Authors:
Walter Savitch ,julia Lobur
Chapter:
More Flow Of Control
Exercise:
Programming Projects
Question:14 | ISBN:9780321531346 | Edition: 7
Question
Write a program that finds and prints all of the prime numbers between 3 and 100. A prime number is a number such that one and itself are the only numbers that evenly divide it (e.g., 3, 5, 7, 11, 13, 17, …).
One way to solve this problem is to use a doubly nested loop. The outer loop can iterate from 3 to 100 while the inner loop checks to see if the counter value for the outer loop is prime. One way to see if number n is prime is to loop from 2 to n−1 and if any of these numbers evenly divides n, then n cannot be prime. If none of the values from 2 to n−1 evenly divide n, then n must be prime. (Note that there are several easy ways to make this algorithm more efficient.)
Answer
PROGRAM CODE:
#include <iostream>
using namespace std;
bool isPrime(int num) {
if (num < 2) {
return false; // Numbers less than 2 are not prime
}
// Check divisibility from 2 to sqrt(num)
for (int i = 2; i * i <= num; i++) {
if (num % i == 0) {
return false; // num is divisible by i, so it's not prime
}
}
return true; // num is prime
}
int main() {
int lowerLimit = 3;
int upperLimit = 100;
cout << "Prime numbers between " << lowerLimit << " and " << upperLimit << " are:\n";
for (int i = lowerLimit; i <= upperLimit; i++) {
if (isPrime(i)) {
cout << i << " ";
}
}
cout << endl;
return 0;
}
OUTPUT OF THE PROGRAM CODE:
Prime numbers between 3 and 100 are:
3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97