Isn't the maximum value of private keys based on the p of secp256k1, which is  2²⁵⁶ - 2³² - 2⁹ - 2⁸ - 2⁷ - 2⁶ - 2⁴ - 1 ?  It's close to  2²⁵⁶, but not exact.  Not to be pedantic, just want to make sure my understanding is correct.

Range of valid private keys
Nearly every 256-bit number is a valid private key. Specifically, any 256-bit number between 0x1 and 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141 is a valid private key.
The range of valid private keys is governed by the secp256k1 ECDSA standard used by Bitcoin.