by Steve Marshall

Created on: April 21, 2009

Prime numbers are simple enough in their basic make up and definition, but there are some unknown aspects of prime numbers that even until today defy the best brains of the best mathematicians in the world of today.

Primes numbers are deceptively simple. They are defined as being any whole number that is divisible only by itself and the number one.

A mathematician would put it more complexly stated maybe something like this:

A prime number is a natural number that is an integer greater than one if its only positive divisors, ( called factors) are one and itself.

An integer can be sometimes be divided by numbers that are known as prime devisors. The prime devisors of the number 15, for example are the numbers 3 and 5, because these devisors are prime numbers. The number 8 can be divided by the numbers 2 and 4, but these are not prime devisors.

Prime numbers are known as the building blocks of all positive numbers. Every positive number is a product of prime numbers in one and only one way. For example the number 100. It's product using only prime numbers is like this: 5 x 5 x 2 x 2. Prime numbers can generate all the other integers in this way.

The number one was once also included within the field of prime numbers, but it is no longer included now because of the more stricter definition of what a prime number is. The number one is somewhat unique in itself and doesn't follow the modern definition of a prime number. Every number has a unique factorization of itself into primes called prime devisors above. The number one doesn't meet this criteria. It is only itself (1 x 1 = 1), and can only be factored into itself. It doesn't have any other prime devisors as such.

It was shown way back in 300 BC by the Greek mathematician Euclid that there are an infinite number of prime numbers and that they are all spaced apart in a funny way. The spacing is irregular and some times they can be far apart, and sometimes there can be a pair of primes that are very close together. For example the prime numbers 41 and 43, and 101 and 103, are instances of being a pair of such primes. Between the numbers 109 and 127 though, there is a large gap where there is only one other prime number, the number 113.

These pairs of primes are also known as twin primes. They differ from the preceding prime number only by the number 2. Strangely enough this occurrence of twin primes is also an infinite occurrence within the field of prime numbers and doesn't stop from ever happening at some stage after

• 1
• 2
• 3
• 4
• Next Page >>