WordNet (r) 3.0 (2006):

magic number
    n 1: the atomic number of an extra stable strongly bound atomic
         nucleus: 2, 8, 20, 28, 50, 82 or 126

The Jargon File (version 4.4.7, 29 Dec 2003):

magic number
 n.

    [Unix/C; common]

    1. In source code, some non-obvious constant whose value is significant to
    the operation of a program and that is inserted inconspicuously in-line (
    hardcoded), rather than expanded in by a symbol set by a commented #define
    . Magic numbers in this sense are bad style.

    2. A number that encodes critical information used in an algorithm in some
    opaque way. The classic examples of these are the numbers used in hash or
    CRC functions, or the coefficients in a linear congruential generator for
    pseudo-random numbers. This sense actually predates and was ancestral to
    the more common sense

    3. Special data located at the beginning of a binary data file to indicate
    its type to a utility. Under Unix, the system and various applications
    programs (especially the linker) distinguish between types of executable
    file by looking for a magic number. Once upon a time, these magic numbers
    were PDP-11 branch instructions that skipped over header data to the
    start of executable code; 0407, for example, was octal for ?branch 16 bytes
    relative?. Many other kinds of files now have magic numbers somewhere; some
    magic numbers are, in fact, strings, like the ! at the beginning of a
    Unix archive file or the %! leading PostScript files. Nowadays only a 
    wizard knows the spells to create magic numbers. How do you choose a fresh
    magic number of your own? Simple ? you pick one at random. See? It's magic!

    4. An input that leads to a computational boundary condition, where
    algorithm behavior becomes discontinuous. Numeric overflows (particularly
    with signed data types) and run-time errors (divide by zero, stack
    overflows) are indications of magic numbers. The Y2K scare was probably the
    most notorious magic number non-incident.

    The magic number, on the other hand, is 7?2. See The magical number seven,
    plus or minus two: some limits on our capacity for processing information
    by George Miller, in the Psychological Review 63:81-97 (1956). This classic
    paper established the number of distinct items (such as numeric digits)
    that humans can hold in short-term memory. Among other things, this
    strongly influenced the interface design of the phone system.


The Free On-line Dictionary of Computing (30 December 2018):

magic number

    1. In source code, some non-obvious
   constant whose value is significant to the operation of a
   program and that is inserted inconspicuously in-line
   (hard-coded), rather than expanded in by a symbol set by a
   commented "#define".  Magic numbers in this sense are bad
   style.

   2. A number that encodes critical information used in an
   algorithm in some opaque way.  The classic examples of these
   are the numbers used in hash or CRC functions or the
   coefficients in a linear congruential generator for
   pseudorandom numbers.  This sense actually predates, and
   was ancestral to, the more common sense 1.

   3. Special data located at the beginning of a binary data
   file to indicate its type to a utility.  Under Unix, the
   system and various applications programs (especially the
   linker) distinguish between types of executable file by
   looking for a magic number.  Once upon a time, these magic
   numbers were PDP-11 branch instructions that skipped over
   header data to the start of executable code; 0407, for
   example, was octal for "branch 16 bytes relative".  Nowadays
   only a wizard knows the spells to create magic numbers.  MS
   DOS executables begin with the magic string "MZ".

   *The* magic number, on the other hand, is 7+/-2.  The paper
   cited below established the number of distinct items (such as
   numeric digits) that humans can hold in short-term memory.
   Among other things, this strongly influenced the interface
   design of the phone system.

   ["The magical number seven, plus or minus two: some limits on
   our capacity for processing information", George Miller, in
   the "Psychological Review" 63:81-97, 1956].

   [Jargon File]

   (2003-07-02)