After loading the developer package, $MaxMachineInteger gives 2147483647 = 2^31-1 for my computer system. My research involves dealing with integers >2^31-1. Thus, I notice a large drop in the speed of my algorithms when I use integers >2^31-1. This doesn't surprise me, as $MaxMachineInteger tells me integers >2^31-1 are not machine.
However, I am working on a Mac Pro, which has a 64-bit processor and 64-bit path and registry. Furthermore, $SystemWordLength gives 64. Thus, I have 2 questions.
1) Why is $MaxMachineInteger returning 2^31-1?
2) What specifically determines the magnitude of what Mathematica considers a machine integer? The documentation tells me that my machine determines it, but with a 64-bit processor, 64-bit path and registry, and 64-bit system word length, why would $MaxMachineInteger give only 2^31-1?
Basically, I want to raise the maximum integer that Mathematica considers "machine" on my computer so that my algorithms do not decrease so drastically in speed when I go over this maximum.
Thank you very much for your attention!