Prime (symbol)
Encyclopedia
The prime symbol double prime symbol ( ″ ), and triple prime symbol ( ), etc., are used to designate several different units, and for various other purposes in mathematics
, the sciences and linguistics
. The prime symbol should not be confused with the apostrophe
, single quotation mark
, acute accent
or grave accent
; the double prime should not be confused with the double quotation mark, the ditto mark
, or the letter double apostrophe
.
.
The double prime ( ″ ) represents inches (in)
, arcseconds (as) and seconds (s)
.
Thus, 3′ 5″ could mean 3 feet and 5 inches (of length), or 3 minutes and 5 seconds (of time). As an angular measurement, 3° 5′ 30″ means 3 degree
s, 5 arcminutes
and 30 arcseconds.
The triple prime ( ) in watchmaking represents a ligne
. It is also occasionally found in 17th- and 18th-century astronomical works to denote
of a second of arc.
s.
Usually, the meaning of x′ is defined when it is first used, but sometimes its meaning is assumed to be understood:
The prime is said to “decorate” the letter to which it applies. The same convention is adopted in functional programming
, particularly in Haskell
.
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′.
In chemistry
, it is used to distinguish between different functional groups connected to an atom in a molecule, such as R and R′, representing different alkyl groups in a ketone
.
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 groups 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 5′ end to the 3′ end, because these carbons are hanging from the ends of the molecule. Prime can also be used to indicate which position a molecule has attached to, such as “5′-monophosphate”.
of some language
s, such as Russian
, to denote palatalization
.
In transcribing Arabic, the prime symbol separates two letters that represent two different sounds, when the combination might otherwise be read as a digraph. For example s′h represents the two sounds s and h, rather than the single sound sh.
The prime is also used in X-bar theory
instead of a bar to indicate bar-levels in syntactic structures, because the bar was difficult to typeset. This is still read as "X bar", not "X prime".
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".
. 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 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 as "x double prime" and "x triple prime", these are still sometimes pronounced in the old manner as "x second" and "x third".
The "modifier letter prime" and "modifier letter double prime" characters are intended for linguistic purposes, such as the indication of stress
or the transliteration of certain Cyrillic characters.
When the character set used does not include the prime or double prime character (e.g., ISO 8859-1 is commonly assumed on IRC), they are often respectively approximated by normal or italic
apostrophes and quotation marks.
In LaTeX
math mode,
. Furthermore, LaTeX provides an oversized prime symbol, 
) for use in subscripts. For example, 
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the sciences and linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
. The prime symbol should not be confused with the apostrophe
Apostrophe
The apostrophe is a punctuation mark, and sometimes a diacritic mark, in languages that use the Latin alphabet or certain other alphabets...
, single quotation mark
Quotation mark
Quotation marks or inverted commas are punctuation marks at the beginning and end of a quotation, direct speech, literal title or name. Quotation marks can also be used to indicate a different meaning of a word or phrase than the one typically associated with it and are often used to express irony...
, acute accent
Acute accent
The acute accent is a diacritic used in many modern written languages with alphabets based on the Latin, Cyrillic, and Greek scripts.-Apex:An early precursor of the acute accent was the apex, used in Latin inscriptions to mark long vowels.-Greek:...
or grave accent
Grave accent
The grave accent is a diacritical mark used in written Breton, Catalan, Corsican, Dutch, French, Greek , Italian, Mohawk, Norwegian, Occitan, Portuguese, Scottish Gaelic, Vietnamese, Welsh, Romansh, and other languages.-Greek:The grave accent was first used in the polytonic orthography of Ancient...
; the double prime should not be confused with the double quotation mark, the ditto mark
Ditto mark
The ditto mark is a typographic symbol indicating that the word or figure above it are to be repeated. For example:It has Unicode code-point U+3003 , though in practice closing double quotation marks or straight double quotation marks are often used instead...
, or the letter double apostrophe
Modifier letter double apostrophe
The modifier letter double apostrophe is a spacing glyph. It is used in the orthography of Tundra Nenets to denote a glottal stop, or in the orthography of Dan to indicate that a syllable has a top tone. It is encoded at .-See also:...
.
Designation of units
The prime symbol ( ′ ) is commonly used to represent feet (ft), arcminutes (am) and minutes (min)Minute
A minute is a unit of measurement of time or of angle. The minute is a unit of time equal to 1/60th of an hour or 60 seconds. In the UTC time scale, a minute on rare occasions has 59 or 61 seconds; see leap second. The minute is not an SI unit; however, it is accepted for use with SI units...
.
The double prime ( ″ ) represents inches (in)
Inch
An inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot...
, arcseconds (as) and seconds (s)
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
.
Thus, 3′ 5″ could mean 3 feet and 5 inches (of length), or 3 minutes and 5 seconds (of time). As an angular measurement, 3° 5′ 30″ means 3 degree
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
s, 5 arcminutes
Minute of arc
A minute of arc, arcminute, or minute of angle , is a unit of angular measurement equal to one sixtieth of one degree. In turn, a second of arc or arcsecond is one sixtieth of one minute of arc....
and 30 arcseconds.
The triple prime ( ) in watchmaking represents a ligne
Ligne
The ligne is a unit of length that was in use prior to the French adoption of the metric system in the late 18th century, and is still used by French and Swiss wristwatch makers to measure the size of a watch movement.- Watchmakers' use :There are 12 lignes to one French inch...
. It is also occasionally found in 17th- and 18th-century astronomical works to denote
of a second of arc.Use in mathematics, statistics, and science
In mathematics, the prime is generally used to generate more variable names for things which are similar, without resorting to subscripts—x′ generally means 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′). The prime symbol is not related to prime numberPrime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s.
Usually, the meaning of x′ is defined when it is first used, but sometimes its meaning is assumed to be understood:
- A derivativeDerivativeIn calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
or derived function: f′(x) and f″(x) are the first and second derivatives of f(x) with respect to x. Similarly, if y = f(x) then y′ and y″ are the first and second derivatives of y with respect to x. (Other notation exists.) - Set complementComplement (set theory)In set theory, a complement of a set A refers to things not in , A. The relative complement of A with respect to a set B, is the set of elements in B but not in A...
: A′ is the complement of the set A (other notation exists) - The negation of an eventEvent (probability theory)In probability theory, an event is a set of outcomes to which a probability is assigned. Typically, when the sample space is finite, any subset of the sample space is an event...
in probability theory: Pr(A′) = 1 − Pr(A) (other notation exists) - The result of a transformationTransformation (mathematics)In mathematics, a transformation could be any function mapping a set X on to another set or on to itself. However, often the set X has some additional algebraic or geometric structure and the term "transformation" refers to a function from X to itself that preserves this structure.Examples include...
: Tx = x′ - The transposeTransposeIn linear algebra, the transpose of a matrix A is another matrix AT created by any one of the following equivalent actions:...
of a matrix.
The prime is said to “decorate” the letter to which it applies. The same convention is adopted in functional programming
Functional programming
In computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast to the imperative programming style, which emphasizes changes in state...
, particularly in Haskell
Haskell (programming language)
Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing. It is named after logician Haskell Curry. In Haskell, "a function is a first-class citizen" of the programming language. As a functional programming language, the...
.
In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, 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
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...
S has coordinates (x′, y′, z′, t′) in frame S′.
In chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, it is used to distinguish between different functional groups connected to an atom in a molecule, such as R and R′, representing different alkyl groups in a ketone
Ketone
In organic chemistry, a ketone is an organic compound with the structure RCR', where R and R' can be a variety of atoms and groups of atoms. It features a carbonyl group bonded to two other carbon atoms. Many ketones are known and many are of great importance in industry and in biology...
.
In molecular biology
Molecular biology
Molecular biology is the branch of biology that deals with the molecular basis of biological activity. This field overlaps with other areas of biology and chemistry, particularly genetics and biochemistry...
, the prime is used to denote the positions of carbon on a ring of deoxyribose
Deoxyribose
Deoxyribose, more, precisely 2-deoxyribose, is a monosaccharide with idealized formula H---3-H. Its name indicates that it is a deoxy sugar, meaning that it is derived from the sugar ribose by loss of an oxygen atom...
or ribose
Ribose
Ribose is an organic compound with the formula C5H10O5; specifically, a monosaccharide with linear form H––4–H, which has all the hydroxyl groups on the same side in the Fischer projection....
. The prime distinguishes places on these two chemicals, rather than places on other parts of DNA
DNA
Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...
or RNA
RNA
Ribonucleic acid , or RNA, is one of the three major macromolecules that are essential for all known forms of life....
, like phosphate groups or nucleic acid
Nucleic acid
Nucleic acids are biological molecules essential for life, and include DNA and RNA . Together with proteins, nucleic acids make up the most important macromolecules; each is found in abundance in all living things, where they function in encoding, transmitting and expressing genetic information...
s. Thus, when indicating the direction of movement of an enzyme
Enzyme
Enzymes are proteins that catalyze chemical reactions. In enzymatic reactions, the molecules at the beginning of the process, called substrates, are converted into different molecules, called products. Almost all chemical reactions in a biological cell need enzymes in order to occur at rates...
along a string of DNA, biologists will say that it moves from the 5′ end to the 3′ end, because these carbons are hanging from the ends of the molecule. 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 transliterationTransliteration
Transliteration is a subset of the science of hermeneutics. It is a form of translation, and is the practice of converting a text from one script into another...
of some language
Language
Language may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...
s, such as Russian
Russian language
Russian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...
, to denote palatalization
Palatalization
In linguistics, palatalization , also palatization, may refer to two different processes by which a sound, usually a consonant, comes to be produced with the tongue in a position in the mouth near the palate....
.
In transcribing Arabic, the prime symbol separates two letters that represent two different sounds, when the combination might otherwise be read as a digraph. For example s′h represents the two sounds s and h, rather than the single sound sh.
The prime is also used in X-bar theory
X-bar theory
X-bar theory is a component of linguistic theory which attempts to identify syntactic features presumably common to all those human languages that fit in a presupposed framework...
instead of a bar to indicate bar-levels in syntactic structures, because the bar was difficult to typeset. This is still read as "X bar", not "X prime".
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 Rubik's Cube notation
In Rubik's Cube move notation the prime is used to invert moves or move sequences. (Where L means "Turn the face on the left 90 degrees clockwise", L means "turn the left face 90 degrees anti-clockwise".)History
The name "prime" is something of a misnomerMisnomer
A misnomer is a term which suggests an interpretation that is known to be untrue. Such incorrect terms sometimes derive their names because of the form, action, or origin of the subject becoming named popularly or widely referenced—long before their true natures were known.- Sources of misnomers...
. 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 third"). It was only later, in the 1950s and 1960s, that the term "prime" began to be applied to the apostrophe
Apostrophe
The apostrophe is a punctuation mark, and sometimes a diacritic mark, in languages that use the Latin alphabet or certain other alphabets...
-like symbol itself. Although it is now more common to pronounce x″ and as "x double prime" and "x triple prime", these are still sometimes pronounced in the old manner as "x second" and "x third".
Representations
Unicode and HTML representations of the prime and related symbols are as follows.| Character | Unicode Unicode Unicode is a computing industry standard for the consistent encoding, representation and handling of text expressed in most of the world's writing systems... |
HTML entity |
| Prime ( ′ ) | U+2032 | ′ |
| Double prime ( ″ ) | U+2033 | ″ |
| Triple prime ( ) | U+2034 | – |
| Quadruple prime ( ) | U+2057 | – |
| Modifier letter prime ( ) | U+02B9 | – |
| Modifier letter double prime ( ) | U+02BA | – |
The "modifier letter prime" and "modifier letter double prime" characters are intended for linguistic purposes, such as the indication of stress
Stress (linguistics)
In linguistics, stress is the relative emphasis that may be given to certain syllables in a word, or to certain words in a phrase or sentence. The term is also used for similar patterns of phonetic prominence inside syllables. The word accent is sometimes also used with this sense.The stress placed...
or the transliteration of certain Cyrillic characters.
When the character set used does not include the prime or double prime character (e.g., ISO 8859-1 is commonly assumed on IRC), they are often respectively approximated by normal or italic
Italic type
In typography, italic type is a cursive typeface based on a stylized form of calligraphic handwriting. Owing to the influence from calligraphy, such typefaces often slant slightly to the right. Different glyph shapes from roman type are also usually used—another influence from calligraphy...
apostrophes and quotation marks.
In LaTeX
LaTeX
LaTeX is a document markup language and document preparation system for the TeX typesetting program. Within the typesetting system, its name is styled as . The term LaTeX refers only to the language in which documents are written, not to the editor used to write those documents. In order to...
math mode,
f' (f with an apostrophe) is rendered as . Furthermore, LaTeX provides an oversized prime symbol, \prime () for use in subscripts. For example, f_\prime^\prime appears as .