// Dave's Prime Number Finder
//
// Source File : primeNumberTheorem.cpp
// Author 	: David J Beaty
// Date    	:
// Course      : CS161 (Summer Term)
// Sources     : Classmate Jesse Wagner


#include <iomanip>
#include <iostream>
#include <math.h>

using namespace std;

bool isPrime (long long n);
double  primeGen (long long n);

int main () {

     // **** PART I ****

     // initialize variables
	int i = 3;
     int j = 1;

	cout << "| 2   | ";
     // generate odd integers > 1 as candidates to be prime
     while (i <= 541) {
        // for each candidate integer, test whether it
        // is prime. if it is, display it.
        if(isPrime(i)) {
            if(j%10 == 0){
                cout << endl;
            }
            j  ;
            cout << "| " << setw(3) << i  << " | ";
         }
         // adding two each time so as only to generate odd #s
         i  = 2;

     }

     cout << endl << endl;

     // **** PART II ****

     // initialize variables
    int max = 100;
    double sumLogs = 0;
    double ratio = 0.0;

    cout << fixed << setprecision(5)
         << setw(15) << "Sum of logs" << setw(11) << 'n'
         << setw(9)  << "Ratio"       << endl;
    // generate odd integers > 1 as candidates to be prime
    while (max <= 10000000) {
        // generate output
        sumLogs = primeGen(max);
        ratio   = sumLogs / max;
        cout << setw(15) << sumLogs << setw(11) << max
             << setw(9)  << ratio   << endl;
        // call max while loop
        max *= 10;

     }

     getchar();
	getchar();
	return 0;
}

// isPrime function (checks whether candidate is prime)
bool isPrime (long long n) {
    int i = 2;
    int max = 0;
    // max is the square root of the candidate int
    max = (int)sqrt((long double) n);

    while (i <= max) {
        if(n%i == 0) {
            return false;
        }
        i  ;
    }
    return true;
}

// function that runs the numbers through isPrime and
double primeGen (long long n) {
    int i               = 3;
    double currentSum   = log(2.0);

    while (i <= n) {
        // for each candidate integer, test whether it
        // is prime. if it is, display it.
        if(isPrime(i)) {
            // get the log and add it to running total
            currentSum  = log((double) i);
        }
        // adding two each time so as only to generate odd #s
        i  = 2;
    }

    return currentSum;
}