Uint256 max value

The uint256 max value can be obtained with type(uint256).max; which is 115792089237316195423570985008687907853269984665640564039457584007913129639935 or 2^256-1

But it's cleaner and safer to use type(uint256).max.

The same can be used for signed integer types

//57896044618658097711785492504343953926634992332820282019728792003956564819967
type(int256).max;

//-57896044618658097711785492504343953926634992332820282019728792003956564819968
type(int256).min;

The math behind maximum values in integers and unsigned integers

For unsigned integers, just put 2 ** n - 1 into the terminal with your favorite interpreted language to get the answer, where n is the size of the uint in question, for example uint128 or uint32 (or even rarely used but valid sizes like uint208). A uintN means there are N bits that represent the number, and when all of them are set to 1, this is the maximum binary representation.

The EVM uses Twos Complement to represent signed numbers, so to get the the maximum value of a signed integer, the formula is 2 ^ (N - 1) - 1 and the most negative value is -2 ^ (N - 1).

Hacky ways to get the uint256 maximum value

You could also specify it with hexadecimal, which would be a little cleaner than using the decimal representation, but still space consuming and error prone.

Uint256 max value in hex

0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

That's exactly 64 'f's, don't get it wrong! The 64 is derived from 256 bits divided by 8 to get the number of bytes (32), and each maximum byte is represented in hex by 0xff.

~uint256(0) is equivalent to the uint256 max value

The maximum value of uint256 is 256 bits all set to one. So how about use the bit flip operator? (~)

type(uint256).max == ~uint256(0) // this will return true

Another ugly solution is to underflow the integer

function maximum() public pure returns(uint256) {
   unchecked { return uint256(0) - uint256(1); }
}

The following code works properly, but it is deceptive and not recommended for use

function maxUint() public pure returns (uint256) {
    return 2**256 - 1;
}

It returns the correct value, which you can verify with

assert(2**256 - 1 == type(uint256).max);

If you write 2**256 as a constant in solidity, the code won't compile because the compiler recognized 2**256 is too large to fit in uint256. But if it is immediately followed by a "- 1", then the compiler recognized the result of the arithmetic is valid with the type.

uint256(-1) doesn't work anymore

In older versions of solidity, uint256(-1) could be used to retrieve the maximum value, but that won't compile anymore.

It's better to just avoid all these gymnastics and just do type(uint256).max;

Just how big is a 2^256 - 1?

To put some context on the number, the estimated number of atoms in the known universe is roughly 10^80. To visualize it, let's place the numbers side by side:

115792089237316195423570985008687907853269984665640564039457584007913129639935

100000000000000000000000000000000000000000000000000000000000000000000000000000000

That roughly means 1,000 uint256 variables could enumerate every atom on the known universe. Since most "things" of interest are made up of far more than 1,000 atoms, a single uint256 can enumerate any useful set of things with plenty of room to spare.

As a corollary, two randomly chosen uint256 values (equivalent to the output of a keccak256 hash), for all practical purposes, won't ever have a collision.

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