/**I've left the programmers comments in. What I am having trouble with is
the part of the code that reads (below this comment block):

If(i % j == 0) {
isPrime = false;
break;
}
What I am having trouble with is that both i and j are the same value incremented each time they run...I think...so wouldn't that mean that the value of i % j would always be zero because it is the same value divided by another? What am I missing? And then also, if there is no remainder wouldn't that indicate that the number is prime? I know there is something I am missing...Please help me out. Thank you. :)

*/


public class Primes {
public static void main(String[] args) {
int nValues = 50; // The maximum value to be checked
boolean isPrime = true; // Is true if we find a prime

// Check all values from 2 to nValues
for(int i = 2; i <= nValues; ++i) {
isPrime=true; // Assume the current i is prime

// Try dividing by all integers from 2 to i-1
for(int j = 2; j < i; ++j) {
if(i % j == 0) { // This is true if j divides exactly
isPrime = false; // If we got here, it was an exact division
break; // so exit the loop
}
}
// We can get here through the break, or through completing the loop
if(isPrime) // So is it prime?
System.out.println(i); // Yes, so output the value
}
}
}
/**
The outputs in the book are:
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47


*/

Let's run through a few cycles of the outer and inner loops:

Iteration 1 - outer loop
isPrime = true // reset isPrime to true
i = 2
Iteration 1 - inner Loop
for (int j = 2 ; j < i; ++j) // false: 2 < 2
// inner loop is not executed
if(isPrime) // true: isPrime = true
System.out.println(i); // 2 is a prime number
// back to beginning of outer loop

Iteration 2 - outer loop
isPrime = true // reset isPrime to true
i = 3
Iteration 1 - inner Loop
for (int j = 2 ; j < i; ++j) // true: 2 < 3
// j gets incremented to 3
if(i % j == 0) { // false: 3 % 2 == 0
// fall thru to end of inner loop
// back to beginning of inner loop
Iteration 2 - inner Loop
j = 3 // j is now 3
for (int j = 2 ; j < i; ++j) // false: 3 < 3
// inner loop is not executed
if(isPrime) // true: isPrime = true
System.out.println(i); // 3 is a prime number
// back to beginning of outer loop

Iteration 3 - outer loop
isPrime = true // reset isPrime to true
i = 4
Iteration 1 - inner Loop
for (int j = 2 ; j < i; ++j) // true: 2 < 4
// j gets incremented to 3
if(i % j == 0) // true: 4 % 2 == 0
isPrime = false; // isPrime is now false
break; // exit from inner loop
if(isPrime) // false: isPrime = false
// back to beginning of outer loop

Iteration 4 - outer loop
isPrime = true // reset isPrime to true
i = 5
Iteration 1 - inner Loop
for (int j = 2 ; j < i; ++j) // true: 2 < 5
// j gets incremented to 3
if(i % j == 0) // false: 5 % 2 == 0
// fall thru to end of inner loop
// back to beginning of inner loop
Iteration 2 - inner Loop
j = 3 // j is now 3
for (int j = 2 ; j < i; ++j) // true: 3 < 5
// j gets incremented to 4
if(i % j == 0) // false: 5 % 3 == 0
// fall thru to end of inner loop
// back to beginning of inner loop
Iteration 3 - inner Loop
j = 4
for (int j = 2 ; j < i; ++j) // true: 4 < 5
// j gets incremented to 5
if(i % j == 0) // false: 5 % 4 == 0
// fall thru to end of inner loop
// back to beginning of inner loop
Iteration 4 - inner Loop
j = 5
for (int j = 2 ; j < i; ++j) // false: 5 < 5
// inner loop is not executed
if(isPrime) // true: isPrime = true
System.out.println(i); // 5 is a prime number
// back to beginning of outer loop

---------------------------
Regarding your second question:
A number is a prime number only if it is divisible by 1 or itself.