Minor fixes related to prime number computation

Doc/Sd1/array.xml

@@ -133,8 +133,8 @@
                   isPrime(final long candidate)</methodname> method classifies
                   prime numbers as such and whether this message is able to
                   tell non-primes as well. We achieve this by defining a
-                  boolean array having indexes ranging from 0 to 100. We
-                  then:</para>
+                  boolean array having indexes ranging from 0 to 100
+                  (inclusive). We then:</para>
 
                   <itemizedlist>
                     <listitem>
@@ -159,7 +159,7 @@
                                 31, 37, 41, 43, 47, 53, 59, 29,
                                 61, 67, 71, 73, 79, 83, 89, 97};
     
-    final boolean[] isPrime = new boolean[101]; //Testing 2,3,..,98,99,100
+    final boolean[] isPrime = new boolean[101]; //Testing 2, 3, 4, .., 99, 100
     for (int i = 2; i &lt;= 100; i++) {
       isPrime[i] = false;
     }
@@ -174,18 +174,18 @@
 
                 <listitem>
                   <para>Executing this test yields an error at index 49. This
-                  is due to an implementation error. The for- loop had been
-                  defined as:</para>
+                  is due to the chosen limit <code>i * i &lt; candidate</code>
+                  in:</para>
 
                   <programlisting language="java">  public static boolean isPrime(final long candidate) {
     for (long i = 2; i * i &lt; candidate; i++) {
   ...</programlisting>
 
                   <para>This is wrong: Having <code>candidate == 49</code> the
-                  last value of i to be considered will be 6. So the test for
-                  the result of <code>49 % 7</code> will never be executed
-                  thus returning true. We actually have to modify the loop's
-                  limit slightly different:</para>
+                  last value of i to be considered will be 6. So the required
+                  test <code>49 % 7</code> will never be executed thus
+                  returning true. We have to modify the loop's limit slightly
+                  by using <code>i * i &lt;= candidate</code>:</para>
 
                   <programlisting language="java">  public static boolean isPrime(final long candidate) {
     for (long i = 2; i * i <emphasis role="bold">&lt;=</emphasis> candidate; i++) {
@@ -202,8 +202,7 @@
                   method allows to estimate the prime number computing
                   performance:</para>
 
-                  <programlisting language="none">prime numbers found:664579
-Elapsed time:14997</programlisting>
+                  <programlisting language="none">Found 664579 prime numbers within 15.136 seconds.</programlisting>
                 </listitem>
               </orderedlist>
             </answer>
@@ -238,8 +237,9 @@ Elapsed time:14997</programlisting>
 
               <para>Learning from <link
               xlink:href="http://en.wikipedia.org/wiki/Prime_factor">prime
-              factorization</link> it actually suffices just to test all
-              primes up to the already discussed square root limit:</para>
+              factorization</link> it actually suffices just to test only
+              prime values up to the already discussed square root
+              limit:</para>
 
               <programlisting language="none">143 % 2 == 0 ? No.
 143 % 3 == 0 ? No.
@@ -247,13 +247,20 @@ Elapsed time:14997</programlisting>
 143 % 7 == 0 ? No.
 143 % 11 == 0 ? Yes ==&gt; 143 is not prime</programlisting>
 
-              <para>The tradeoff is even bigger for higher prime numbers. Thus
-              if we store all computed prime numbers without gaps they will
-              save us a lot of operations. You may want to reuse your unsorted
-              <classname
+              <para>The trade off is even bigger for higher prime number
+              values. Thus if we store computed prime numbers without gaps the
+              required computation time should decrease.</para>
+
+              <para>Storing prime numbers requires an array (or another type
+              of container). Since we do not know the number of prime numbers
+              below a given limit the required array size is not yet known
+              when starting the application. You may want to reuse your
+              unsorted <classname
               xlink:href="Ref/api/P/Array/integerStoreUnbounded/de/hdm_stuttgart/mi/sd1/store/IntegerStore.html">IntegerStore</classname>
-              implementation. Implement the above algorithm and compare the
-              elapsed execution time.</para>
+              implementation to provide a dynamically growing array.</para>
+
+              <para>Implement the above algorithm and compare the elapsed
+              execution time.</para>
             </question>
 
             <answer>
@@ -261,7 +268,7 @@ Elapsed time:14997</programlisting>
                 <para role="eclipse">Sd1/Prime/V2</para>
               </annotation>
 
-              <para>This time we only need ~18% of the previous time:</para>
+              <para>This time we save ~80% of execution time:</para>
 
               <programlisting language="none">prime numbers found:664578
 Elapsed time:2639</programlisting>

P/Sd1/Prime/V1/src/main/java/de/hdm_stuttgart/mi/sd1/main/PrimeNumbers.java

@@ -11,9 +11,11 @@ public class PrimeNumbers {
   public static void main(String[] args) {
 
     final long startTime = System.currentTimeMillis();
-    System.out.println("prime numbers found:" + findPrimeNumbers(10_000_000));
+    final long numberOfPrimes = findPrimeNumbers(10_000_000);
     final long endTime = System.currentTimeMillis();
-    System.out.println("Elapsed time:" + (endTime - startTime));
+    
+    System.out.println("Found " + numberOfPrimes + " prime numbers within " +
+          (endTime - startTime) / 1000. + " seconds.");
   }
   
   /**

P/Sd1/Prime/V2/src/main/java/de/hdm_stuttgart/mi/sd1/main/PrimeNumbers.java

@@ -13,12 +13,15 @@ public class PrimeNumbers {
   /**
    * @param args unused
    */
-  public static void main(String[] args) {
-
+  public static void main(String[] args) {    
+    
     final long startTime = System.currentTimeMillis();
-    System.out.println("prime numbers found:" + findPrimeNumbers(10_000_000));
+    final long numberOfPrimes = findPrimeNumbers(10_000_000);
     final long endTime = System.currentTimeMillis();
-    System.out.println("Elapsed time:" + (endTime - startTime));
+    
+    System.out.println("Found " + numberOfPrimes + " prime numbers within " +
+          (endTime - startTime) / 1000. + " seconds.");
+
   }
   
   /**
@@ -35,8 +38,7 @@ public class PrimeNumbers {
   public static long findPrimeNumbers(long limit) {
     primes.addValue(2); // Add a seed: The first prime number
     for (long i = 3; i <= limit; i++) {
-      if (isPrime(i)) {
-      }
+       isPrime(i);
     }
     return primes.getNumValues();
   }