Beckham in his prime number
The number chosen by the England captain
for his Real Madrid shirt is rich in mysterious connotations.
The mathematician Marcus du Sautoy explains
In pubs and clubs, and on internet sites, there has been much
debate over the mystical meaning behind Beckham's choice of the
number 23 shirt to play for Real Madrid: we have 23 pairs of chromosomes,
Michael Jordan wore the number 23 shirt, Caesar was stabbed 23
times, 23mph is the maximum speed of an American crow; and let's
not forget AA23, the cell in which Princess Leia was held in the
original Star Wars movie.
This week, as Real Madrid prepare for a match against China's
Dragon team, I would like to back a new theory to explain why
Beckham has plumped for number 23. As a member of Oxford University's
Mathematical Institute, and football fanatic, I feel moved to
point out that many pundits seem to have missed the true significance
of Beckham's choice: 23 is a prime number - the smallest with
consecutive digits. Although many have said this in passing, few
realise what a profound observation this is.
Prime numbers are those indivisible numbers. They are nature's
most important numbers because they are the "atoms" of mathematics,
the hydrogen and oxygen of the world of numbers. Every number
is built by multiplying prime numbers together, a fact obviously
not missed by Real Madrid.
The key building blocks of Real Madrid's team are all prime numbers:
Carlos, No 3; Zidane, No 5; Raul, No 7; Ronaldo, No 11. So giving
Beckham the 23 shirt is a clear indication that Real's president,
Florentino Prez, is intending to build on Beckham.
But there are other more subtle reasons why Beckham might be seeking
out another prime-number shirt to replace his No 7 at Man U. The
Ancient Chinese believed each number had its own sexuality. Even
numbers were feminine, odd numbers were masculine.
But of all the odd numbers, the primes were considered the most
masculine. These numbers that can't be broken down into smaller
numbers are the macho numbers of mathematics. Given the macho
culture of Spanish football, perhaps Beckham felt the need to
balance his feminine side by sticking a stonking great prime on
his back.
Or perhaps it is his survival instinct coming to the fore. In
nature, primes are the key to the survival of a strange species
of insect. The prime-number cicadas hide in the ground for 17
years, then emerge en masse from the earth into the forest. They
sing loudly, eat, have sex, lay eggs and then die after six weeks
of intensive partying. The forest goes quiet again for 17 years.
But why did the cicadas choose 17, a prime number, for their hibernation?
Scientists believe there is a predator that likes to crash their
party and also emerges periodically after a certain number of
years. The cicadas found that by choosing a prime-number cycle
for their party, they could keep out of step of the predator more
often than if they'd chosen a non-prime such as 15.
For the cicadas, the primes aren't just some abstract curiosity,
but the secret to their survival. Perhaps Beckham, too, hopes
that a prime-number shirt might help him avoid getting another
stray flying football boot in the eye.
Evolution might have helped the cicadas to find primes, but is
there some pattern that can help Real Madrid to go on choosing
primes for their growing selection of star players?
Despite 2,000 years of scrutiny, mathematicians are stumped by
the task of predicting when the next prime will occur. Indeed,
they have begun to suspect that there are no patterns. Two years
ago a record big prime number with more than four million digits
was discovered.
It will always be possible to beat the current record, since the
Ancient Greeks proved there are infinitely many prime numbers.
Yet mathematicians have found no method that will help them to
predict where to look for the next record prime. Present techniques
share more in common with astronomers randomly trailing the sky
for new supernovae.
Nature, mathematicians believe, has chosen the primes randomly
as if playing some game of prime-number lottery: 23 is, therefore,
one of nature's lucky numbers.
Even the scriptwriters of Channel 4's series Sex and the City
have cottoned on to the random, chaotic behaviour of the primes.
In the episode The F*** Buddy, the sexually promiscuous Samantha
compares herself to a prime number to illustrate her wild and
random choice in men. Perhaps Victoria should be rather wary of
her husband's addiction to primes.
Despite all the evidence that primes look random, we aren't sure
whether, as we count higher and higher, some strange pattern might
emerge. The greatest unsolved problem of mathematics, called the
Riemann Hypothesis, is to understand why there don't seem to be
any patterns in the primes. And as if mathematical immortality
were not enough, a proof of this enigma will win you $1 million
courtesy of a businessman in America.
If you think all this stuff about primes is just some abstract
game, then think again. The fact that we don't fully understand
the primes is at the heart of a very real-world application of
prime numbers.
Every time you use your credit card on the internet to buy a ticket
to see Real Madrid play, your account is kept secret from hackers
thanks to the power of prime numbers. Prime numbers have become
the locks that preserve the secrets that are racing through the
electronic shopping mall.
Each e-business chooses two big primes, p and q, which they keep
secret. The product of these primes, N = p x q, is made public.
A calculation using N encrypts your credit card, but the only
way to undo the calculation and decrypt the secret message is
to know the secret primes p and q. Cracking codes is the same
as cracking the public number N into its prime building blocks.
It's a bit like a chemist who wants to know the atoms inside a
compound. Although chemists have solved their problem, mathematicians
lack any fast way to do this prime-number spectroscopy - to the
relief of internet cryptographers.
Perhaps Beckham is subconsciously seeking some security by his
choice of a prime-number shirt. But any deeper understanding that
we might gain about prime numbers could help to bring e-business
to its knees.
Whatever his real reasons, Beckham isn't alone in choosing 23
as his favourite prime. It was also the choice of Nobel prize-winning
economist John Forbes Nash, who was recently depicted by Russell
Crowe in a Hollywood movie.
One of the first indications of Nash's failing mind was his claim
that a picture on the cover of Life magazine of Pope John XXIII
was in fact Nash in disguise, the proof being that 23 was his
favourite prime. Is Beckham's choice of the 23 shirt the beginning
of the footballer's
decline, or is it simply a case of a Beautiful Mind meets the
beautiful game?
16 July
2003

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