel Sidea: Whether the next PM is called Cameron or Miliband doesn't really matter to Europe
Extras

indybest
News

people
News

Who is standing in your area in the general election – and which box should you cross?

election 2015
Independent Dating
and

By clicking 'Search' you
are agreeing to our

Ashdown Group: Helpdesk Analyst - Devon - £20,000

£18000 - £20000 per annum: Ashdown Group: Helpdesk Analyst - Devon - £20,000 ...

Ashdown Group: Data Scientist - London - £50,000 + bonus

£35000 - £50000 per annum + generous bonus: Ashdown Group: Business Analytics ...

Ashdown Group: IT Project Coordinator (Software Development) - Kingston

£45000 - £50000 per annum: Ashdown Group: IT Project Coordinator (Software Dev...

Ashdown Group: Editor-in-chief - Financial Services - City, London

£60000 - £70000 per annum + benefits : Ashdown Group: A highly successful, glo...

Miliband's unlikely journey from hapless geek to heart-throb

He was meant to be Labour's biggest handicap - but has become almost an asset

On the margins

From Militant Elvis to Women's Equality: a guide to the underdogs standing in the election

'This is the battle of young Egypt for the future of our country'

Ex-Muslim Brotherhood minister Amr Darrag still believes the opposition can rid Egypt of its military regime and replace it with 'moderate' Islamic rule, he tells Robert Fisk

Why patients must rely less on doctors

Improving our own health is the 'blockbuster drug of the century'

Flesh in Venice

Sarah Lucas has filled the British pavilion at the Venice Biennale with slinky cats and casts of her female friends' private parts. It makes you proud to be a woman, says Karen Wright

11 best anti-ageing day creams

Slow down the ageing process with one of these high-performance, hardworking anti-agers

Five things we learnt from the Italian's Champions League first leg win over the Spanish giants

Ashes series looks a lost cause for England...

Whoever takes over as ECB director of cricket, says Stephen Brenkley

Fishing is on Nigel Farage's mind

Ukip leader casts a line to the disaffected

Who is bombing whom in the Middle East?

Robert Fisk untangles the countries and factions

China's influence on fashion

At the top of the game both creatively and commercially

The man known as GOD has a reputation for getting the job done

Lord O'Donnell's three principles of rule