Allocating an array of 1 billion integers throws OutOfMemoryError

Question

I'm trying to create an integer-array with 1 billion (1 000 000 000) elements, like this:

int[] prime_table = new int[1000000000];

but the VM runs out of Heap-memory on the line above:

Exception in thread "main" java.lang.OutOfMemoryError: Java heap space
    at algorithms.Algorithm.run(Algorithm.java:34)
    at Main.main(Main.java:18)

So I investigated a bit: in Java, an Integer is 32bit, so that means I'm allocating a 32 000 000 000 bit field, which is roughly 3 814.69727 megabytes. I launched the VM with enough heap:

java -Xms4g -Xmx4g Main

and this tells me, the VM is getting 3926MB of heap-size (just before allocating the array):

System.out.println( Runtime.getRuntime().totalMemory() / (1024*1024) +"MB");

That seems fine, so why is it throwing the error?