Function that finds prime numbers between two intervals - c++

Question

I have written the bulk majority of the program, I'm just having trouble debugging it. Something must be wrong with my computation of the prime numbers. For anything I try, it says there are 0 prime numbers. Any help would be greatly appreciated. Code and output are below.
Note: For this program, I am not allowed to use vectors or arrays.
#include <iostream>
#include <cmath>
using namespace std;
// FUNCTION PROTOTYPE FOR read_range
void read_range(int &lower, int &upper);
// FUNCTION PROTOTYPE FOR is_prime
bool is_prime(const int num);
// FUNCTION PROTOTYPE FOR display_primes
void display_primes(const string &prime, const int lower, const int upper);
// DO NOT MODIFY THE MAIN ROUTINE IN ANY WAY
int main()
{
int imin(0), imax(0);
// Read in range
read_range(imin, imax);
// Print prime numbers
cout << endl;
display_primes("Primes: ", imin, imax);
return 0;
}
// DEFINE FUNCTION read_range() HERE:
void read_range(int &lower, int &upper){
cout << "Enter minimum and maximum: ";
cin >> lower >> upper;
while (lower < 2 || upper < 2 || lower > upper){
if (lower < 2 || upper < 2) {
cout << "Error. Minimum and maximum must be at least 2." << endl; }
else if (lower > upper) {
cout << "Error. Minimum must be less than maximum." << endl; }
cout << "Enter minimum and maximum: ";
cin >> lower >> upper; }}
// DEFINE FUNCTION is_prime() HERE:
bool is_prime(const int num) {
for (int i = 2; i <= sqrt(num); i++) {
if (num % i == 0) {
return 0; } // Is not prime
else {
return 1; }}} // Is prime
// DEFINE FUNCTION display_primes() HERE:
void display_primes(const string &prime, const int lower, const int upper) {
int count = 0;
int commaCheck = 0;
for (int i = lower; i <= upper; i++) {
if (is_prime(i)) {
count = count + 1; }}
if (count == 1) {
cout << "There is " << count << " prime number in this range." << endl; }
else {
cout << "There are " << count << " prime numbers in this range." << endl; }
if (count != 0) {
cout << prime;
for (int i = lower; i <= upper; i++) {
if (is_prime(i)) {
if (count == 1) {
cout << i;}
else {
commaCheck = commaCheck + 1; }
if (commaCheck != count) {
cout << i << ","; }
else {
cout << i; }}}
cout << endl; }
else {
cout << "No primes to display." << endl; }}
Output (with input of 2,3)
Enter minimum and maximum:
There are 0 prime numbers in this range.
No primes to display.

Answer 1

is_prime has two issues.
If sqrt(num) is less than 2 the loop never executes and your function has undefined behaviour as it ends without returning (your compiler probably should have warned you about this issue)
If the number is not even then in the first iteration of the loop you call return 1 which means all odd numbers will be labelled as prime.
Changing your loop to this will work (if not be very efficient, there are much better algorithms for finding prime numbers):
bool is_prime(const int num) {
for (int i = 2; i <= sqrt(num); i++) {
if (num % i == 0) {
return false;
}
}
return true;
}

Answer 2

This is one of the default algorithms for checking how many numbers between two intervals are prime numbers, there are many alternatives, but this is what i prefer and is short and easy to remember
#include <iostream>
using namespace std;
int main(){
int i1min, i1max;
int i, j, k = 0;
bool primeTest;
cin >> i1min;
cin >> i1max;
for(i=i1min; i<=i1max; i++) {
primeTest = false;
for (j=2; j<=i/2; j++) {
if (i % j == 0) {
primeTest = true;
break;
}
}
if (primeTest == false)
k++;
}
cout << k;
return 0;
}