Why is array element referencing a constant time operation?

Let me briefly explain how I think array element referencing works.

Start address of the array + Data type size*index of the element to be fetched = Address of the required array element

Basically, the above operation is executed when suppose b[i] is written (where b is an array and i is the index of the desired element). This operation is supposed to be a constant-time operation. However, I think otherwise. Consider the following examples,

Example 1

579015713945 (start address) + 16 (datatype size) * 2789280 (index of the required element) = Address of the required element.

Example 2

579015713945 (start address) + 16 (datatype size) * 1 (index of the required element) = Address of the required element.

Example 3

100 (start address) + 8 (datatype size) * 1 (index of the required element) = Address of the required element.

Will a machine not be able to compute examples 2 and 3 faster than example 1? So, how is the operation a constant-time operation then when there are variable amounts of time needed?

I computed the value of example 1 and 3 on colab, and both took 0 seconds to compute (haha). Particular numbers do not matter here. I could have made the numbers much bigger to make the execution time difference between example 1 and example 3 greater. Then example 1 probably would have taken 1 second, and example 3 would have taken 0.1 second. At any rate, I think I have been able to convey my general question.

ALUs in CPUs are fixed size and operate on a fixed number of bits -- on a 64-bit machine, the ALUs will be 64 bits and will do an add or multiply¹ of 64 bit values in constant time. Thus as long as your addresses and indexes are less that 2⁶⁴ (which they must be to be valid addresses), the time will be constant

¹_{On some machines, multiplies of some corner case values (such as mulitplying by 0) may take less time, bit this is usually ignored when talking about complexity or Big-O time. The distinction may be important in other domains (such a cryptography), so you need to be careful about exactly what "constant" means in your domain. It varies.}