Problem 41 : Pandigital prime

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.

What is the largest n-digit pandigital prime that exists?

#include <iostream>
#include
 
 <cmath>      // sqrt()
#include <algorithm>  // sort()
#include <cassert>    // assert()

using namespace std;
    
class PE0041
{
private:
    static const int m_max = 10000000; // ten million
    bool *m_primeSieve;

    static const int max_digits = 9; // 1,2...,9
    int m_digits[max_digits];
    int
 
 m_numOfDigits;

    void getDigits(int number);
    void createPrimeSieve();
    bool checkPrime(int number);
    bool checkPandigital(int number);

public:
    PE0041() { m_primeSieve = new bool [m_max]; createPrimeSieve(); }
    ~PE0041() { delete [] m_primeSieve; }

    int getNumOfDigits() const { return
 
 m_numOfDigits; }
    int findLargestPandigitalPrime();
};

// create a prime Sieve of Eratosthenes below max value
void PE0041::createPrimeSieve()
{
    memset(m_primeSieve, true, m_max*sizeof(bool)); 

    m_primeSieve[0] = m_primeSieve[1] = false;

    for (int i=2; i<=(int)sqrt((double)m_max); i++) 
    {
        if (true == m_primeSieve[i]) 
        {
            for (int j=i*i; j<m_max; j+=i)
            {
                m_primeSieve[j] = false;
            }
        }
    }
}

void PE0041::getDigits(int number)
{
    m_numOfDigits = 0;

    while (number > 0)
    {
        m_digits[m_numOfDigits++] = number%10;
        number /= 10;
    }
}

bool PE0041::checkPrime(int number)
{
    return m_primeSieve[number];
}

bool PE0041::checkPandigital(int number)
{
    getDigits(number);

    sort(m_digits, m_digits+m_numOfDigits);

    for (int i=1; i<m_numOfDigits; i++)  // look like 1 2 3 4 ...
    {
        if (m_digits[i-1] != i)
        {
            return false;
        }
    }

    return true;
}

int PE0041::findLargestPandigitalPrime()
{
    // if the sum of digits of one number x is divided by 3, 
    // the number x is not a prime.
    //
    // 1+2+3+4+5+6+7+8+9 = 45 = 3 * 15,  x=3k is not a prime
    // 1+2+3+4+5+6+7+8 = 36 = 3 * 12, x=3k is not a prime
    // 1+2+3+4+5+6 = 21 = 3 * 7, x=3k is not a prime
    // 1+2+3+4+5 = 15 = 3 * 5, x=3k is not a prime 
    // 1+2+3 = 6 = 3 * 2, x=3k is not a prime
    // 1+2 = 3 = 3 * 1, x=3k is not a prime 
    //
    // 1+2+3+4+5+6+7 = 28 <> 3k
    // 1+2+3+4 = 10 <> 3k   

    int number = 2143;   // 4-digit pandigital prime

    assert(true == checkPrime(number) && true == checkPandigital(number));

    for (number=7654321; number>=1234567; number--)
    {
        if (true == checkPrime(number) && true == checkPandigital(number))
        {
            break;
        }
    }
    return number;
}
    
int main()
{
    PE0041 pe0041;

    int number = pe0041.findLargestPandigitalPrime();

    cout << number << " is the largest " << pe0041.getNumOfDigits();
    cout << "-digit pandigital prime that exists." << endl;

    return 0;
}