View source for Prime (symbol)

{{Short description|Typographical symbol}}
{{hatgrp|{{Redirect-multi|2|Prime 2|Prime 3|the respective games in the ''Metroid Prime'' series|Metroid Prime 2: Echoes{{!}}''Metroid Prime 2: Echoes''|and|Metroid Prime 3: Corruption{{!}}''Metroid Prime 3: Corruption''}}
{{Distinguish|prime number|apostrophe}}}}
{{Infobox punctuation mark|mark={{prime}}|name=Prime<!--
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The '''prime''' symbol {{char|{{prime}}}}, '''double prime''' symbol {{char|{{pprime}}}}, '''triple prime''' symbol {{char|‴}}, and '''quadruple prime''' symbol {{char|⁗}} are used to designate units and for other purposes in [[mathematics]], [[science]], [[linguistics]] and [[music]].

Although the characters differ little in appearance from those of the [[apostrophe]] and single and double [[quotation mark]]s, the uses of the prime symbol are quite different.<ref>{{cite book |first=Ron |last=Goldberg |chapter=Quotes |chapter-url=https://books.google.com/books?id=uo1j1buy2qYC&pg=PA67 |editor1=Frank J. Romano |title=Digital Typography: Practical Advice for Getting the Type You Want When You Want It |publisher=Windsor Professional Information |location=[[San Diego]] |year=2000 |page=[https://archive.org/details/digitaltypograph0000gold/page/68 68] |isbn=1-893190-05-6 |oclc=44619239 |url=https://archive.org/details/digitaltypograph0000gold/page/67 }}</ref> While an apostrophe is now often used in place of the prime, and a double quote in place of the double prime (due to the lack of prime symbols on everyday writing keyboards), such substitutions are not considered appropriate in formal materials or in [[typesetting]].

==Designation of units==
{{See also|Positional notation#Sexagesimal system}}The prime symbol {{char|{{prime}}}} is commonly used to represent [[foot (length)|feet (ft)]], and the double prime {{char|{{pprime}}}} is used to represent [[inch|inches (in)]].<ref>{{cite book| title = Chicago Manual of Style | edition = 17th | date = 2017 | publisher = University of Chicago Press | at = ¶ 10.66}}</ref> The triple prime {{char|‴}}, as used in [[watchmaking]], represents a {{lang|fr|[[ligne]]}} ({{frac|1|12}} of a "French" inch, or ''[[pouce]]'', about {{convert|2.26|mm|disp=or}}).<ref>{{cite magazine|url = https://www.lepoint.fr/montres/Magazine/Le-saviez-vous/pourquoi-les-horlogers-utilisent-ils-la-ligne-pour-mesurer-le-diametre-d-encageage-d-un-mouvement-06-12-2012-2002329_3013.php# | title = Pourquoi les horlogers utilisent-ils la ligne pour mesurer le diamètre d'encageage d'un mouvement? |lang =fr | trans-title = Why do watchmakers use the ''ligne'' to measure the casing diameter of a movement? |magazine = [[Le Point]] | date=  | quote = Une ligne équivaut à 2,2558 mm, que l'on arrondit généralement à 2,26 mm. |trans-quote=A ''ligne'' equates to 2.2558 mm, which is typically rounded to 2.26mm}}</ref>

Primes are also used for [[angle|angles]]. The prime symbol {{char|{{prime}}}} is used for [[arcminute]]s ({{frac|1|60}} of a degree), and the double prime {{char|{{pprime}}}} for [[arcsecond]]s ({{frac|1|60}} of an arcminute).<ref name="Las Cumbres">{{cite web|title=Positions and Sizes of Cosmic Objects|url=https://lco.global/spacebook/using-angles-describe-positions-and-apparent-sizes-objects/|publisher=Las Cumbres Observatory|year=2019}}</ref> As an angular measurement, {{char|3°&nbsp;5{{prime}}&nbsp;30{{pprime}}}} means 3 [[degree (angle)|degree]]s, 5 arcminutes and 30 arcseconds. In historical astronomical works, the triple prime was used to denote "[[third (angle)|thirds]]" ({{frac|1|60}} of an arcsecond)<ref name="Schultz_1797">{{cite book| first=Johann | last=Schultz | title=Kurzer Lehrbegriff der Mathematik. Zum Gebrauch der Vorlesungen und für Schulen | location=Königsberg | date=1797 | page=185 | language=German <!-- | url=http: google books erBEAAAAcAAJ -->}}</ref><ref>{{cite book | title=A natural history of vision | url=https://archive.org/details/naturalhistoryof0000wade | url-access=registration | last=Wade | first=Nicholas | publisher=MIT Press | year=1998 | isbn=978-0-262-73129-4 | page=[https://archive.org/details/naturalhistoryof0000wade/page/193 193]}}</ref> and a quadruple prime {{char|⁗}} "[[fourth (angle)|fourth]]s" ({{frac|1|60}} of a third of arc),{{efn|[[John Wallis]], in his ''Mathesis universalis'', generalized this notation to include higher multiples of 60; giving as an example the number {{nowrap|49‵‵‵‵36‵‵‵25‵‵15‵1°15{{prime}}2{{pprime}}36‴49⁗}}; where the numbers to the left are multiplied by higher powers of 60, the numbers to the right are divided by powers of 60, and the number marked with the superscripted zero is multiplied by 1.<ref>{{citation | last = Cajori | first = Florian | authorlink = Florian Cajori | title = A History of Mathematical Notations | publisher = Cosimo, Inc.  | volume = 1 | orig-year = 1928 | year = 2007 | location = New York | page = 216 | url = https://books.google.com/books?id=OQZxHpG2y3UC | isbn = 9781602066854 }}</ref>}} but modern usage has replaced this with [[Decimal#Decimal_fractions|decimal fractions]] of an arcsecond.

Primes are sometimes used to indicate minutes, and double primes to indicate seconds of time, as in the [[John Cage]] composition ''[[4′33″|4{{prime}}33{{pprime}}]]'' (spoken as "four thirty-three"), a composition that lasts exactly 4 minutes 33 seconds. This notation only applies to duration, and is seldom used for durations longer than 60 minutes.<ref>{{cite web |title=time - English notation for hour, minutes and seconds |url=https://english.stackexchange.com/questions/114205/english-notation-for-hour-minutes-and-seconds |website=English Language & Usage Stack Exchange |access-date=6 June 2020}}</ref>{{better source|reason=This is an open-access forum, not a [[wp:reliable source]]|date=June 2020}}

==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 {{math|''{{prime|x}}''}} generally meaning something related to (or derived from) {{math|''x''}}. For example, if a point is represented by the [[Cartesian coordinates]] {{math|(''x'', ''y'')}}, then that point rotated, translated or reflected might be represented as {{math|(''{{prime|x}}'', ''{{prime|y}}'')}}.

Usually, the meaning of {{math|''{{prime|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]], {{math|''f''{{thinsp}}{{prime}}(''x'')}} and {{math|''f''{{thinsp}}&Prime;(''x'')}} are the first and second derivatives of {{math|''f''{{thinsp}}(''x'')}} with respect to {{math|''x''}}. Likewise for {{math|''f''{{thinsp}}‴(''x'')}} and {{math|''f''{{thinsp}}⁗(''x'')}} . Similarly, if {{math|1=''y'' = ''f''{{thinsp}}(''x'')}}, then {{math|''{{prime|y}}''}} and {{math|''y''&Prime;}} are the first and second derivatives of {{math|''y''}} with respect to {{math|''x''}}. Other notation for derivatives also exists (see [[Notation for differentiation]]).
* [[Set (mathematics)|Set]] [[complement (set theory)|complement]]: {{math|''{{prime|A}}''}} is the complement of the set {{math|''A''}} (other notation also exists).<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Prime|url=https://mathworld.wolfram.com/Prime.html|access-date=2020-08-31|website=mathworld.wolfram.com|language=en}}</ref>
* The negation of an [[Event (probability theory)|event]] in probability theory: {{math|1=Pr(''{{prime|A}}'') = 1 &minus; Pr(''A'')}} (other notation also exists).
* The result of a [[Transformation (mathematics)|transformation]]: {{math|1=''Tx'' = ''{{prime|x}}''}}
* The [[transpose]] of a matrix (other notation also exists)
*The [[Dual space|dual]] of a [[vector space]]
The prime is said to "decorate" the letter to which it applies. The same convention is adopted in [[functional programming]], particularly in [[Haskell (programming language)|Haskell]].

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, {{math|''v''<sub>A</sub>{{prime}}}} would indicate the velocity of object A after an event. It is also commonly used in relativity: the event at {{math|(x, y,  z, t)}} in [[Inertial frame of reference|frame]] {{math|''S''}}, has coordinates {{math|({{prime|x}}, {{prime|y}}, {{prime|z}}, {{prime|t}})}} in frame {{math|''{{prime|S}}''}}.

In [[chemistry]], it is used to distinguish between different functional groups connected to an atom in a molecule, such as {{chem|R}} and {{chem|{{prime|R}}}}, representing different [[alkyl]] groups in an [[organic compound]]. The [[carbonyl]] carbon in proteins is denoted as {{chem|{{prime|C}}}}, which distinguishes it from the other [[Protein#Biochemistry|backbone]] carbon, the [[Alpha and beta carbon|alpha carbon]], which is denoted as {{chem|C<sub>α</sub>}}. In [[physical chemistry]], it is used to distinguish between the lower state and the upper state of a [[quantum number]] during a transition. For example, {{chem|''J''{{hairsp}}{{prime}}}} denotes the upper state of the quantum number {{chem|''J''}} while {{chem|''J''{{hairsp}}&Prime;}} denotes the lower state of the quantum number {{chem|''J''}}.<ref>{{cite web|url=https://physics.nist.gov/PhysRefData/MolSpec/Triatomic/Html/sec4.html|title=Triatomic Spectral Database - List of Symbols|author=|date=|website=www.physics.nist.gov|access-date=22 January 2020}}</ref>

In [[molecular biology]], the prime is used to denote the positions of carbon on a ring of [[deoxyribose]] or [[ribose]]. The prime distinguishes places on these two chemicals, rather than places on other parts of [[DNA]] or [[RNA]], like [[phosphate group]]s or [[nucleic acid]]s. Thus, when indicating the direction of movement of an [[enzyme]] along a string of DNA, biologists will say that it moves from the {{chem|5{{prime}}}} end to the {{chem|3{{prime}}}} end, because these carbons are on the ends of the DNA molecule. The chemistry of this reaction demands that the {{chem|3{{prime}} OH}} be extended by DNA synthesis. Prime can also be used to indicate which position a molecule has attached to, such as {{chem|5{{prime}}-monophosphate.}}

==Use in linguistics==
The prime can be used in the [[transliteration]] of some [[language]]s, such as [[Slavic languages]], to denote [[Palatalization (phonetics)|palatalization]]. Prime and double prime are used to transliterate Cyrillic [[Soft sign|yeri]] (the soft sign, ь) and [[yer]] (the hard sign, ъ).<ref>{{cite book |last = Bethin |first= Christina Y |year= 1998 |title=Slavic Prosody: Language Change and Phonological Theory | publisher= Cambridge University Press |page= 6 | isbn=978-0-52-159148-5 }}</ref> However, in [[ISO 9]], the corresponding modifier letters are used instead.

Originally, [[X-bar theory]] used a bar over syntactic units to indicate bar-levels in [[syntactic structure]], generally rendered as an [[overbar]]. 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==
{{Contains special characters|Uncommon Unicode|section|compact=y}}
[[File:Helmholtz pitch notation c.svg|200px|left|thumb|Prime, double prime and triple prime]]
The prime symbol is used in combination with lower case letters in the [[Helmholtz pitch notation]] system to distinguish notes in different [[octave]]s from [[middle C]] upwards.  Thus {{char|c}} represents the {{angbr|C}} below middle C, {{char|{{prime|c}}}} represents middle C, {{char|c{{pprime}}}} represents the {{angbr|C}} in the octave above middle C, and {{char|c&#x2034;}} the {{angbr|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 {{char|C}} represents the {{angbr|C}} below the bass stave, while {{char|C ͵}} represents the {{angbr|C}} in the octave below that.

In some musical scores, the double prime {{char|{{pprime}}}} is used to indicate a length of time in seconds. It is used over a [[fermata]] {{char|𝄐}} denoting a long note or rest.{{efn|Some systems fail to display this symbol. In picture form, it is [[Image:Fermata.svg|frameless|upright 0.1 |alt=Image of a fermata symbol, a horizontal concave curve enclosing a dot below]].}}

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

* {{unichar|2032|Prime|html=}} (lower case p)
* {{unichar|2033|Double prime|html=}} (upper case P)
* {{unichar|2034|Triple prime|html=}}
* {{unichar|2035|Reversed prime|html=}}
* {{unichar|2036|Reversed double prime|html=}}
* {{unichar|2037|Reversed triple prime|html=}}
* {{unichar|2057|Quadruple prime|html=}}
* {{unichar|02B9|Modifier letter prime|html=}}
* {{unichar|02BA|Modifier letter double prime|html=}}

The "[[modifier letter prime]]" and "modifier letter double prime" characters are intended for linguistic purposes, such as the indication of [[Stress (linguistics)|stress]] or the transliteration of certain [[Cyrillic]] characters.{{Citation needed|date=June 2021|reason=As said in https://en.wikipedia.org/wiki/Stress_(linguistics)
acute accent and grave accent are used to indicate stress in Russian, Belarusian, and Ukrainian. These might be used in transliteration but without a reliable, published sources it looks like original research.}}

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, {{code|\prime}} (<math>\prime</math>), which, when used in super- or sub-scripts, renders appropriately; e.g., <code>f_\prime^\prime</code> appears as <math>f_\prime^\prime</math>. An apostrophe, {{code|'}}, is a shortcut for a superscript prime; e.g., {{code|f'}} appears as <math>f'\,\!</math>.

== See also ==

* {{annotated link|List of mathematical symbols by subject}}
* {{annotated link|List of typographical symbols and punctuation marks}}
* [[Rubik's Cube#Move notation|Rubik's Cube move notation]], where the prime is used to invert moves or move sequences.<ref>{{cite web|url=https://www.worldcubeassociation.org/regulations/#article-12-notation|title=WCA Regulations - World Cube Association|author=|date=|website=www.worldcubeassociation.org|access-date=22 March 2018}}</ref>
* {{annotated link|Table of mathematical symbols by introduction date}}
* {{annotated link|Typewriter#Typewriter conventions|Typewriter conventions}}

==Notes==
{{notelist}}

==References==
{{reflist}}

== External links ==
* [http://unicode.org/charts/PDF/U2000.pdf Unicode General Punctuation code chart]
* [https://www.unicode.org/charts/PDF/U02B0.pdf Unicode Spacing Modifier Letters code chart]

{{Typography terms}}
{{navbox punctuation}} <!-- and typographic marks -->
{{Use dmy dates|date=May 2020}}

[[Category:Mathematical symbols]]
[[Category:Typographical symbols]]