$MaxMachineNumber is the largest machine-precision number that can be used on a particular computer system.
Numbers larger than $MaxMachineNumber are represented in arbitrary-precision form.
$MaxMachineNumber is typically , where is the maximum exponent that can be used in the internal representation of machine-precision numbers.
See The Mathematica Book: Section 3.1.6.
See also: $MinMachineNumber, $MachineEpsilon, $MachinePrecision.
Related package: NumericalMath`ComputerArithmetic`.