Yes, the main difference in a 64-bit virtual machine is access to a larger maximum amount of memory.
The whole point of Java is that compiled .class files work on any Java system, no matter what the hardware is based on.
Your program will work on both a 32-bit and a 64-bit system, but if necessary, if the equipment and the OS work, your application will be able to get much more memory when working in a 64-bit virtual machine compared to a 32-bit virtual machine.
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