Question

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What does BigInteger having no limit mean?

The Javadoc for BigInteger does not define any maximum or minimum. However, it does say:

(emphasis added)

Immutable arbitrary-precision integers

Is there such a maximum, even in theory? Or is the way BigInteger operates fundamentally different, such that there is in reality no maximum except for the amount of memory available on the computer?

Answer 1

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.

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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).