What to do when your program doesn't work.

Question

A huge number of posts here seem to relate to code that has been written (one presumes by the poster), but which doesn't work.
I get the impression that people don't know what to do next.
It's really not that difficult. When you're writing your program you constantly have in mind what you expect will happen as a result of each bit of code that you put.
If at the end of the day, the program as a whole doesn't behave as you expected, then somewhere in there there must be a point at which the program starts doing something that doesn't correspond to what you anticipated. So, you add some System.err.println statements to test your beliefs.
Consider this program that tests whether a number is prime.
public class Test
    public static void main(String args[])
        // Get the number to test.
        int number = Integer.parseInt(args[0]);
        // Try each possible factor.
        int factor;
        for(factor = 2; factor < number; factor++)
            // See whether it is really a factor.
            if(number / factor == 0)
                break;
        if(factor == number)
            System.out.println("Number is not prime.");
        else
            System.out.println("Number is prime.");
}Straight forward enough, but it doesn't actually work :( It seems to say that every number is not prime. (Actually, not quite true, but I didn't test it that carefully, since it didn't work).
Now, I could scrutinise it for errors, and then, having failed to find the problem, I could post it here. But let's suppose I'm too proud for that.
What might be going wrong. Well, how sure am I that I'm even managing to capture the number of interest, number. Let's put in a System.err.println() to test that.
Is the program in fact trying the factors I expect? Put in System.err.println() for that.
Is the program correctly determining whether a number is a factor? Need another System.err.prinln (or two) for that.
public class Test
    public static void main(String args[])
        // Get the number to test.
        int number = Integer.parseInt(args[0]);
        System.err.println("Number to check is " + number);
        // Try each possible factor.
        int factor;
        for(factor = 2; factor < number; factor++)
            System.err.println("Trying factor " + factor);
            // See whether it is really a factor.
            if(number / factor == 0)
                System.err.println(factor + " is a factor.");
                break;
            System.err.println(factor + " is not a factor.");
        if(factor == number)
            System.out.println("Number is not prime.");
        else
            System.out.println("Number is prime.");
}Let's try with on the number 6.
The output is:
Number to check is 6
Trying factor 2
2 is not a factor.
Trying factor 3
3 is not a factor.
Trying factor 4
4 is not a factor.
Trying factor 5
5 is not a factor.
Number is not prime.
Whoah! That's not right. Clearly, the problem is that it's not correctly deciding whether a number is a factor. Well, we know exactly where that test is done. It's this statement:
            if(number / factor == 0)Hmm.... let's try 6 / 3, 'cos 3 is a factor.
6 / 3 = 2.
But that's not zero. What the.... Oh - I see, it should have been number % factor.
Ok - let's fix that, and run it again.
Now the output is:
Number to check is 6
Trying factor 2
2 is a factor.
Number is prime.
Not the right answer, but at least it's now figured out that 2 is a factor of 6. Let's try a different number.
Number to check is 9
Trying factor 2
2 is not a factor.
Trying factor 3
3 is a factor.
Number is prime.
Again, got the right factor, but still the wrong answer. Let's try a prime:
Number to check is 7
Trying factor 2
2 is not a factor.
Trying factor 3
3 is not a factor.
Trying factor 4
4 is not a factor.
Trying factor 5
5 is not a factor.
Trying factor 6
6 is not a factor.
Number is not prime.
Aagh! Obvious - the final test is the wrong way round. Just fix that, remove that System.err.println()s and we're done.
Sylvia.

Answer 1

Consider this program that tests whether a number is
prime.
[attempt to divide by each integer from 2 to n-1]At risk of lowering the signal to noise ratio, I
should point out that the algorithm given is just
about the worst possible.
I know that the point was to illustrate debugging
and not good prime test algorithms, and I disagree
with the correspondent who thought the post was
condescending.
Anyway, the java libraries have good prime testing
methods based on advanced number theory research that the
non-specialist is unlikely to know. Looking at the java
libraries first is always a good idea.
Even with the naive approach, dramatic improvements
are possible.
First, only try putative divisors up to the square root
of the number. For 999997 this is about 1000 times faster.
Next only try dividing by prime numbers. This is about
7 times faster again. The snag, of course, is to find the
prime numbers up to 1000, so there might not be much
advantage unless you already have such a list. The sieve
of Erastosthenes could be used. This involves 31 passes
through an array of 1000 booleans and might allow an
improvement in speed at the expense of space.
Sorry if I've added too much noise :-)