Prime numbers program

Question

I'm currently trying out some questions just to practice my programming skills. ( Not taking it in school or anything yet, self taught ) I came across this problem which required me to read in a number from a given txt file. This number would be N. Now I'm suppose to find the Nth prime number for N <= 10 000. After I find it, I'm suppose to print it out to another txt file. Now for most parts of the question I'm able to understand and devise a method to get N. The problem is that I'm using an array to save previously found prime numbers so as to use them to check against future numbers. Even when my array was size 100, as long as the input integer was roughly < 15, the program crashes.

#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <fstream>
using namespace std;

int main() {
    ifstream trial;
    trial.open("C:\\Users\\User\\Documents\\trial.txt");
    int prime;
    trial >> prime;
    ofstream write;
    write.open("C:\\Users\\User\\Documents\\answer.txt");
    int num[100], b, c, e;
    bool check;
    b = 0;
    switch (prime) {
        case 1:
        {
            write << 2 << endl;
            break;
        }
        case 2:
        {
            write << 3 << endl;
            break;
        }
        case 3:
        {
            write << 5 << endl;
            break;
        }
        case 4:
        {
            write << 7 << endl;
            break;
        }
        default:
        {
            for (int a = 10; a <= 1000000; a++) {
                check = false;
                if (((a % 2) != 0) && ((a % 3) != 0) && ((a % 5) != 0) && ((a % 7) != 0)) // first filter
                {
                    for (int d = 0; d <= b; d++) {
                        c = num[d];
                        if ((a % c) == 0) {
                            check = true; // second filter based on previous recorded primes in array
                            break;
                        }

                    }
                    if (!check) {
                        e = a;
                        if (b <= 100) {
                            num[b] = a;
                        }

                        b = b + 1;
                    }
                }
                if ((b) == (prime - 4)) {
                    write << e << endl;
                    break;
                }
            }
        }
    }
    trial.close();
    write.close();
    return 0;
}

I did this entirely base on my dummies guide and myself so do forgive some code inefficiency and general newbie-ness of my algorithm. Also for up to 15 it displays the prime numbers correctly.

Could anyone tell me how I should go about improving this current code? I'm thinking of using a txt file in place of the array. Is that possible? Any help is appreciated.

Answer 1

There are a two approaches to testing for primality you might want to consider:

1. The problem domain is small enough that just looping over the numbers until you find the Nth prime would probably be an acceptable solution and take less than a few milliseconds to complete. There are a number of simple optimizations you can make to this approach for example you only need to test to see if it's divisible by 2 once and then you only have to check against the odd numbers and you only have to check numbers less than or equal to the aquare root of the number being tested.
2. The Sieve of Eratosthenes is very effective and easy to implement and incredibly light on the math end of things.

As for why you code is crashing I suspect changing the line that reads

for( int d=0; d<=b; d++) 

to

for( int d=0; d<b; d++) 

will fix the problem because you are trying to read from a potentially uninitialized element of the array which probably contains garbage.

Answer 2

It looks like as you go around the main for() loop, the value of b increases.

Then, this results in a crash because you access memory off the end of your array:

                for (int d = 0; d <= b; d++) {
                    c = num[d];

I think you need to get the algorithm clearer in your head and then approach the code again.

Answer 3

Since you will need larger prime number values for later questions, I suggest you follow dreeves advice, and do a sieve. It is a very useful arrow to have in your quiver.

Answer 4

For one, you'd have less code (which is always a good thing!) if you didn't have special cases for 3, 5 and 7.

Also, you can avoid the special case for 2 if you just set num[b] = 2 and only test for divisibility by things in your array.

Answer 5

#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <fstream>

using namespace std;

int main()
{
ifstream trial;
trial.open("C:\\Users\\User\\Documents\\trial.txt");
int prime, e;
trial>>prime;
ofstream write; 
write.open("C:\\Users\\User\\Documents\\answer.txt");
int num[10000], currentPrime, c, primePrint;
bool check;
currentPrime=0;
num[currentPrime] = 2;
currentPrime=1;

for(int currentInt=2; currentInt<=1000000; currentInt++) 
{check = false; 
for( int arrayPrime=0; arrayPrime<currentPrime; arrayPrime++) 
        { c=num[arrayPrime];
            if ((currentInt%c)==0) { check = true;// second filter based on previous recorded primes in array
                    break;}
               }


 if (!check)
    { e=currentInt;  
    if( currentInt!= 2 ) { 
    num[currentPrime]= currentInt;}
    currentPrime = currentPrime+1;}
    if(currentPrime==prime)
    {
    write<<e<<endl;
    break;}
    }
trial.close();
write.close();
return 0;
}

This is the finalized version base on my original code. It works perfectly and if you want to increase the range of prime numbers simply increase the array number. Thanks for the help =)

Answer 6

Running your code through a debugger, I've found that it crashes with a floating point exception at "if ((a % c) == 0)". The reason for this is that you haven't initialized anything in num, so you're doing "a % 0".