Prime number generator in C++ ( alex allain jumping into c++) - c++

Question

i just started learning C++ , I am an art major (i know) and i started learning c++ from Alex Allain's jumping into c++ and in that book i have understood most of the stuff , I am currently stuck on prime number generator and i am having difficulty in the grasping the algothrim.I am not able to understand it after the first for loop
#include <iostream>
// note the use of function prototypes
bool isDivisible (int number, int divisor);
bool isPrime (int number);
using namespace std;
int main()
{
for (int i = 0; i < 100; i++) {
if (isPrime(i)) {
cout << i << endl;
}
}
}
bool isPrime(int number)// i don't understand from this point onward.
{
for (int i = 2; i < number; i++) {
if (isDivisible(number, i)) {
return false;
}
}
return true;
}
bool isDivisible(int number, int divisor)
{
return number % divisor == 0;
}
I humbly request anyone to help me understand this code step by step.
thank you so much

Answer 1

To understand the above code you first need to understand what are prime numbers.
A prime number is a number that is only divisible by 1 and itself.
For example:-
5 is divisible by 1 and 5 only (prime)
4 is divisible by 1, 2 and 4 (not prime)
So to check whether the number is prime or not we need to check whether it is divisible by any other number other than 1 and itself and if it is divisible by any other number then it is not prime.
So now let's understand this using the above code :-
bool isPrime(int number) {
for(int i=2;i<number;i++) { // this loops runs from 2 to number - 1
if(isDivisible(number,i)) { // this checks if the number is divisible by i if the number is divisible by i then the function isDivisible will return true
return false; // If the above condition is true that means the number is divisible by i and that means the number is not prime so we return false
}
}
return true; // and if the number is not divisible by any number between (2 to number-1) that means it is prime so we return true
}
for the second part of the code, we check whether the number is divisible by i
bool isDivisible(int number ,int divisor) {
return number % divisor == 0; /* it return true if number is divisible by divisor and false otherwise.
example:-
1. number = 4 divisor = 2
4%2 == 0 true
2. number = 5 divisor = 3
5%3 == 0 false
*/
}
So now let's see the whole code in working.
example:-
number = 5
isPrime(5)
we loop from 2 to 4
isDivisible(5,2) = false;
isDivisible(5,3) = false;
isDivisible(5,4) = false;
loop ends and we return true (the number is prime);
number = 4
isPrime(4)
we loop from 2 to 3
isDivisible(4,2) = true;
the above condition is true so we return false (the number is not prime);
Hope this helped you in understanding the above code