Prime (symbol)

"Prime 2" and "Prime 3" redirect here. For the respective games in the Metroid Prime series, see Metroid Prime 2: Echoes and Metroid Prime 3: Corruption.

Not to be confused with prime number or apostrophe.

See also:

Primes are also used for

of an arcsecond.

Primes are sometimes used to indicate minutes, and double primes to indicate seconds of time, as in the

better source needed

]

Use in mathematics, statistics, and science

In mathematics, the prime is generally used to generate more variable names for similar things without resorting to subscripts, with x′ generally meaning something related to (or derived from) x. For example, if a point is represented by the

Cartesian coordinates

(x, y), then that point rotated, translated or reflected might be represented as (x′, y′).

Usually, the meaning of x′ is defined when it is first used, but sometimes, its meaning is assumed to be understood:

• A
  Lagrange's notation, f ′(x) and f ″(x) are the first and second derivatives of f (x) with respect to x. Likewise are f ‴(x) and f ⁗(x) . Similarly, if y = f (x), then y′ and y″ are the first and second derivatives of y with respect to x. Other notation for derivatives also exists (see Notation for differentiation
  ).
• Set complement: A′ is the complement of the set A (other notation also exists).^[9]
• The negation of an event in probability theory: Pr(A′) = 1 − Pr(A) (other notation also exists).
• The result of a
  transformation
  : Tx = x′
• The transpose of a matrix (other notation also exists)
• The dual of a vector space

The prime is said to "decorate" the letter to which it applies. The same convention is adopted in

.

In geometry, geography and astronomy, prime and double prime are used as abbreviations for minute and second of arc (and thus latitude, longitude, elevation and right ascension).

In physics, the prime is used to denote variables after an event. For example, v_A′ would indicate the velocity of object A after an event. It is also commonly used in relativity: the event at (x, y,  z, t) in frame S, has coordinates (x′, y′, z′, t′) in frame S′.

In

In

along a string of DNA, biologists will say that it moves from the 5′ end to the 3′ end, because these carbons are on the ends of the DNA molecule. The chemistry of this reaction demands that the 3′ OH be extended by DNA synthesis. Prime can also be used to indicate which position a molecule has attached to, such as 5′-monophosphate.

Use in linguistics

The prime can be used in the transliteration of some languages, such as Slavic languages, to denote palatalization. Prime and double prime are used to transliterate Cyrillic yeri (the soft sign, ь) and yer (the hard sign, ъ).^[11] However, in ISO 9, the corresponding modifier letters are used instead.

Originally,

, typesetting bars is considerably simpler; nevertheless, both prime and bar markups are accepted usages.

Some X-bar notations use a double prime (standing in for a double-bar) to indicate a phrasal level, indicated in most notations by "XP".

Use in music

The prime symbol is used in combination with lower case letters in the

upwards. Thus c represents the ⟨C⟩ below middle C, c′ represents middle C, c″ represents the ⟨C⟩ in the octave above middle C, and c‴ the ⟨C⟩ in the octave two octaves above middle C. A combination of upper case letters and sub-prime symbols is used to represent notes in lower octaves. Thus C represents the ⟨C⟩ below the bass stave, while C ͵ represents the ⟨C⟩ in the octave below that.

In some musical scores, the double prime ″ is used to indicate a length of time in seconds. It is used over a fermata 𝄐 denoting a long note or rest.^[b]

Computer encodings

Unicode and HTML representations of the prime and related symbols are as follows.

• U+2032 ′ PRIME (′) (lower case p)
• U+2033 ″ DOUBLE PRIME (″) (upper case P)
• U+2034 ‴ TRIPLE PRIME (‴)
• U+2035 ‵ REVERSED PRIME (‵, ‵)
• U+2036 ‶ REVERSED DOUBLE PRIME
• U+2037 ‷ REVERSED TRIPLE PRIME
• U+2057 ⁗ QUADRUPLE PRIME (⁗)
• U+02B9 ʹ MODIFIER LETTER PRIME
• U+02BA ʺ MODIFIER LETTER DOUBLE PRIME

The "

]

In a context when the character set used does not include the prime or double prime character (e.g., in an online discussion context where only ASCII or

ISO 8859-1

[ISO Latin 1] is expected), they are often respectively approximated by ASCII apostrophe (U+0027) or quotation mark (U+0022).

LaTeX provides an oversized prime symbol, \prime (${\displaystyle \prime }$), which, when used in super- or sub-scripts, renders appropriately; e.g., f_\prime^\prime appears as ${\displaystyle f_{\prime }^{\prime }}$. An apostrophe, ', is a shortcut for a superscript prime; e.g., f' appears as ${\displaystyle f'\,\!}$.

See also

• List of mathematical symbols by subject
   – Meanings of symbols used in mathematicsPages displaying short descriptions of redirect targets
• List of typographical symbols and punctuation marks
• Rubik's Cube move notation, where the prime is used to invert moves or move sequences.^[12]
• Table of mathematical symbols by introduction date
• Typewriter conventions – Mechanical device for typing characters

Notes

References

External links

• Unicode General Punctuation code chart
• Unicode Spacing Modifier Letters code chart