## Prime Factors Facts

In number theory, we are concerned with natural numbers. Amongst those, the most important are the so-called prime numbers. A prime number is a number which cannot be divided by any other number except 1 and itself. A number which is not prime is composite. Composite numbers are “composed” of prime numbers; to be precise, the fundamental theorem of arithmetic says that any number can be written as product of powers of prime numbers uniquely up to rearrangement. So, prime numbers are the building blocks or atoms of all numbers !! By the way, 1 is considered neither prime nor composite.

So, what are the examples of prime numbers? Take the Sieve of Eratosthenes. (Google this !!!). The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, …

Surprisingly, as you pass 100, the “density of primes” starts lessening. If you go deeper into this, you are concerned with the “distribution of primes’…Many immortal mathematicians have devoted a major part of their lives to the study of primes…Carl Friedrich Gauss (one of his hobbies was to keep on finding more and more primes…); Bernhard Riemann who gave us a million dollar math problem on prime numbers (http://www.claymath.org ) etc.

If you are curious, or just want to take a one hour coffee break, refer to “A Brief History of Primes” by Prof. Manindra Agarwal of IIT, Kanpur http://claymath.msri.org/agrawal2002.mov

More later,

Nalin Pithwa

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