Royal Institute Christmas Lectures 2006
The Curious Incident of the Never Ending Number
The Number Mysteries
Professor du Sautoy introduced the 178th Royal Institute Christmas Lecture by explaining that this year's lectures would reveal how mathematicians have helped solve some of the big mysteries of the universe and how mathematics can make us rich.
Million Dollar Bang
An explosion of dollar bills, one million of them to be precise, cascades onto the heads of the audience in truly extravagant style.
A Million Dollar Explosion
Professor Marcus du Sautoy explains that while mathematics has solved a lot of the mysteries of the universe, there are still a lot of problems that even the cleverest of mathematicians cannot understand. A businessman in America has offered one million dollars to anybody who can solve any of these mysteries. Why is a businessman offering money for mathematics problems? He realises that mathematics can help us answer problems of science, technology, the economy, it can even help us to save the planet. So each of this year's five lectures will be an introduction to how to win this million dollars.
In Professor du Sautoy's opinion the most enigmatic of all numbers are the prime numbers. A prime number is one that is only divisible by itself and one.
Intriguingly starting with the number one we discover that current thinking has decided that this is not a prime number. It is divisible by 1 and itself (1) but as this produces the same result it is not prime.
Remembering that the Christmas Lectures are aimed, primarily, at younger viewers, Marcus demonstrates a way of discovering all of the prime numbers between 1 and 50. A frames with 50 numbered balloons is brought on stage. It has already been decided that 1 is not a prime number so Marcus bursts this balloon. The next number is 2 which is prime so it will stay, but any higher number that is divisible by 2 is not prime, so one of the young volunteers depresses his detonator and all the balloons with numbers above 2 which appear in the two-times table are exploded. 3 is a prime number so the exercise is repeated with the numbers in the three-times table, and the 5 and the 7.
The observant among you will notice that the number 31 is missing, this was a technical hitch with the balloon popper. 31 is a prime number. While this is a useful demonstration it is an ungainly way to identify larger prime numbers.
Professor du Sautoy explains that one of the skills of a mathematician is to see and identify patterns and that the importance of prime numbers is that they are the building-blocks of his subject.
He then poses a question: Who were the first to discover the primes? a) The Ancient Greeks b) Insects c) The Ancient Chinese.
Surprisingly it wasn't a mathematician at all. A curious little insect which lives in the forests of North America hides underground doing absolutely nothing for 17 years, after which time the Cicadas emerge en-masse for a brief breeding season of only six weeks. Is it a coincidence that the 17 year period is a prime number? Apparently not, there is another species that stays underground for 13 years and yet another that stays underground for 7 years. Why should a prime number period help the Cicadas? Professor du Sautoy is not sure, but he has a hypothesis. A predator that may appear periodically is less likely to coincide with the Cicada's breeding season boosting the evolutionary survival rate of the Cicada.
Prime numbers are used as building-blocks for Internet security. Each secure Internet transaction uses a very large prime number to encode it.
The largest prime number so far discovered was found by an amateur with his desktop computer. It has 9.8 million digits and can be expressed as 232,582,657 - 1. This is the 44th Mersenne Prime.
This number is known as a Mersenne prime named after Marin Mersenne a 17th century French Monk who, while not primarily a mathematician, did extensive work with prime numbers.
GIMPS (The Great Internet Mersenne Prime Search) is a global project where tens of thousands of volunteers use idle time on their PCs to help discover the next Mersenne Prime. There is a $100,000 prize up for grabs for the first person to discover a 10 million digit prime number.