C++ PrimeNumber Class

Question

Here is the problem I am trying to solve:

Define a class named PrimeNumber that stores a prime number. The default constructor should set the prime number to 1. Add another constructor that allows the caller to set the prime number. Also, add a function to get the prime number. Finally, overload the prefix and postfix ++ and -- operators so they return a PrimeNumber object that is the next largest prime number (for ++) and the next smallest prime number (for --). For example, if the object's prime number is set to 13, then invoking ++ should return a PrimeNumber object whose prime number is set to 17. Create an appropriate test program for the class.

This is not for a class, I am just trying to teach myself C++ because I need it as I will start my PhD in financial mathematics at FSU this fall. Here is my code thus far:

#include <iostream>
#include "PrimeNumber.h"
using namespace std;

int main() {
int x;
cout << "\nenter prime number: ";
cin >> x;

PrimeNumber p(x);
    PrimeNumber q(x);
p++;
    q--;
    cout << "\nprime before is " << q.GetPrime() << endl;
cout << "\nnext prime is " << p.GetPrime() << endl;

return 0;


}


class PrimeNumber {
int prime;
public:
PrimeNumber():prime(0){};
PrimeNumber(int num);
void SetPrime(int num);
int GetPrime(){return prime;};
PrimeNumber& operator++(int);
PrimeNumber& operator--(int);
static bool isPrime(int num);


};

void PrimeNumber::SetPrime(int num) {
if(isPrime(num)){
    prime = num;
}else{
    cout << num << " is not a prime Defaulting to 0.\n";
    prime = 0;
  }
 }

 PrimeNumber::PrimeNumber(int num){
  if(isPrime(num))
    prime = num;
  else {
    cout << num << " is not prime. Defaulting to 0.\n";
    prime = 0;
  }
 }


PrimeNumber& PrimeNumber::operator++(int){
//increment prime by 1 and test primality
//loop until a prime is found
do 
{
    this->prime += 1;
} 
while (! PrimeNumber::isPrime(this->prime));

}

PrimeNumber& PrimeNumber::operator--(int){
do 
{
    this->prime -= 1;
} 
while (!PrimeNumber::isPrime(this->prime));

}

bool PrimeNumber::isPrime(int num) {
if(num < 2)
    return false;

if(num == 2)
    return true;

if(num % 2 == 0)
    return false;

const int max_divisor = sqrt(num);
for(int div = 3; div < max_divisor; div += 2) // iterate odd numbers only
    if(num % div == 0)
        return false;
return true;
 }

So, my question here is that for the bool isPrime function, I first say OK the prime numbers 2 and 3 are primes and then I eliminate any numbers that are multiples of 2 or 3. What I want to do is perhaps create a while loop that would eliminate the other multiples of the number leaving the prime numbers only. Although, I am not exactly sure how to achieve this, if anyone has any suggestions, I would greatly appreciate it.

Now that is taken care of, I can't seem to get the ++ and -- operators working correctly. Sometimes it works and sometimes it doesn't.

Answer 1

What I want to do is perhaps create a while loop that would eliminate the other multiples of the number leaving the prime numbers only. Although, I am not exactly sure how to achieve this, if anyone has any suggestions, I would greatly appreciate it.

The algorithm you want to apply is called the Sieve of Erathostenes.

Instead of doing that (it would require that you store more and more prime numbers as you increment an instance), consider the algorithm proposed by Juraj Blaho (that tends to be the simplest).

Edit: consider this algorithm instead:

bool PrimeNumber::isPrime(int num) {
    if(num < 2)
        return false;
    if(num == 2)
        return true;
    if(num % 2 == 0)
        return false;

    const int root = sqrt(num);
    for(int div = 3; div <= root; div += 2) // iterate odd numbers only
        if(num % div == 0)
            return false;
    return true;
}

This is much faster (for large numbers) than the solution proposed by Juraj Blaho.

End Edit.

If you are instead looking for partial solutions (almost prime numbers, numbers that are "probably prime") consider the Rabin-Miller probabilistic primality test (or other tests linked to, from that page).

Answer 2

To check if a number is prime, you just need to check the remainder after division of each number smaller than square root of the tested number. Additionally some extra checks need to be performed for numbers smaller or equal to 1.

bool isPrime(int x)
{
  if (x <= 1)
    return false;

  for (int i = 2; i * i <= x; ++i)
    if (x % i == 0)
      return false;

  return true;
}

If an optimized version without any floating point calculations and square roots is needed:

bool isPrime(int x)
{
  if (x <= 1)
    return false;
  if (x <= 3)
    return true;
  if (x % 2 == 0)
    return false;

  for (int i = 2; ; i += 2)
  {
    const auto result = std::div(x, i);
    if (result.rem == 0)
      return false;
    if (result.quot < i)
      return true;
  }

  return true;
}