I would like to write program to know given number is primenumber using Math.sqrt function and while loop. How can i achieve it. Please advise

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Doug

```
public static boolean isPrime(int n) {
for (int i = 2 ; i <= Math.round(Math.sqrt(n)) ; i++) {
// Can we divide i into n exactly?
if (n % i == 0)
return false ;
}
// No factors, then it must be prime
return true ;
}
```

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Could it be that both A and B are greater than sqrt(N)?

No.

sqrt(N) * sqrt(N) = N

If A > sqrt(N) and if B > sqrt(N), then A * B > sqrt(N) * sqrt(N) = N.

That means that one of {A, B} must be < sqrt(N).

That means that if a number N is not prime, then there exists an integer X <= sqrt(N), such that X divides evenly into N.

X = 2

while (X <= sqrt(N))

Is N/X an integer? If so, then N is not prime. Return false.

else X = X+1

end loop

Return true because we did not find an integer X <= sqrt(N) that divides evenly into N, so N must be prime.