Does BigInteger ever overflows?

Question

The API docs says

All of the details in the Spec concerning overflow are ignored, as BigIntegers are made as large as necessary to accommodate the r

Answer 1

Correct, BigInteger never overflows, it uses software operations and dynamic allocation to store arbitrarily sized numbers.

As with all things in computing, "arbitrarily sized" is anothe way of saying "until you run out of resources on the underlying system".