program logic of printing the prime numbers

Question

Can any body help to understand this java program?

It just prints prime numbers, as you enter how many you want and it works well.

class PrimeNumbers
{           


        

Answer 1

A number N is prime if the only integers that satisfy N = A*B are 1 and N (or N and 1).

Now to check a number N as prime we could search all A from 2 to N and B from 2 to N, to see if N=A*B. That would take O(N^2) time, and is really inefficient.

It turns out that we only need to divide N by a number and see if there is a remainder. This brings it down to O(N).

And further, we don't need to check all the way from A=2 to A=N. If A is greater than sqrt(N), then B must be less than sqrt(N). Therefore we only need to check A from 2 to sqrt(N) to see if N/A has a remainder.