Question

The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite lie., not prime) the multiples of each prime, starting with the multiples of 2 The sieve of Eratosthenes can be expressed in pseudocode, as follows: Input: an integer n Let A be an array of 8oo1ean values, indexed by integers 2 to n, initially all set to true. for t - 2, 3, 4, ..., not exceeding A if ?i] is true: for j. t, iat, t?+21, th31, , not exceeding n: ALJ)-false. Output: al1 t such that A[4) is true. This algorithm produces all primes <= n. It includes common optimization, which is to start enumerating the multiples of each prime i from P. The time complexity of this algorithm is Oin log log n). Write a multi-threaded program that outputs prime numbers. The program should work as follows: the user will run the program and enter a number on the command line. The program creates a thread that outputs all the prime numbers less than or equal to the number entered by the user. Also, create a separate thread that outputs this subset of the above primes that have the following property: the number that is derived by reversing the digits is also prime (e-g., 79 and 97).

Answer 1

Explanation:

Below is the Java code for above problem with proper description provided within comments itself. Below code some sample output screenshots are attached.

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Java code :

import java.util.Scanner;

// create thread
class ThreadDemo extends Thread {

        // local n
        private int n;

        ThreadDemo(int n) {
                this.n = n;
        }

        // algorithm
        public boolean[] printPrime(int n) {
                boolean A[] = new boolean[n];
                for (int i = 2; i < n; i++)
                        A[i] = true;

                for (int i = 2; i < n; i++) {
                        if (A[i]) {
                                int count = 1;
                                for (int j = (int) Math.pow(i, 2); j < n;) {
                                        A[j] = false;
                                        j = (int) Math.pow(i, 2) + (count++) * i;
                                }
                        }
                }

                for (int i = 2; i < n; i++) {
                        if (A[i])
                                System.out.print(i + " ");
                }

                return A;
        }

        void printReversePrime(boolean A[]) {
                for (int i = 2; i < n; i++) {
                        if (A[i] && reverse(i) < A.length && A[reverse(i)])
                                System.out.print(i + " ");
                }
        }

        // reverse a number
        int reverse(int n) {
                String input = String.valueOf(n);
                String result = "";
                for (int i = input.length() - 1; i >= 0; i--) {
                        result = result + input.charAt(i);
                }
                int reversedInt = Integer.parseInt(result);
                return reversedInt;
        }

        // run the thread
        public void run() {
                try {

                        // System.out.println("Thread: " + threadName);
                        System.out.print("Prime : ");
                        boolean A[] = this.printPrime(this.n);
                        System.out.print("\n\nReverese Prime : ");
                        new ThreadDemo(n).printReversePrime(A);
                        Thread.sleep(50);

                } catch (InterruptedException e) {
                        System.out.println("Thread interrupted.");
                }

        }

}

// test class
public class TestThread {

        public static void main(String args[]) {
                Scanner sc = new Scanner(System.in);
                System.out.println("Enter the n : ");
                
                ThreadDemo T1 = new ThreadDemo(Integer.parseInt(sc.nextLine()));
                T1.start();
                sc.close();
        }
}

Sample Output :

, problems-Console × @Javadoc E. Declarationずsearch-"Terminal眷Debug i. Display <terminated> TestThread lava Application] C:Program Files Javajre1.8.0_131\bin\javaw.exe (Apr 3, 2018, 12:04:43 AM) Enter the n : 100 Prime 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 Reverese Prime 2 3 5 7 11 13 17 31 37 71 73 79 97