What's the largest value an NSNumber can store?
// ok
NSNumber *value = @(1 << 31);
// gives compiler error, so max NSNumber is 32-bit uint?
NSNumber *value = @(1 << 32);
NSNumber is actually a class cluster, meaning that when you create an instance you may be getting any of a variety of concrete subclasses, each capable of storing a different kind of numeric type. The actual types available, and their sizes, may be machine-dependent.
Looking at the NSNumber documentation shows you the different kinds of numbers you can store: the two largest integer options would be +numberWithLongLong: (or +numberWithUnsignedLongLong:), which stores a long long, and +numberWithInteger: (or +numberWithUnsignedInteger:), which stores an NSInteger. The maximum NSNumber values are therefore limited by these types.
The Foundation documentation states:
When building 32-bit applications, NSInteger is a 32-bit integer. A 64-bit application treats NSInteger as a 64-bit integer.
The compiler is smart and will create an NSNumber of the same type as your numeric literal. As mentioned in the comments above, you can use @(1ULL << 32) if your machine has an unsigned long long type with more than 32 bits.
Furthermore, NSNumber is toll-free bridged to CFNumber, meaning you can try out functions like CFNumberGetByteSize() for yourself — and have a look at the CFNumberType documentation. You'll see these are basically the same as the NSNumber options.
Additionally, the NSDecimalNumber class, a subclass of NSNumber, provides the +maximumDecimalNumber method which you can use to find the maximum value that can be stored in an NSDecimalNumber. NSDecimalNumber, and the floating-point types, may be able to store bigger numbers than the integer types, though with decreasing precision.