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

Since your question is about programming rather than math, I will try to keep my answer that way too.

The first glance of your code makes me wonder what on earth you are doing here... If you read the answers, you will realize that some of them didn't bother to understand your code, and some just dump your code to a debugger and see what's going on. Is it that we are that impatient? Or is it simply that your code is too difficult to understand for a relatively easy problem?

To improve your code, try ask yourself some questions:

1. What are a, b, c, etc? Wouldn't it better to give more meaningful names?
2. What exactly is your algorithm? Can you write down a clearly written paragraph in English about what you are doing (in an exact way)? Can you modify the paragraph into a series of steps that you can mentally carry out on any input and can be sure that it is correct?
3. Are all steps necessary? Can we combine or even eliminate some of them?
4. What are the steps that are easy to express in English but require, say, more than 10 lines in C/C++?
5. Does your list of steps have any structures? Loops? Big (probably repeated) chunks that can be put as a single step with sub-steps?

After you have going through the questions, you will probably have a clearly laid out pseudo-code that solves the problem, which is easy to explain and understand. After that you can implement your pseudo-code in C/C++, or, in fact, any general purpose language.