(12C) Combination and Permutation

[Joe Horn]

(08-18-2017 12:50 PM)pier4r Wrote:  The hp 50g does the same (and I guess all the math environments with exact computations/big integers , as long as the memory is enough).

Actually, both the 50g and Prime have built-in limitations on large integers, in different ways.

The 50g doesn't allow integer exponents greater than 9999 (e.g. 2^9999 works but 2^10000 says "^ Error: Integer too large"). However, the 50g allows the integers themselves to be as big as available memory (as you said), e.g. 2^9999 can be squared without error, and squared again, and so on, until you run out of memory.

Prime however imposes a maximum size on large integers themselves, regardless of available memory. It seems to be 2^8599-1, but I've not seen that documented anywhere. Try this in CAS on your Prime: \[\left ( 2^{8598}-1 \right )\cdot 2+1\]This yields an integer that contains 2589 digits. But now try to add 1 to it, and it yields infinity. So I think that's Prime's largest allowed integer, approximately 3.6E2588.