C++ Program To Print Prime Numbers From 1 To N

Explore our efficient C++ program to print prime numbers from 1 to N. Designed for beginners and advanced programmers alike, this guide provides a clear and concise program that systematically finds and prints prime numbers within a user-specified range. Whether you’re learning about prime numbers, enhancing your problem-solving skills, or seeking a practical implementation of loops and conditionals in C++, this example offers valuable insights.

What is Prime Numbers ?

Prime numbers are a fundamental concept in mathematics, particularly in the field of number theory. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. In simpler terms, a prime number is a number that can only be divided evenly (without a remainder) by 1 and itself.

Examples: The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29,…

Pseudo code for C++ Program to Print Prime Numbers From 1 to N.

Begin
    Declare N, i, j

    // Prompt user to enter the value of N
    Print "Enter the value of N: "
    Read N

    // Loop from 2 to N (1 is not a prime number)
    For i = 2 to N do
        Declare isPrime = true

        // Check if the number i is prime
        For j = 2 to sqrt(i) do
            If i is divisible by j then
                Set isPrime = false
                Break the loop
            EndIf
        EndFor

        // If isPrime is true, print the number
        If isPrime is true then
            Print i
        EndIf
    EndFor
End

Explanation:

  1. Start: This signifies the beginning of the program.
  2. Declare variables: N, i, j, isPrime:
    • N: This will hold the upper limit up to which prime numbers are to be found.
    • i and j: These are loop counters. i is used to iterate through each number from 2 to N, and j is used for checking the divisibility of i.
    • isPrime: A boolean variable used to determine if the current number i is prime or not.
  3. Input the value of N: Here, the program will take an input from the user, which is the value of N, the upper limit for finding prime numbers.
  4. For i = 2 to N, do steps 5-9: This is a loop that starts with i = 2 and continues until i equals N. Each iteration of this loop will check if the current value of i is a prime number.
    1. Set isPrime = true: Initially, for each number i, it is assumed to be prime (isPrime is set to true).
    2. For j = 2 to i/2, do step 7: This is a nested loop inside the i loop. This loop checks if the number i is divisible by any number from 2 to i/2. If a number is not divisible by any other number up to its half, it is prime.
      1. If i mod j is 0, set isPrime = false and break the loop: This step checks if i is divisible by j (using the modulus operator %). If i is divisible by j, then i is not a prime number, so isPrime is set to false, and the loop is exited using the break statement.
    3. If isPrime is true, print i: After the inner loop, if isPrime is still true, it means that i is a prime number, and it is printed.
  5. End For: This marks the end of the outer loop. The program will continue to iterate until all numbers from 2 to N have been checked.
  6. End: This signifies the end of the program.

Approach for C++ Program to Print Prime Numbers From 1 to N

To create a C++ program that prints prime numbers from 1 to N, you can follow this approach:

  1. Input the Upper Limit (N):
    • Begin by asking the user to input the upper limit, N. This is the number up to which you want to find prime numbers.
  2. Initialize Variables:
    • You’ll need variables for loop control (commonly i and j) and a flag variable (like isPrime) to indicate whether a number is prime.
  3. Iterate Through Numbers from 2 to N:
    • Start a loop with i from 2 up to N (inclusive). We start from 2 because 1 is not considered a prime number.
  4. Check for Prime Numbers:
    • For each number i, check if it is a prime number.
      • Set isPrime to true initially for each i.
      • Run an inner loop with j from 2 to i/2. This range is sufficient because a number greater than half of i cannot evenly divide i.
      • In the inner loop, check if i is divisible by j (i.e., i % j == 0). If so, set isPrime to false and break out of the inner loop, as this means i is not a prime number.
  5. Print the Prime Number:
    • After the inner loop, if isPrime is still true, it means i is a prime number, so print i.
  6. Repeat for Next Number:
    • Continue the outer loop to check the next number in the sequence until you reach N.
  7. End of Program:
    • Once the loop completes, the program ends. All prime numbers between 1 and N will have been printed.

Logic for Prime Number from 1 to N

  1. Input the upper limit (N): Prompt the user to enter the value of N.
  2. Check for prime numbers: For each number i from 2 to N (since 1 is not a prime number), check if it is a prime number.
  3. Prime number checking logic: A number is prime if it is only divisible by 1 and itself. So, for each number i, we check if it can be divided by any number from 2 to sqrt(i). If it can’t be divided by any of these numbers, it is a prime number.
  4. Print the prime numbers: If a number is found to be prime, print it.

C++ Program to Print Prime Numbers From 1 to N

#include <iostream>int main() {
    int N, i, j;
    bool isPrime;

    // Asking for upper limit
    std::cout << "Enter the upper limit (N): ";
    std::cin >> N;

    // Loop through each number from 2 to N
    for (i = 2; i <= N; i++) {
        isPrime = true; // Assume the current number is prime

        // Check if the number is divisible by any number from 2 to i/2
        for (j = 2; j <= i / 2; j++) {
            if (i % j == 0) {
                isPrime = false; // If divisible, it's not prime
                break; // No need to check further
            }
        }

        // If isPrime is still true, the number is prime
        if (isPrime) {
            std::cout << i << " ";
        }
    }

    return 0;
}

Explanation of the Program:

  1. Include Headers:
    • #include <iostream>: This includes the IOstream library for input-output operations.
  2. Main Function:
    • int main() { ... }: The entry point of the program.
  3. Variable Declaration:
    • int N, i, j;: Declares integers N (upper limit), i (number to check), and j (divisor).
    • bool isPrime;: A boolean variable to flag whether a number is prime.
  4. Input Upper Limit (N):
    • The user is prompted to enter the upper limit N.
  5. Loop to Check Prime Numbers:
    • The outer loop for (i = 2; i <= N; i++) iterates through each number from 2 to N.
    • isPrime is initially set to true for each number i.
  6. Check for Divisibility:
    • The inner loop for (j = 2; j <= i / 2; j++) checks if i is divisible by any number from 2 to its half.
    • If i % j == 0, isPrime is set to false, and the loop breaks.
  7. Print Prime Numbers:
    • If isPrime is true after the inner loop, i is a prime number and is printed.
  8. End of Program:
    • The program ends with return 0;, which is a successful termination.

When you run this program, it will ask for an upper limit N. It will then print all prime numbers from 2 up to and including N. The logic behind only checking up to i/2 for divisors is that a number cannot have a factor greater than half of its value, other than itself. This makes the program more efficient.

Output:

Enter the upper limit (N): 10
2 3 5 7

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