# Difference between the largest and the smallest primes in an array in Java

JavaObject Oriented ProgrammingProgramming

## Problem Statement

With a given array of integers where all elements are less than 1000000. Find the difference between the largest and the smallest primes in an array.

## Example

Array: [ 1, 2, 3, 4, 5 ]

Largest Prime Number = 5
Smallest Prime Number = 2

Difference = 5 - 3 = 2.

## Solution

Use Sieve of Eratosthenes approach, which is an efficient way to find out all prime numbers smaller than a given number. Then we will figure out the largest and smallest prime number to get the required difference.

## Example

Live Demo

Following is the program in Java to find the required output.

public class JavaTester {

static int MAX = 1000000;
static boolean prime[] = new boolean[MAX + 1];

public static void runSieveOfEratosthenes(){
//reset prime flags to be true
for(int i=0; i< MAX+1; i++) prime[i] = true;
//set 1 as non-prime
prime = false;

for (int p = 2; p * p <= MAX; p++) {
// If prime[p] is not modified, then it is a prime
if (prime[p]) {
// Update all multiples of p
for (int i = p * 2; i <= MAX; i += p) prime[i] = false;
}
}
}

public static int difference(int arr[]){
int min = MAX + 2;
int max = -1;
for (int i = 0; i < arr.length; i++) {
// check if the number is prime or not
if (prime[arr[i]] == true) {
// set the max and min values
if (arr[i] > max) max = arr[i];
if (arr[i] < min) min = arr[i];
}
}
return max - min;
}

public static void main(String args[]){
// run the sieve
runSieveOfEratosthenes();
int arr[] = { 1, 2, 3, 4, 5 };
System.out.println(difference(arr));
}
}

## Output

3