Is there an upper bound to BigInteger? [duplicate]

The number is held in an int[] – the maximum size of an array is Integer.MAX_VALUE. So the maximum BigInteger probably is (2 ^ 32) ^ Integer.MAX_VALUE.

Admittedly, this is implementation dependent, not part of the specification.

In Java 8, some information was added to the BigInteger javadoc, giving a minimum supported range and the actual limit of the current implementation:

BigInteger must support values in the range -2Integer.MAX_VALUE (exclusive) to +2Integer.MAX_VALUE (exclusive) and may support values outside of that range.

Implementation note: BigInteger constructors and operations throw ArithmeticException when the result is out of the supported range of -2Integer.MAX_VALUE (exclusive) to +2Integer.MAX_VALUE (exclusive).