A prime number is an integer greater than 1 that is divisible by only itself and 1. For example the first ten primes are:
A positive integer greater
than 1 that is not a prime is called composite. The number 1 itself is considered neither prime nor composite. In fact Ernst Gabor Strauss
The primes are the building bricks for arithmetic,
and 1 is just not a brick!
One of the few things we know about primes is that there are infinitely many of them. This was proved by the ancient Greeks, and Euclid in particular, in about 350 B.C. The largest prime known today is
which was discovered on the 14th of November 2001. This prime has a whopping 4,053,946 digits. The discovery of a new prime used to be celebrated with a glass of wine or a postage stamp;
nowadays it is boasted about by computer manufacturers or software companies to seek publicity.
Primes certainly would occupy a less central position in number theory were it not for a result known as the Fundamental Theorem of Arithmetic which states:
Any positive integer (other than 1) can be written as the product of prime numbers uniquely.
As the name suggests it is one of the most basic but important propositions in all of mathematics.
Primes, once associated exclusively with pure mathematics, have recently found an unexpected ally in the areas of national security and in particular public-key cryptography. This uses the principle that it is very difficult to find the factors of a product of two very large primes.