Java Reference
In-Depth Information
sion between the for loop parentheses to increment number in steps of two because you don't want to
check even numbers. The for loop ends when count is equal to the length of the array. You test the value
in number in the inner for loop by dividing number by all of the prime numbers you have in the primes
array that are less than, or equal to, the square root of the candidate. If you get an exact division, the value
in number is not prime, so you go immediately to the next iteration of the outer loop via the continue
You calculate the limit for divisors you need to try with the following statement:
long limit = (long)ceil(sqrt((double)number));
The sqrt() method from the Math class produces the square root of number as a double value, so if
number has the value 7, for example, a value of about 2.64575 is returned. This is passed to the ceil()
method, which is also a member of the Math class. The ceil() method returns a value of type double
that is the minimum whole number that is not less than the value passed to it. With number as 7, this
returns 3.0, the smallest integral value not less than the square root of 7. You want to use this number
as the limit for your integer divisors, so you cast it to type long and store the result in limit . You are
able to call the sqrt() and ceil() methods without qualifying their names with the class to which they
belong because you have imported their names into the source file.
The cast of number to type double is not strictly necessary. You could write the statement as:
long limit = (long)ceil(sqrt(number));
The compiler will insert the cast for you. However, by putting the explicit cast in, you indicate that it was
your intention.
If you don't get an exact division, you exit normally from the inner loop and execute the statement:
primes[count++] = number; // We got one!
Because count is the number of values you have stored, it also corresponds to the index for the next free
element in the primes array. Thus, you use count as the index to the array element in which you want to
store the value of number and then increment count .
When you have filled the primes array, the outer loop ends and you output all the values in the array in
the loop:
for(long n : primes) {
System.out.println(n); // Output all the primes
This loop iterates through all the elements of type long in the primes array in sequence. On each itera-
tion n contains the value of the current element, so that is written out by the println() method.
You can express the logical process of this program as the following sequence of steps:
1. Take the number in question and determine its square root.
2. Set the limit for divisors to be the smallest integer that is greater than this square root value.
3. Test to see if the number can be divided exactly (without remainder) by any of the primes already
in the primes array that are less than the limit for divisors.
4. If any of the existing primes divide into the current number , discard the current number and start
a new iteration of the loop with the next candidate number .
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