Finding out wheather a number is composite

TO find out wheather a number- X is composite we must look for a factor -Y such that:

1 <Y <X Eg:for number 8 we must look In set {2 3 4 5 6 7}

But this takes a long time so we can look for a factor Y such that 1 <Y<X/2 as all other factors of a number fall within this range Eg: for number 8 we can look in {2 3 4 }

But it is enough even if we find 1 other factor of the number to show that it is composite. We can do this using the this property of numbers

If X=a X b.(where b>=a) Either a=b=X(^1/2) or a<X(^1/2).

So we use use 2 smaller ranges to find out wheather the number is prime:-

1. 1 <Y <=X(^1/2)

2. X(^1/2) <=Y < =X/2 Eg: for 6 we must look in

1.{2}

2.{3}

But after a particular number one of the methods is more advantageous .

Which is that number(intiger)?(If no such number exists type 0)