Not to be confused with prime number.
While an apostrophe is often used in place of the prime (and a double quote in place of the double prime) due to the lack of the prime and double prime symbols on everyday keyboards, such substitutions would not normally be considered appropriate in formal materials or in typesetting.
Designation of units
See also: Positional notation § Sexagesimal system
Primes are also used for angles.
In historical astronomical works, the triple prime was used to denote "thirds" (⁄60 of an arcsecond) and a quadruple prime ⁗ "fourths" (⁄60 of a third of arc), but modern usage has replaced this with decimal values of arcseconds.
Primes are sometimes used to indicate minutes, and double primes to indicate seconds of time, as in the John Cage composition 4'33", pronounced (and the composition itself lasting) 4 minutes 33 seconds.
This notation only applies to duration, and is seldom used for durations longer than 60 minutes.
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 derivative or differentiated function: in 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).
- 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 prime is said to "decorate" the letter to which it applies.
In physics, the prime is used to denote variables after an event.
For example, vA′ 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′.
For example, J ′ denotes the upper state of the quantum number J while J ″ denotes the lower state of the quantum number J.
Thus, when indicating the direction of movement of an enzyme 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 is 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
However, in ISO 9, the corresponding modifier letters are used instead.
While easy to write, the bar notation proved difficult to typeset, leading to the adoption of the prime symbol to indicate a bar.
(Despite the lack of bar, the unit would still be read as "X bar", as opposed to "X prime".)
With contemporary development of typesetting software such as LaTeX, 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
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.
The name "prime" is something of a metonymy.
Through the early part of the 20th century, the notation x′ was read as "x prime" not because it was an x followed by a "prime symbol", but because it was the first in the series that continued with x″ ("x second") and x‴ ("x third").
It was only later, in the 1950s and 1960s, that the term "prime" began to be applied to the apostrophe-like symbol itself.
Although it is now more common to pronounce x″ and x‴ as "x double prime" and "x triple prime", these are still sometimes pronounced in the old manner as "x second" and "x third".
Unicode and HTML representations of the prime and related symbols are as follows.
- U+2032 ′ PRIME (HTML ′ · ′) (lower case p)
- U+2033 ″ DOUBLE PRIME (HTML ″ · ″) (upper case P)
- U+2034 ‴ TRIPLE PRIME (HTML ‴ · ‴)
- U+2035 ‵ REVERSED PRIME (HTML ‵ · ‵, ‵)
- U+2036 ‶ REVERSED DOUBLE PRIME (HTML ‶)
- U+2037 ‷ REVERSED TRIPLE PRIME (HTML ‷)
- U+2057 ⁗ QUADRUPLE PRIME (HTML ⁗ · ⁗)
- U+02B9 ʹ MODIFIER LETTER PRIME (HTML ʹ)
- U+02BA ʺ MODIFIER LETTER DOUBLE PRIME (HTML ʺ)
- U+0022 " QUOTATION MARK (HTML " · ", ") (often misused as double prime)
- U+0027 ' APOSTROPHE (HTML ' · ') (often misused as a single prime)
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).
- List of typographical symbols and punctuation marks
- Table of mathematical symbols by introduction date
- Typewriter conventions
- Rubik's Cube move notation, where the prime is used to invert moves or move sequences.
Credits to the contents of this page go to the authors of the corresponding Wikipedia page: en.wikipedia.org/wiki/Prime (symbol).