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Numbers of wonder part 1 February 15, 2009

Posted by Anand Mallaya in mathematics, technology.
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Wonder what numbers has to do in a tech blog? I will tell you.
In a series of posts we will explore a group of numbers that are fascinating and mysterious. Let us start with prime numbers.

Prime Numbers

A prime number is a number which has only two factors, 1 and the number itself. In other words it is divisible only by 1 and itself.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97….
Prime numbers are enigma not only for the school children but the top mathematicians and even the best computing machines of our time. I was fascinated by the beauty of the numbers many times. They are the building blocks or atoms of all other numbers. Any other number can be represented as a product of two or more prime numbers. The fact that they are still mysterious even in the time of super computers of teraflops of computing power, makes them more enigmatic and appealing for the world’s top brains.

Though the distribution may seem random, they forms special patterns when arranged in certain manners(image below).

(image courtesy http://www.franken.de)

If it is not fascinating then what is?. It looks as mysterious as theNazca Lines .

Nature has a special place for numbers in its creativity. You will see numbers like Golden ratio, Fibonasci numbers, pi, e, and Phi. Suddenly it comes to my mind that Prime numbers too have significance that we have not found yet(or may be I). Though the numbers are easy to understand, their identification and computation are done using complex algorithms that takes lot of computing power, especially when the number of digits are high. Thus some of those algorithms are used to benchmark computer chips.
In my point of view,  there are lot more to be revealed about the prime numbers. The largest prime number revealed to us can be seen as a benchmark for the level of technological advancement of human civilization itself.
Prime numbers are important in computing as well. Several public-key cryptography algorithms, such as RSA, are based on prime numbers .
They are so important that there are a number of distributed computing projects initiated in order to find large prime numbers that require large amount of computing power.
Some of the projects are:

Here are some links for more information
Prime numbers on Wikipedia
Patterns in Primes
Prime Numbers at MathWorld
Article from The Seed magazine
Some Results of Computational Research in Prime Numbers
End of Numbers of wonder part 1
more numbers to come

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