2, 3, 5, 7, 11, 13, 17…
These are Prime Numbers, and they go on into infinity.
Last month a team of researchers in Missouri successfully calculated the highest latest prime number and it is 9.1 million digits long. For nearly two and a half thousand years since Euclid first described the prime numbers in his book “Elements“, mathematicians have struggled to write a rule to predict what comes next in the sequence. The Swiss mathematician Leonhard Euler feared that it’s a mystery into which the human mind will never penetrate. 
But others have been more hopeful. In the middle of the 19th century, the German mathematician Bernhard Riemann discovered the connection between prime numbers and a complex mathematical function called the Zeta function. Ever since, mathematicians have laboured to prove the existence of this connection and reveal the rules behind the elusive sequence.
What are prime numbers and what is their significance?
Prime Numbers, which most people remember from school, are numbers which are not divisible by anything. A number like 17 can’t be made up of two smaller numbers multiplied together. But 15 can be written as 3 times 5, so it’s not a prime number.
They are so important to many mathematicians because they are the building blocks of all numbers. So if you take any number, it can be built by multiplying these prime numbers together. So a number like 105 is built by multiplying 3 x 5 x 7. So the primes are like the atoms of arithmetic – the hydrogen and oxygen of the world of mathematics. They are a little bit like the Periodic Table for a mathematician.
Mathematicians are constantly having to go back to understanding the primes, because primes build numbers, from numbers you get mathematics, from mathematics you get the whole of science. Quite often a mathematician will be exploring a subject and will find they need to find out more about the primes to make progress.
Did you know that prime numbers are fundamental now to the codes that protect our privacy on the Internet? Every time you send your credit card details to a shop online, we’re using prime numbers to keep that information secure. Currently we rely on the fact that we don’t understand the primes well enough to crack the encryption.
This is where it gets really interesting – prime numbers occurred in nature long before man knew about them. Many animals depend on prime numbers for their survival. Take a listen to this fascinating BBC Radio programme to discover the secrets and modern day uses of these amazing numbers.
olivia
According to Euclid there is an infinite series of prime numbers. His proof:
Suppose p is the largest prime number. Construct a new number q=p!+1=1*2*3*4*…*p+1. This number is not dividable by any number 2,3,4,etc or p (we will always get a result of at least 1). So q is therefore either a prime number or has a prime factor larger than p’s. (apologies if I wrote this up wrong, but you get the gist.)
Onto the infinity and loop thing, I see 1 and infinity as looping into each other while still satisfying the infinite abundance of possible primes:
1 is not a prime number because even though it is divisible by itself and by 1, it does not have two different factors.
On the opposite end, I see infinity, though a concept, as a prime number since it is divisible by itsself and by 1, but it can never be divided by any other number since we can never know its value.
So I see 1 and infinity come together as the perfect opposites in my head, infinity folding over itsself back to 1.
nathan
Hmmm. I haven’t listened yet and find this topic incredibly interesting, however, if Prime Numbers don’t consist of each and every single number, then they don’t go on into infinity.
Based on the idea that time and space are like loops, in that they circle back on themselves, then the only thing seperating a fixed amount of time/space from stretching on into infinity is the gap left in the loop between the start and finish points of that period of time/space. So, once you have gaps in a number sequence, you lose infinity.
I’m guessing that science hasn’t established this yet, but they will or, and should have by now.
Fuschia Faery
I heard that programme on radio 4 driving to work! It was intriguing, especially the natural patterns involving prime numbers.
Hans
I have discovered a truly remarkable proof which this margin is too small to contain….Sorry, could not help myself.
And now, for the readers of this blog, what is this obscure reference about?
Cheers,
Hans