C++ program to calculate the square root of all prime numbers between 1 and 10,000.

Segun is a C++ programmer working for Microsoft. He is going to teach a class on C++ programming to a class of interns. Assume that Segun has written a C++ program that calculates the square root of all prime numbers between 1 and 10,000. Please generate the most optimal code that Segun could have written. Please make sure that the code is very well commented.

Creating an efficient C++ program to calculate the square root of all prime numbers between 1 and 10,000 requires careful design and implementation. Here's a well-commented code that Segun could have written for this task:

#include <iostream>
#include <cmath>

using namespace std;

// Function to check if a number is prime
bool isPrime(int num) {
if (num <= 1) return false;
if (num <= 3) return true;
if (num % 2 == 0 || num % 3 == 0) return false;

for (int i = 5; i * i <= num; i += 6) {
if (num % i == 0 || num % (i + 2) == 0) return false;
}

return true;
}

int main() {
cout << "Square roots of prime numbers between 1 and 10,000:" << endl;

for (int i = 2; i <= 10000; ++i) {
if (isPrime(i)) {
double sqrtResult = sqrt(i); // Calculate square root

// Print the prime number and its square root with precision
cout << "Prime: " << i << ", Square Root: " << fixed << sqrtResult << endl;
}
}

return 0;
}

Explanation of the code:

1. We include the necessary headers for input/output and mathematical operations.

2. The `isPrime` function checks whether a given number is prime. It uses a fast primality testing algorithm based on the fact that prime numbers greater than 3 can be expressed in the form 6k ± 1.

3. In the `main` function, we iterate from 2 to 10,000, checking each number for primality using the `isPrime` function.

4. If a number is prime, we calculate its square root using the `sqrt` function and print both the prime number and its square root with fixed precision.

This code efficiently calculates the square root of all prime numbers between 1 and 10,000, ensuring that the code is well-commented to make it understandable for Segun's class of interns.

Please show the output of running the program after it has been compiled.

I'm unable to execute code directly, but I can simulate the expected output for you. When you compile and run the program, the output should look something like this:

Square roots of prime numbers between 1 and 10,000:
Prime: 2, Square Root: 1.414214
Prime: 3, Square Root: 1.732051
Prime: 5, Square Root: 2.236068
Prime: 7, Square Root: 2.645751
Prime: 11, Square Root: 3.316625
Prime: 13, Square Root: 3.605551
Prime: 17, Square Root: 4.123105
Prime: 19, Square Root: 4.358899
Prime: 23, Square Root: 4.795832
Prime: 29, Square Root: 5.385165
Prime: 31, Square Root: 5.567764
Prime: 37, Square Root: 6.082763
Prime: 41, Square Root: 6.403124
Prime: 43, Square Root: 6.557439
Prime: 47, Square Root: 6.855655
Prime: 53, Square Root: 7.280110
Prime: 59, Square Root: 7.681146
Prime: 61, Square Root: 7.810250
Prime: 67, Square Root: 8.185353
Prime: 71, Square Root: 8.426150
Prime: 73, Square Root: 8.544004
Prime: 79, Square Root: 8.888194
Prime: 83, Square Root: 9.110434
Prime: 89, Square Root: 9.433981
Prime: 97, Square Root: 9.848858
...

The program calculates and prints the square roots of prime numbers between 1 and 10,000, displaying both the prime number and its square root with fixed precision.

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