This WikiProject is aimed at improving editing practice on articles devoted to numbers. General guideline advise is given below to assist in creating and improving these articles.

Number Article Guidelines

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WP:NUM/G

This is an essay on article content. It contains the advice and/or opinions of one or more WikiProjects on how the content policies may be interpreted within their area of interest.

This information is not a formal Wikipedia policy or guideline, as it has not been thoroughly vetted by the community.

General guidelines

When should an article exist?

See Wikipedia:Notability (numbers) § Notability of specific individual numbers for guidelines on when an article on a number should exist.

The sections #Assessing mathematical number facts and #Assessing content outside of pure mathematics on this page have guidelines for what content should go on such articles.

Outline

Articles can be divided into section based on how much content there is for each area; an "In mathematics" grouping is common but optional (e.g. if there is only mathematical information). Mathematical content should come before non-mathematical content, such as practical uses, significant appearances in science, cultural associations, or history of the symbol.

Mathematical coverage should open with simple mathematical properties of the number and list some simple associated objects (its associated polygon, factors, whether it is a prime, etc.). Then it should move on to more obscure number facts (type of prime), its role in mathematical history and associations with more obscure objects (number of platonic solids, interesting group with n elements, etc.). Facts that should not be included in a number article include: figurate numbers, arbitrary properties of the number (for example its square or square root), anything having to with a specific base of expression, the aliquot sum, its position in a specific OEIS sequence (unless several works of mathematical literature consider this to be of interest).

Infobox

**Example number infobox**
← N − 1 N N + 1 →
← x₀ x₁ x₂ x₃ x₄ N x₆ x₇ x₈ x₉ →
List of numbers ‧ Integers
← y 2y 3y 4y 5y 6y 7y 8y 9y 10y →
Cardinal	en
Ordinal	Nth
Factorization	1 × N (prime) or p_a × p_b × ...
Divisors	1, p_a, p_b, p_c, ..., p_a × p_b, ..., N
Roman numeral	"N"
Binary	"N₂"
...	...
Hexadecimal	"N₁₆"

The infobox (added at the top of the page using the template {{Infobox number}}) should include the symbol of the number in all known numeral systems for which Unicode characters exist, as long as it fits within a reasonable amount of space. Examples include Egyptian, Roman, Tamil, Cyrillic, and Burmese (refer to in infobox at the article for 1 for a good list of examples and relevant Wiki markup.)
Divisors should be listed in the infobox (if they fit in a reasonable amount of space); they can be omitted from the article prose.

These are exceptions to the usual practice of only summarizing body text in the infobox (see MOS:INFOBOXEXCEPTIONS).

Symbolic and linguistic representations

For numbers which are also individual characters, information about entymology, history, and appearance etc. should remain in the articles about the specific numeral systems (e.g. Roman numerals, Tamil numerals), which should be linked from their symbols in the infobox. An exception is made for the English numerals, where their etymology and history of symbolic representation should be written in summary style with a {{main}} template at the start of the section, e.g.:
Defer translations (of which there are a huge number) to Wiktionary. Make sure there is a link (produced with {{wiktionary}}) in the "See also" section or lower (for numbers where a Wiktionary entry exists; numeral preferred - e.g. wikt:1 - but word or words if needed - e.g. wikt:one million).
Defer explanation about how to construct number names in words to the articles Cardinal numeral and Ordinal numeral, which are automatically linked from the infobox. (These cover all languages, so language-specific details are further deferred to articles like English numerals.)

Assessing mathematical number facts

The purpose of number articles is to provide a broad overview of a number's history, properties, and uses, without going into excessive detail (see WP:Summary). While there is an endless array of true mathematical facts about a given number, not all of them are appropriate for inclusion. Deciding which facts to include has been a source of considerable WP:Wikidrama. Even if a fact is on topic, it may still not be interesting enough to warrant inclusion (see the interesting number paradox). This section provides several criteria for assessing the suitability of a mathematical number fact.

Simple facts

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WP:NUM/SIMPLE

Simple facts are helpful, easily understood details about a number. They do not have to be sourced and should be included in a number article, although they are usually not sufficient reason to justify the existence of an article on their own. This criterion should be applied sparingly. A good rule of thumb is: "Would someone with no background in mathematics be expected to know this?".

Examples of simple facts:

On 1729: 1729 is the natural number following 1728 and preceding 1730.
On 1729: 1729 is a composite number with factors 1, 7, 13, 19, 91, 133, 247, and 1729.

Examples that are not simple facts:

On 9: "The aliquot sum of 9 is 4".
On 11: The rows of Pascal's triangle can be seen as representations of the powers of 11.

Routine facts

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WP:NUM/ROUTINE

Routine facts are true for nearly every other number upon a slight modification, and their admission as a property relating to numbers depends on the complexity and usefulness of both the mathematical expressions of the routine or non-routine facts, and the consequence of the number having or generating said property or relationship (through uses). These will come from formulaic expressions, including algebraic formulae, or through recursive methods, as well as those that involve modular arithmetic, or even solutions from concepts that involve different ring operations. Significance of the defining mathematical expressions that generate these routine facts need to have been covered separately by primary and secondary sources, to be of interest.

The first few (non-trivial) elements of a non-routine integer sequence should be included, and for finite sequences, the last should be included as well (including from "nice", "core", or relevant "hard" OEIS sequences). Integer entries from a large set that are not part of the first few or last members of solutions to expressions can be included if they are covered with due weight in the mathematical literature. Ideally, the specific integer entry being referenced should have applications in an unsolved or important solved problem in mathematics.

Examples that are routine:

On 5: "5 is the third odd number."
On 5: "5 is the first pentagonal number after 1."
On 9: "The aliquot sum of 9 is 4".
On 19: "The Collatz sequence for nine requires nineteen steps to return to one, more than any other number below it. On the other hand, nineteen requires twenty steps, like eighteen. Less than ten thousand, only thirty-one other numbers require nineteen steps to return to one."
On 1729: "It is the tenth centered cube number, the nineteenth dodecagonal number, the thirteenth 24-gonal and the seventh 84-gonal number."
On 197: "197 is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37"
On 69: "69 is the third composite number in the 13-aliquot tree, following 27 and 35."
On 744: "The number partitions of the square of seven (49) into prime parts is 744."

Examples that are non-routine:

On 3: "3 is the first odd prime".
On 19: "19 forms a twin prime with 17, a cousin prime with 23, and a sexy prime with 13".
On 11: "11 is the first prime exponent that does not yield a Mersenne prime, where $2^{11}-1=2047$ , which is composite."
On 42: The 1806th Bernoulli number is the only Bernoulli number whose denominator is the same as its index (1806) in the sequence of Bernoulli numbers.

Off-topic facts

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WP:NUM/OFFTOPIC

Facts on the page for number X should be as much as possible about number X and not about number or object Y, even if X and Y are related. In many cases, it is acceptable to describe the relationship between X and Y, but that doesn't mean that the subject of the article suddenly becomes Y.

Examples that are off topic:

On 5: "The factorial of five 5! = 120 is multiply perfect".
On 5: "A magic constant of 505 is generated by a 10 × 10 normal magic square". (The only connection here being that 505 contains two 5s.)
On 744: "The twentieth prime number is 71, where 31 is the eleventh; in turn, 20 is the eleventh composite number that is also the sixth self-convolution of Fibonacci numbers before 38, which is the prime index of 163."

Examples that are on topic (but which may still be excluded by other rules):

On 5: "5 is the first of the three known Wilson primes 5, 13, 563".
On 9: "The aliquot sum of 9 is 4".
On 19: "19 forms a twin prime with 17, a cousin prime with 23, and a sexy prime with 13".
On 11: The rows of Pascal's triangle can be seen as representation of the powers of 11.

Connection

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WP:NUM/CONNECTION

The existence of a connection between a number and an important or prominent object is usually acceptable.

Examples that are a connection to an important object:

On 5: "In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: $K 5$ , the complete graph with five vertices, where every pair of distinct vertices in a pentagon is joined by unique edges belonging to a pentagram."
On 9: "A polygon with nine sides is called a nonagon".

No Wikipedia page

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WP:NUM/NOPAGE

If a property is not important enough to have a Wikipedia page, it probably isn't important that the number in question satisfies it. The logical inverse also holds, but is weaker.

OEIS

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WP:NUM/OEIS

OEIS is considered a reliable source. However, a mathematical fact appearing in OEIS is not by itself a good reason to include it in a Wikipedia article. OEIS has hundreds of thousands of sequences, most of which do not belong on Wikipedia. If an OEIS sequence has almost no mentions outside of OEIS, the number $N$ being part of that sequence shouldn't be on the page for $N$ . If $N$ is a member of an OEIS sequence that is discussed in sources other than OEIS, this rule does not disqualify $N$ being a member of that sequence from inclusion on the page for $N$ .

No original research and no synthesis

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WP:NUM/ORSYNTH

Violations of WP:OR and WP:SYNTH should be removed even if they pass all of the previous tests. Most facts need to be stated in a reliable source, external to Wikipedia, prior to inclusion.

Assessing content outside of pure mathematics

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WP:NUM/OTHER

It is preferable to have a stub article than to pad an article with trivial or tenuously related information. Normal Wikipedia policies, and guidelines, should be considered when choosing which content to include. Specifically, this also applies to scientific and other associations in fields benefiting from applications of mathematical knowledge, and as such they must also be verifiable, and covered with due weight.

Aside from WP:DUE and WP:UNDUE content as described in sections above for mathematics-specific content, metrics for information that is due and not strictly dealing in pure mathematics, yet is either applied mathematics or regarding specific associations that are philosophical, cultural, or from other specific traditional uses in society, can be outlined.

Applied mathematics

A scientific notion referenced in a number article depends on the mathematics of its properties and characteristics, and how substantial they are, as aforementioned. Examples include:

a statement such as, there is theoretical and empirical evidence to suggest that brain computation is organized via power-of-two-based permutation logic,
three soap films meet along a Plateau border at 120 degree angles.

Philosophy and symbolism

Symbolism in lucky or unlucky numbers (as a form of numerology) can be included, such as a direct reference to mathematical properties of the number, even if mystical (i.e. The One in the philosophy of neoplatonism), or by popular association (including associations with numerals only); for example, the number 666 as the number of the beast. Per WP:FRINGE, all such examples need reliable mainstream sourcing.

What not to include

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WP:NUM/NOT

Do not include content that relates to the article's title only as an identifier, or label, or simple enumeration, or measurement, or as a trivial mention. This includes:

telephone number calling codes,
route or road numbers, bus routes,
firearms (i.e. Glock 17),
military and transportation classes of vehicles, aircraft, or otherwise,
album titles or song titles that include a numeral
book titles (except for when they deal directly with mathematics),
sports jerseys (identified with numbers, or letters and numbers), NASCAR car numbers, etc.,
world records of any sort, aside from records that could be of cultural interest in mathematics, such as enumerating digits of pi by memory, etc.,
marketed items, such as bubble gum 5,

or any other concept or item that is not directly related to the number itself (in this case, only its numeral is being referenced). If there is plausible ambiguity between the number and another use of the numeral, they should be mentioned on a disambiguation page for the number. If necessary, a hatnote can be added at the top of the article to link to another article for disambiguation. This enables the article to remain focused on content specifically related to the number.

Examples of items to not include:

Route 66 which does not have a significant relationship with the number 66 - rather, the "66" is an identification code.
86 (novel series) is not about the number 86.
The 35 in 35 mm film is a measurement, not a property of, or reference to, the number 35.
The 9 in ISO 9 is a simple enumeration of a series of items, with no significant relationship with the number 9.
The centre-forward in association football wearing the number 9 shirt is a trivial mention of the number 9.

Editing practice

Naming compliance

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WP:NUM/NAME

For most cases, articles should be named N (number), with the literal spelling of the numbers redirected accordingly (e.g., Four hundred and ninety-six redirects to 496 (number)).

Numbers deserving their own article that are greater than 999, should have the article title written in digits without any separators between the digits of the integer part. Writing the number with separators may of course be acknowledged in the body of the article. Thus, the article on the taxicab number 1,729 should be 1729 (number), though the article can mention that the number may be written "1,729" or "1.729."

Besides −1, there are no articles on negative integers. Adding information about a negative number therefore can fall under articles representative of numbers' positive, absolute values. One half is the chosen article name for 1⁄2.

Referencing

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WP:NUM/REF

Just as with any information in Wikipedia, articles on numbers need to cite sources. (See Wikipedia:Citing sources for general information on citing sources.) Some statements that are easily verified with a pocket calculator might not need citations (e.g., the fact that 2×3 = 6), but anything slightly more difficult to verify does. It is acceptable for a number article to have few citations if the articles to which it links have primary and secondary sourcing. For example, to avoid footnote overkill, an article about a number p that is a certain type of prime does not need citations to background reading about that type of prime.

It is not the place of this project to prescribe a citation format. Until Wikipedia decides on a uniform citation format, number articles may use whatever citation format would be acceptable in a mathematics journal. Consistency within an article is generally preferred.

Web versions of respected professional journals are reliable sources. On the other hand, preprints on the arXiv that have not been peer-reviewed are generally unsuitable for our purposes. The On-Line Encyclopedia of Integer Sequences should be used with care: it is curated by experts and generally accurate, but it is by design rather indiscriminate about what it includes. From the standpoint of serious mathematical literature, some OEIS entries are mere curiosities. Those that are more noteworthy will include references into the literature that include more substantial discussions; consider supplementing citations to the OEIS with direct pointers to the peer-reviewed papers that it cites. MathWorld has a history of being less than reliable, for example by including neologisms that have not become accepted mathematical terminology. It should be avoided.

Edit summaries

Every project member (indeed anyone who edits Wikipedia) is encouraged to write brief but complete edit summaries. Please refer to Wikipedia:Edit summary for a guide on writing good edit summaries.

Progress

The following is the status of the project as of January, 2023.

Priority of mathematics articles

Following the level of priority set by WikiProject Mathematics:

Top-priority

There are four main top-priority mathematics number articles:

Integers: 0 and 1.
Constants: π and $e$

Currently, articles for 0 and 1 are well-written within their respective mathematics sections, however they are not generally referenced (even though they contain due links, they could use primary sourcing where possible, even when generalizing). The article for π is a featured article, and the article for $e$ is a good article.

High-priority

Another fourteen relevant mathematics number articles are categorized as high-priority:

Integers: −1, 1⁄2, 2, 3, 4, 5, 6, 7, 8, 9, and 10, as well as 1000.
Constants: $i$ and φ

These have all recently been improved (2022-).

Mid-priority

At least four relevant mid-priority mathematical article are listed:

0.999... which has featured status.
Constants: $\sqrt 2$ , $\sqrt 3$ , $\sqrt 5$

Low-priority

Articles that are listed as low-priority include:

Integers: 261 and 666, as well as 2,147,483,647 and 4,294,967,295
Constants: δ_s, $\sqrt 7$

Methodical priority assignments to integer number articles have not really taken place, which is something that could be further investigated. For example, 24 (number) could be elevated to mid-priority, given the many important geometric and algebraic properties ligated to it. 12 is another such candidate.

Overview of the Project

There are continuous individual articles for positive integers from 1 to 299.

From 300 to 1000, articles contain information for individual integers in ranges of hundreds (i.e. 400 through 499 in one page), with some entries linked to individual articles (such as with 360, and 720).
From 1000 to 10000, they group in thousands, following the same scheme used for the groups of hundreds; again, some (1001 and 1729 spring to mind) have their own articles.
From 10000 to 100000 articles grow in increments of ten thousand, with a few articles in between for individual numbers (like 65,536 and 65,537).
From 10⁵ through 10⁹ articles are grouped in ranges of increments of powers of ten (i.e. the largest consecutive 10ⁿ article we have is for one billion).
There are select number articles greater than 10⁹ such as 2,147,483,647 and 4,294,967,295, and even extending to 10¹², a googolplex, and Graham's number.

Navigation bars inside Docuan tables of number articles have been created with the follow functionality:

Increments of 1 for all numbers between 0 and 270 (including redirects back to 260 between 260-269).
Increments of 10 from 0 through 300 (bugging between 280 and 300, however).
Increments of 100 from 0 through 1000 (starting at 100), of 1000 between 1000-9000, and of 10000 between 10000-90000.
Increments by factors of 10¹ between 10⁰ and 10⁹ (i.e. 10⁰, 10¹, 10², ... 10⁹ with links starting at 10⁵).

Status of disambiguation pages:

11 is a disambiguation page linking to 11 (number), AD 11 and other articles. Similarly for 12 to 99 inclusive.
100 (disambiguation) links to 100 (number page), AD 100, and other articles.
101 is a disambiguation page linking to 101 (number), AD 101, and other articles. Similarly from 102 to 150 inclusive.
The next disambiguation number page is 163 (disambiguation), linking to 163 (number), 163 (the year) and other articles.

Articles for deletion

Current

For up-to-date and automatically updated list of articles for deletion, see Category:AfD debates subsection 0–9.

Participation

If you'd like to be part of the project, simply add your username!

Active members

4pq1injbok
Allan Nonymous, armed with a frankly unhealthy amount of mathematical knowledge, is here to remove trivial factoids and other WP:CRUFT
Barnards.tar.gz
Buaidh (tables of numbers)
Dhrm77
Doctormatt
Egil
Fritzmann2002 (Working on fractions)
Gap9551
Imaginatorium
KingAntenor
Mathwriter2718
Newystats
Paintspot (standardizing the pages for lists of integers bigger than 300)
Polyamorph
Radlrb (focusing on 1 - 35 first, with a priority on 1 - 12)
Sj (finally found this page. :))

Inactive or past members

Bigdon128
Certes
Citizensadvice11 (Standardizing, categorizing and citation cleanup)
Cpu502
Docu
EditingMachine
Eequor
J kasd
QQ
Qscgy256
Radiant!
ral315
Reyk
Rich Farmbrough
Slord

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Result

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Numbers.

Usage

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WikiProject Numbers

Usage

Some of the following talk pages include it: What links here

Talk

To add a message of this project to talk pages of number articles, use Template:NumberTalk that can be displayed with {{WikiProject Numbers}}.

Numbers

This article is within the scope of WikiProject Numbers, a collaborative effort to improve the coverage of Numbers on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.NumbersWikipedia:WikiProject NumbersTemplate:WikiProject NumbersNumbers articles

Resources

Wikipedia:Notability (numbers)
List of numbers and list of prime numbers
List of mathematics articles (0–9) containing all mathematics articles starting with a number.
List of natural number articles containing all natural number articles from 1 to 10,000, including red links.

External links

numbertheory.org – lists of important contributions, number theorists, and concepts of interest

v t e Fractions and ratios
	Division and ratio	Dividend ÷ Divisor = Quotient
	Fraction	⁠Numerator/Denominator⁠ = Quotient
	Algebraic Aspect Binary Continued Decimal Dyadic Egyptian Golden Silver Integer Irreducible Reduction Just intonation LCD Musical interval Paper size Percentage Unit

v t e Infinity ( $\infty$ )
History	Ananta (infinite) Apeiron Controversy over Cantor's theory Galileo's paradox Hilbert's paradox of the Grand Hotel Infinity (philosophy) Paradoxes of infinity Paradoxes of set theory
Branches of mathematics	Complex analysis Internal set theory Nonstandard analysis Set theory Synthetic differential geometry
Formalizations of infinity	0.999... Absolute infinite Actual infinity Aleph number Beth number Cardinal numbers Cardinality of the continuum Dedekind-infinite set Directed infinity Division by zero (Complex infinity) Epsilon number Gimel function Hilbert space Hyperreal numbers Infinite set Infinitesimal Ordinal numbers Point at infinity Regular cardinal Sphere at infinity (Kleinian group) Supertask Surreal numbers Transfinite numbers
Geometries	Differential geometry of surfaces Möbius plane Möbius transformation Riemannian manifold
Mathematicians	Georg Cantor David Hilbert Gottfried Wilhelm Leibniz August Ferdinand Möbius Bernhard Riemann Abraham Robinson

v t e Number systems
Sets of definable numbers	Natural numbers ( $\mathbb {N}$ ) Integers ( $\mathbb {Z}$ ) Rational numbers ( $\mathbb {Q}$ ) Constructible numbers Algebraic numbers ( $\mathbb {A}$ ) Closed-form numbers Periods Computable numbers Arithmetical numbers Set-theoretically definable numbers Gaussian integers Gaussian rationals Eisenstein integers
Composition algebras	Division algebras: Real numbers ( $\mathbb {R}$ ) Complex numbers ( $\mathbb {C}$ ) Quaternions ( $\mathbb {H}$ ) Octonions ( $\mathbb {O}$ )
Split types	Over $\mathbb {R}$ : Split-complex numbers Split-quaternions Split-octonions Over $\mathbb {C}$ : Bicomplex numbers Biquaternions Bioctonions
Other hypercomplex	Dual numbers Dual quaternions Dual-complex numbers Hyperbolic quaternions Sedenions ( $\mathbb {S}$ ) Split-biquaternions Multicomplex numbers Geometric algebra/Clifford algebra Algebra of physical space Spacetime algebra Plane-based geometric algebra
Infinities and infinitesimals	Cardinal numbers Extended natural numbers Extended real numbers Projective Extended complex numbers Hyperreal numbers Levi-Civita field Ordinal numbers Supernatural numbers Surreal numbers Superreal numbers
Other types	Irrational numbers Fuzzy numbers Transcendental numbers p-adic numbers (p-adic solenoids) Profinite integers Normal numbers
Classification List

v t e Number theory
Fields	Algebraic number theory (class field theory, non-abelian class field theory, Iwasawa theory, Iwasawa–Tate theory, Kummer theory) Analytic number theory (analytic theory of L-functions, probabilistic number theory, sieve theory) Geometric number theory Computational number theory Transcendental number theory Diophantine geometry (Arakelov theory, Hodge–Arakelov theory) Arithmetic combinatorics (additive number theory) Arithmetic geometry (anabelian geometry, P-adic Hodge theory) Arithmetic topology Arithmetic dynamics
Key concepts	Numbers 0 Natural numbers Unity Prime numbers Composite numbers Rational numbers Irrational numbers Algebraic numbers Transcendental numbers P-adic numbers (P-adic analysis) Arithmetic Modular arithmetic Chinese remainder theorem Arithmetic functions
Advanced concepts	Quadratic forms Modular forms L-functions Diophantine equations Diophantine approximation Continued fractions
Category List of topics List of recreational topics Wikibook Wikiversity

Number Article Guidelines

General guidelines

When should an article exist?

Outline

Infobox

Symbolic and linguistic representations

Assessing mathematical number facts

Simple facts

Routine facts

Off-topic facts

Connection

No Wikipedia page

OEIS

No original research and no synthesis

Assessing content outside of pure mathematics

Applied mathematics

Philosophy and symbolism

What not to include

Editing practice

Naming compliance

Referencing

Edit summaries

Progress

Priority of mathematics articles

Top-priority

High-priority

Mid-priority

Low-priority

Overview of the Project

Articles for deletion

Current

Participation

Active members

Inactive or past members

Userboxes

Talk

Resources

See also

External links