HP Prime CAS & Large numbers

[Mario Blasone]

(09-08-2022 09:14 AM)Mario Blasone Wrote:  I tried to find the largest integer number that the Prime can manage in CAS.
I guess CAS integer are internally formatted in binary, so I empirically searched the largest power of 2 before the Prime returns "undefined": it is 2^8598.
I guess that the largest integer is (mathematically) 2^8599-1, but you can't write this expression on Prima without getting "undefined".

Your conclusions seems substantially correct.
Just to be more precise, the max_integer obtained with Sum(2^n,0,2598) is 8599 bits long (not 8598), because each addend is a binary 1 at position n followed by all binary 0, but n ranger from 0 to 8598; i.e 8599 positions (bits). It is more evident if the expression to get the max_integer on HP Prime is written in this equivalent mode: Sum(2^(n-1),1,8599) i.e. summation of 8599 terms from 2^0 to 2^8598.
Min negative integer (max negative) is Sum(-2^n,1,8598).
Globally speaking, on HP CAS, integers seems to be stored in binary form with 8600 digits (including sign), ranging from -2^8598 (through 0) up to 2^8599.