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Java program to display prime numbers between intervals using function
In this article, we will understand how to display prime numbers between intervals using a function in Java. We will be using two approaches: one with user input and the other with predefined input.
Prime numbers
The prime numbers are special numbers that have only two factors 1 and itself and cannot be divided by any other number.
A number is a prime number if its only factors are 1 and itself. 11 is a prime number. Its factors are 1 and 11 itself. Some examples of prime numbers are 2, 3, 5, 7, 11, 13, and so on. 2 is the only even prime number. All other prime numbers are odd numbers.
Problem Statement
Write a program in Java to display prime numbers between intervals using a function. Below is a demonstration of the same ?
Input
Starting number : 1 Ending number : 75
Output
The prime numbers between the interval 1 and 75 are: 1 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73
Approaches to display prime numbers between intervals
Following are the steps to display prime numbers between intervals using the function ?
Basic Iterative Check
This approach is straightforward and works by individually checking each number in the given range to determine if it is a prime. A prime number is defined as a number greater than 1 that is divisible only by 1 and itself.
Following are the steps to display prime numbers between intervals using the function ?
- This function takes a number as input and checks divisibility for all integers from 2 to the square root of the number.
- If any divisor is found, the function returns false, meaning the number is not prime.
- Otherwise, it returns true.
Example
Following is an example of displaying prime numbers between intervals using an iterative approach ?
public class PrimeNumbers {
public static void main(String[] args) {
int start = 10, end = 50;
System.out.println("Prime numbers between " + start + " and " + end + " are:");
for (int i = start; i <= end; i++) {
if (isPrime(i)) {
System.out.print(i + " ");
}
}
}
// Function to check if a number is prime
public static boolean isPrime(int num) {
if (num <= 1) {
return false;
}
for (int i = 2; i <= Math.sqrt(num); i++) {
if (num % i == 0) {
return false;
}
}
return true;
}
}
Output
Prime numbers between 10 and 50 are:
11 13 17 19 23 29 31 37 41 43 47
Time Complexity: O(m*sqrt{N}), as each number in the range is checked up to its square root.
Space Complexity: O(1), as it uses no extra data structures.
Using Sieve of Eratosthenes
The Sieve of Eratosthenes is an efficient algorithm for finding all prime numbers up to a given limit. Instead of testing each number in the range individually, this approach preprocesses prime numbers using a boolean array.
How it Works?
- We create a boolean array isPrime where each index represents whether the corresponding number is prime.
- All numbers are initially marked as prime (set to true), except for 0 and 1, which are not prime.
- Starting from the smallest prime number (2), we iteratively mark all multiples of each prime as false (not prime).
- After preprocessing, the array contains all prime numbers up to end.
- Finally, we filter and print the prime numbers in the specified range [start, end].
Example
Following is an example of displaying prime numbers between intervals using the Sieve of Eratosthenes ?
import java.util.Arrays;
public class PrimeNumbers {
public static void main(String[] args) {
int start = 10, end = 50;
System.out.println("Prime numbers between " + start + " and " + end + " are:");
sievePrimes(start, end);
}
// Sieve of Eratosthenes to find all primes in a range
public static void sievePrimes(int start, int end) {
boolean[] isPrime = new boolean[end + 1];
Arrays.fill(isPrime, true); // Assume all numbers are prime
isPrime[0] = isPrime[1] = false; // 0 and 1 are not prime
for (int i = 2; i * i <= end; i++) {
if (isPrime[i]) {
for (int j = i * i; j <= end; j += i) {
isPrime[j] = false; // Mark multiples as non-prime
}
}
}
// Print primes in the specified range
for (int i = start; i <= end; i++) {
if (isPrime[i]) {
System.out.print(i + " ");
}
}
}
}
Output
Prime numbers between 10 and 50 are:
11 13 17 19 23 29 31 37 41 43 47
Time Complexity: O(nlog?(log?(n+m))) where n = end, due to sieve preprocessing and range filtering.
Space Complexity: O(n), as it uses a boolean array to store primality up to the end.
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