confusion 1: Loop used to test if i is divisible by any number, the condition j<=(i/j) is used so that numbers wont be checked twice. if no number is divisible, then the loop will not break in between result j>(i/j)

This is how the author of the book explained it:
"You can stop at the value
of i / j because a number that is larger than i / j cannot be a factor of i"

for example 6 = 1*6 or 2*3 or 3*2 or 6*1, and you want to find out if 6 is divisible by any other number, you only have to go through 1,2 and 3 instead of 1-6

That code is kind of confusing if you do not know the meaning of i/j.

Take i = 10 for example, and we want to see if 10 is a prime number. To do this, what
your code does is run to all numbers from j = 2 to j < i/j. If it successfuly runs through the whole loop then its a prime, if not then your "confusion2" checks if the loop ended prematurely.

Personally, that code is looks confusing to beginners, and I would suggest something like this to beginners. That is after they have learned about function.

#include <iostream>
using namespace std;
//returns true, if the 'lhs' is evenly divisible by 'rhs'
bool isEvenlyDivisible(int lhs, int rhs){
return lhs % rhs == 0;
}
/* A number is a prime if its evenly divisionable by
1 and its self only. Ex, 2 is a prime because 2 divides into 1 evenly
and 2 divideds to 2 evenly. Anything else divided into 2 has a remainder */
//function returns true if 'num' is a prime otherwise returns false
bool isPrime(int num){
//if num < 2 then its by definition not a prime
if(num < 2) return false;
//initial condition, assume num is prime
bool isAPrime = true;
//runs through i = 2 to num, to check if any number evenly divides into 'num'
//notice how checkFacotor is never equal to 1, or num. So if its divisible by any
//number in between, then 'num' is not a prime
for(int checkFactor = 2; checkFactor < num; ++checkFactor){
//is num is evenly divisible by checkFactor, where checkFactor is not 1 or num
if(isEvenlyDivisible(num,checkFactor)){
isAPrime = false; //then num is not a prime
break; // since its not a prime then exit the loop
}
}
return isAPrime;
}
int main()
{
//runs through all numbers in range of [0,100) to check if its a prime
for(int i = 0; i < 100; ++i)
{
if(isPrime(i)){
cout << i << " is a prime\n";
}
}
}

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