hi Sudarshan,

> Its been a thrill to me to use the pari to factorize

> large numbers.

You might also like to try out MIRACL's factoring

package below.

http://indigo.ie/~mscott/#other
> The question:-

> The probability that a given big number n is a

> mobius number is very

> high. What is the mathematical reasoning behind

> this.

According to mathworld (URL below) the asymptotic

density of square free numbers is 6/(pi^2) which is

approximately 60%. So you should hit a squareful

number nearly 40% of the time. With what probability

did you find that the number under test to be

squarefree and for how many integers did you test?

http://mathworld.wolfram.com/Squarefree.html
Sarad.

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