Java program will compile but not run in command prompt

You are not missing anything about the command prompt. You have created an infinite loop - your program is doing the same thing over and over again.

Recall that in Java (and C, and many languages with C-derived syntax), a for loop like this one:

for (i=1; i<= count3; ++i)
    sum3 += 15*i; //creates sum for where sets intersect

does the same as this:

i=1;
while(i <= count3)
{
    sum3 += 15*i; //creates sum for where sets intersect
    ++i;
}

which means that your code is equivalent to this: (I've also changed the formatting slightly and removed the comments for brevity)

i=1;
while(i<1000)
{
    if (i%3 == 0)
        count1 += 1;

    if (i%5 == 0)
        count2 += 1;

    if (i%3 == 0 && i%5 ==0)
        count3 += 1;

    i=1;
    while(i <= count1)
    {
        sum1 += 3*i;
        ++i;
    }

    i=1;
    while(i <= count2)
    {
        sum1 += 5*i;
        ++i;
    }

    i=1;
    while(i <= count3)
    {
        sum1 += 15*i;
        ++i;
    }

    // HERE

    ++i;
}

Notice that each time the program gets to the line I marked "HERE", i will be equal to count3 + 1 (since if it was less than or equal to count3 then it would still be in the loop just before "HERE").

The next instruction is ++i, which just adds 1 to i. So at the end of the loop (just before the }, i will be equal to count3 + 2 (that is count3 + 1 + 1).

count3 is the number of multiples of 15 that your program has encountered so far, so that will be 0 at the start. So this effectively resets i to 2 just before the end of the loop, and i never gets past 2.

You probably meant to use a different variable in your inner for loops:

for (int j=1; j<=count1; ++j)
    sum1 += 3*j; //creates sum for all multiples of 3

for (int j=1; j<=count2; ++j)
    sum2 += 5*j; //creates sum for all multiples of 5

for (int j=1; j<= count3; ++j)
    sum3 += 15*j; //creates sum for where sets intersect

Notice that I have changed i to j (and declared j in each loop; this way each loop gets a separate variable called j, but you could declare it once at the start of main if you wanted and it would make no difference).

Your program will still not work properly (it will give you a wrong answer), but this will fix the infinite loop which is what you asked about.

You are resetting your i variable in your for loop, causing it to never end. try this modified code:

public class ProjectOne
{
    public static void main (String[] args)
    {
        int i, count1 = 0, count2 = 0, count3 = 0;
        int sum1 = 0, sum2 = 0, sum3 = 0, total;

        for(i=1; i<1000; ++i) //creates loop that will iterate for every number
        {
            if (i%3 == 0)

                count1 += 1; //gathers total #'s <1000 that can be divided by 3

            if (i%5 == 0)

                count2 += 1; //same as above, but divisible by 5

            if (i%3 == 0 && i%5 ==0)

                count3 += 1; //gathers count for where sets intersect

            for (int j=1; j<=count1; ++j)

                sum1 += 3*j; //creates sum for all multiples of 3

            for (int j=1; j<=count2; ++j)

                sum2 += 5*j; //creates sum for all multiples of 5

            for (int j=1; j<= count3; ++j)

                sum3 += 15*j; //creates sum for where sets intersect

        }

        total = (sum1 + sum2) - sum3; //totals two sums while subtracting
                                        //the intersections that would double
        System.out.print (total); // prints total value
    }
}

I hope this will be your solution.