Software Engineering

# Is a Number Prime in Java

## The challenge#

Define a function that takes one integer argument and returns a logical value `true` or `false` depending on if the integer is a prime.

Per Wikipedia, a prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Requirements:

• You can assume you will be given an integer input.
• You can not assume that the integer will be only positive. You may be given negative numbers as well (or “).
• NOTE on performance: There are no fancy optimizations required, but still the most trivial solutions might time out. Numbers go up to 2^31 (or similar, depends on language version). Looping all the way up to `n`, or `n/2`, will be too slow.

Examples:

``````is_prime(1)  /* false */
is_prime(2)  /* true  */
is_prime(-1) /* false */
``````

## The solution in Java code#

Option 1:

``````public class Prime {
public static boolean isPrime(int num) {
return num > 1 && java.math.BigInteger.valueOf(num).isProbablePrime(20);
}
}
``````

Option 2:

``````public class Prime {
public static boolean isPrime(int number) {
if(number < 2)
return false;
for (int i=2; i<=Math.sqrt(number); i++){
if(number % i == 0)
return false;
}
return true;
}
}
``````

Option 3:

``````public class Prime {
public static boolean isPrime(int num) {
if (num == 2) return true;
if (num < 2 || num % 2 == 0) return false;
for (int i = 3; num >= i*i; i+=2) {
if (num % i == 0) return false;
}
return true;
}
}
``````

## Test cases to validate our solution#

``````import static org.junit.Assert.assertTrue;
import static org.junit.Assert.assertFalse;
import org.junit.Test;

public class PrimeTest {
@Test
public void testBasic() {
assertFalse("0  is not prime", Prime.isPrime(0));
assertFalse("1  is not prime", Prime.isPrime(1));
assertTrue ("2  is prime",     Prime.isPrime(2));
assertTrue ("73 is prime",     Prime.isPrime(73));
assertFalse("75 is not prime", Prime.isPrime(75));
assertFalse("-1 is not prime", Prime.isPrime(-1));
}
@Test
public void testPrime() {
assertTrue("3 is prime", Prime.isPrime(3));
assertTrue("5 is prime", Prime.isPrime(5));
assertTrue("7 is prime", Prime.isPrime(7));
assertTrue("41 is prime", Prime.isPrime(41));
assertTrue("5099 is prime", Prime.isPrime(5099));
}
@Test
public void testNotPrime() {
assertFalse("4 is not prime", Prime.isPrime(4));
assertFalse("6 is not prime", Prime.isPrime(6));
assertFalse("8 is not prime", Prime.isPrime(8));
assertFalse("9 is not prime", Prime.isPrime(9));
assertFalse("45 is not prime", Prime.isPrime(45));
assertFalse("-5 is not prime", Prime.isPrime(-5));
assertFalse("-8 is not prime", Prime.isPrime(-8));
assertFalse("-41 is not prime", Prime.isPrime(-41));
}
}
``````