BigNumber is an object which safely allows mathematical operations on numbers of any magnitude
uint256 has a range from 0 to (2^256) - 1. Therefore, the maximum number that can be held by the uint256 datatype is astronomically large.
Specifically, the maximum value for uint256 is:
ibraries used for interacting with Ethereum nodes - ethers.js and web3.js - both come with support for BigNumbers.
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