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

The line in question is basically trying to find numbers that are factors of your given number (and eliminating them as not-primes). If you find no factors of a given number then you can say that the number is prime.

As far as finding factors goes, you only need to go up to sqrt(N) because if you go any higher you are looking at numbers you have already seen before. This is because every time you find a factor you actually find two factors. If a is a factor of N then N/a and a are both factors of N.