C++ Exercises: Prints a twin prime which has the maximum size among twin primes less than or equals to n

Last update on December 20 2024 12:20:57 (UTC/GMT +8 hours)

Max Twin Prime Below n

Write a C++ program that reads the integer n and prints a twin prime that has the maximum size among twin primes less than or equal to n.

According to wikipedia "A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two".

Visual Presentation:

Sample Solution:

C++ Code :

#include <iostream> // Including input-output stream header file
#include <cmath>    // Including math functions header file
using namespace std; // Using the standard namespace

int main() { // Start of the main function
    const int num_primes = 10005; // Constant to define the maximum limit for finding primes
    bool primes[num_primes]; // Declaring an array to store prime flags for numbers up to num_primes

    // Initializing the prime number flags to true for all indices except 0 and 1
    for (int i = 2; i != num_primes; ++i) {
        primes[i] = true;
    }

    // Loop to sieve out non-prime numbers using the Sieve of Eratosthenes algorithm
    for (int i = 2; i != int(sqrt(num_primes)); ++i) {
        if (primes[i]) { // Checking if the current number is marked as a prime
            // Marking all multiples of the current prime as non-prime
            for (int j = 2; i * j < num_primes; ++j) {
                primes[i * j] = false;
            }
        }
    }

    int n;
    cout << "Input an integer:\n"; // Asking the user to input an integer
    cin >> n; // Reading the input from the user

    cout << "Twin primes are:\n"; // Displaying twin primes

    // Loop to find and display twin primes starting from the given input number
    for (int i = n; i - 2 >= 0; --i) {
        if (primes[i] && primes[i - 2]) { // Checking if the current number and its preceding number are both prime
            cout << i - 2 << " " << i << endl; // Displaying the twin primes
            break; // Exiting the loop after finding the first twin primes
        }
    }

    return 0; // Indicating successful completion of the program
}

Sample Output:

Input an integer:
Twin primes are:
11 13

Flowchart:

C++ Code Editor:

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