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answers:

1

200,000,000 is much less than the maximum 32-bit INTEGER, 2,147,483,647.

+11  A: 

A stack overflow happens not when your notation runs out of bits, but when your computer runs out of memory. A 200M-entry array would need 800Mb of memory. That is very large to put on the stack.

Ned Batchelder
It's not a question of size of memory in general, but rather of stack size, which is smaller than total RAM amount. For example, on my Mac OS laptop with 4GB of RAM, default stack size is 8MB.
FX