What is the maximum value of NSInteger?

The maximum value for an NSInteger is NSIntegerMax

(from Foundation Constants Reference)

For 32-bit & 64 bit, there are two conventions: a)ILP32 b)LP64

The 32-bit runtime uses a convention called ILP32, in which integers, long integers, and pointers are 32-bit quantities. The 64-bit runtime uses the LP64 convention; integers are 32-bit quantities, and long integers and pointers are 64-bit quantities. These conventions match the ABI for apps running on OS X (and similarly, the Cocoa Touch conventions match the data types used in Cocoa), making it easy to write interoperable code between the two operating systems.

Table 1-1 all of the integer types commonly used in Objective-C code. Each entry includes the size of the data type and its expected alignment in memory. The highlighted table entries indicate places where the LP64 convention differs from the ILP32 convention. These size differences indicate places where your code’s behavior changes when compiled for the 64-bit runtime. The compiler defines the LP64 macro when compiling for the 64-bit runtime.

for 64 bit max range for NSInteger is : LONG_MAX : 9223372036854775807

The maximum value of an NSInteger is NSIntegerMax.