查看“︁User:ColorfulGalaxy/Encyclopedia of numbers”︁的源代码

__NOTOC__
This article is inspired by [http://mathigon.org/almanac this] article, which was biased towards decimal properties and did not mention imaginary numbers. This article, instead, is biased towards septenary and tetradecimal properties, though the numbers are written in decimal. [[Shidinn language|Shidinn]]-related entries are also welcome.

{| border="0" class="toccolours wikitable"
|-
! colspan="9" | {{MediaWiki:Toc}}
|-
| align="center" | [[#0|0]] || [[#1|1]] || [[#2|2]] || [[#7|7]] || [[#14|14]] || [[#49|49]] || [[#196|196]] || [[#343|343]] || [[#2744|2744]] __NOTOC__
|-
| align="center" colspan="9" | [[#top|Top of page]] &mdash; [[#Legend|Legend]] &mdash; [[#See also|See also]] &mdash; [[#External links|External links]]
|}

==Legend==

<div style="border:2px solid blue;">Positive prime numbers </div>
<div style="border:2px solid #ff00ff;">Number (excluding positive prime numbers) whose absolute value is an integer</div>
<div style="border:2px solid orange;">Number whose absolute value is a rational number that is not integer</div>
<div style="border:2px solid #00ffff;">Number whose absolute value is an algebraic irrational number</div>
<div style="border:2px solid green;">Number whose absolute value is a transcendental real number</div>
<div style="border:2px solid red;">Unknown/approximation</div>

Some terms can have subscripts. For example, "digit<sub>14</sub>"<ref name="digit"/> is read as "tetradecimal digit".

==Numbers==

===0===
<div style="border:2px solid #ff00ff">
* ... is the smallest non-negative number.
* ... is the additive identity.
</div>

===1===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive number.
* ... is the multiplicative identity.
</div>

===2===
<div style="border:2px solid blue">
* ... is the smallest positive prime number.
* ... is the only even positive prime number.
* ... is an RDI<sub>7</sub><ref name="rdi"/> of order 2.
</div>

===3===
<div style="border:2px solid blue">
* ... is the smallest odd positive prime number.
* ... is the smallest Full Reptend Prime<sub>14</sub><ref name="frp"/>.
</div>

===4===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive composite number.
* ... is the 2nd square number.
* ... is the largest known positive integer ''n'' such that there exists an arithmetic progression with ''n'' terms (all positive, indexed 1 through ''n'') satisfying the fact that the number of positive factors each term has is exactly equal to the term's index.
</div>

===5===
<div style="border:2px solid blue">
* ... is the smallest positive odd number that is not a repunit<sub>2</sub><ref name="repunit"/> number.
* ... is the number of Platonic solids.
* ... is the number of letters in the longest word in Shidinn. There are 278 known five-letter words.
* ... was the number of members in the Shidinn community administration committee when it started.
</div>

===6===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive composite number that is not a perfect power.
* ... is the largest digit<sub>7</sub><ref name="digit"/>.
* ... is the smallest perfect number.
</div>

===7===
<div style="border:2px solid blue">
* ... is the third smallest repunit<sub>2</sub><ref name="repunit"/> number.
* ... is the smallest positive two-digit<sub>7</sub><ref name="digit"/> number.
* ... is the second smallest positive 1-automorphic<sub>14</sub><ref name="automorphic"/> number.
* ... is the smallest positive strobogrammatic<sub>[[希顶字母数字|xdi8]]</sub> number.
* ... is the number of classical elements in Shidinn culture. See [[Seven elements]].
* ... is the smallest positive non-unity integer ''n'' such that there exists a four-digit<sub>n</sub><ref name="digit"/> repdigit<sub>n</sub><ref name="repdigit"/> square number.
* ... is the smallest known positive non-unity integer ''n'' such that there exists a three-digit<sub>n</sub><ref name="digit"/> number k=a×n<sup>2</sup>+b×n+c satisfying that k-1, k and k+1 have a, b and c (i. e. its digits) positive factors respectively.
* ... is the number that represents God in western culture.
</div>

===8===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive composite cube number.
* ... is the smallest positive composite Fibonacci number.
* ... is the largest cube in the Fibonacci sequence.
* ... is the second smallest repunit<sub>7</sub><ref name="repunit"/> number.
* ... is the smallest known repfigit<sub>7</sub><ref name="repfigit"/> number.
* ... is the third smallest positive 1-automorphic<sub>14</sub><ref name="automorphic"/> number.
* ... is the second cubic number.
</div>

===9===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive odd composite number.
* ... is the second smallest Smarandache<sub>7</sub><ref name="smarandache"/> number.
* ... is the smallest positive integer ''n'' such that 3<sup>''n''</sup> starts with three identical digits<sub>7</sub><ref name="digit"/>.
* ... is the smallest positive integer ''n'' such that ''n''<sup>''n''</sup> is pandigital<sub>7</sub><ref name="pandigital"/>.
* ... is the largest digit in base-10.
</div>

===10===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive even number ''n'' where ''n''-1 is a Fermat pseudoprime<sub>''n''</sub>.
* ... is the smallest positive integer that is not a Harshad<sub>7</sub><ref name="harshad"/> number.
* ... is a Narcissistic<sub>7</sub><ref name="narcissistic"/> number.
* ... is a disarium<sub>7</sub><ref name="disarium"/> number.
* ... is a strobogrammatic<sub>[[希顶字母数字|xdi8]]</sub> number.
* ... is the number of current members in the Shidinn community administration committee.
</div>

===11===
<div style="border:2px solid blue">
* ... is the smallest positive odd prime number that is not palindromic<sub>2</sub><ref name="palindromic"/>.
</div>

===12===
<div style="border:2px solid #ff00ff">
* ... is the smallest abundant number.
* ... is the number of two-digit<sub>7</sub><ref name="digit"/> prime numbers.
* ... is the smallest known positive non-unity integer ''n'' such that there exists a five-digit<sub>n</sub><ref name="digit"/> number k=a×n<sup>4</sup>+b×n<sup>3</sup>+c×n<sup>2</sup>+d×n+f satisfying that k-2, k-1, k, k+1 and k+2 have a, b, c, d and f (i. e. its digits) positive factors respectively. More surprisingly, that number is a repdigit<sub>12</sub><ref name="repdigit"/> number.
* ... is the smallest true composite number.
</div>

===13===
<div style="border:2px solid blue">
* ... is the number of Archimedean solids.
* ... is the largest digit<sub>14</sub><ref name="digit"/>.
* ... is the third smallest repunit<sub>3</sub><ref name="repunit"/> number.
* ... is an RDI<sub>7</sub><ref name="rdi"/> of order 2.
* ... is the smallest positive odd Fibonacci number that is not palindromic<sub>2</sub><ref name="palindromic"/>.
* ... is the number that represents Devil in western culture.
</div>

===14===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive two-digit<sub>14</sub><ref name="digit"/> number.
* ... is the smallest two-digit<sub>7</sub><ref name="digit"/> "kind<sub>7</sub>"<ref name="a185186"/> number.
* ... is the index of the nasal sibilant in the [[Shidinn alphabet]].
</div>

===15===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive odd composite number that is not a perfect power.
* ... is the second smallest repunit<sub>14</sub><ref name="repunit"/> number.
</div>

===16===
<div style="border:2px solid #ff00ff">
* ... is the second smallest positive tesseractic number.
* ... is the smallest positive integer with five positive factors.
* ... is a repdigit<sub>7</sub><ref name="repdigit"/> number.
* ... is the second smallest Smarandache<sub>14</sub><ref name="smarandache"/> number.
* ... is the smallest positive composite number whose reversal<sub>14</sub><ref name="reversal"/> is prime.
</div>

===17===
<div style="border:2px solid blue">
* ... is a Fermat prime.
* ... is the smallest prime number that is the concatenation<sub>7</sub><ref name="concatenation"/> of two prime numbers.
</div>

===18===
<div style="border:2px solid #ff00ff">
* ... is the smallest two-digit<sub>14</sub><ref name="digit"/> number in the Fibonacci-like sequence starting with 2 and 1.
</div>

===19===
<div style="border:2px solid blue">
* ... is the smallest positive odd prime number whose reversal<sub>2</sub><ref name="reversal"/> is composite.
</div>

===20===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> is pandigital<sub>7</sub><ref name="pandigital"/>.
* ... is the smallest positive non-repdigit<sub>7</sub> integer whose square is repdigit<sub>7</sub><ref name="repdigit"/>.
* ... is the integer that caused an "e-mail war" between Shidinn enthusiasts on February 24, 2025.
</div>

===21===
<div style="border:2px solid #ff00ff">
* ... is the sum of all the one-digit<sub>7</sub><ref name="digit"/> numbers. It is also the numbers of dots on the dice used in most of the board games.
* ... is the third smallest repunit<sub>4</sub><ref name="repunit"/> number.
* ... is the third smallest<sup>&#91;lɤ ɛyuə iq<small><small>8</small></small> q<small><small>6</small></small>&#93;</sup> positive integer whose tesseractic is a happy<sub>14</sub><ref name="happy"/> number.
</div>

===22===
<div style="border:2px solid #ff00ff">

</div>

===23===
<div style="border:2px solid blue">
* ... is the smallest prime number that is not a twin prime.
* ... is the smaller prime factor of 2047, the smallest Mersenne composite number.
</div>

===24===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> ends in three identical digits<sub>7</sub><ref name="digit"/>.
</div>

===25===
<div style="border:2px solid #ff00ff">
* ... is a narcissistic<sub>7</sub><ref name="narcissistic"/> number.
* ... is an RDI<sub>14</sub><ref name="rdi"/> of order 2.
* ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> starts in three identical digits<sub>7</sub><ref name="digit"/> and ends in three identical digits<sub>7</sub>.
</div>

===26===
<div style="border:2px solid #ff00ff">

</div>

===27===
<div style="border:2px solid #ff00ff">

</div>

===28===
<div style="border:2px solid #ff00ff">

</div>

===29===
<div style="border:2px solid blue">
* ... is the smallest positive odd prime number whose reversal<sub>14</sub><ref name="reversal"/> is composite.
* ... is the second smallest two-digit<sub>14</sub><ref name="digit"/> number in the Fibonacci-like sequence starting with 2 and 1.
* ... is a repfigit<sub>14</sub><ref name="repfigit"/> number.
</div>

===30===
<div style="border:2px solid #ff00ff">
* ... is a repdigit<sub>14</sub><ref name="repdigit"/> number.
* ... is the number of two-digit<sub>7</sub><ref name="digit"/> composite numbers.
* ... is a strobogrammatic<sub>[[希顶字母数字|xdi8]]</sub> number.
</div>

===31===
<div style="border:2px solid blue">
* ... is a Mersenne prime.
* ... is the smallest prime number that is the concatenation<sub>14</sub><ref name="concatenation"/> of two prime numbers.
* ... is the third smallest repunit<sub>5</sub><ref name="repunit"/> number.
</div>

===32===
<div style="border:2px solid #ff00ff">
* ... is a repdigit<sub>7</sub><ref name="repdigit"/> number.
* ... is a narcissistic<sub>7</sub><ref name="narcissistic"/> number.
</div>

===33===
<div style="border:2px solid #ff00ff">

</div>

===34===
<div style="border:2px solid #ff00ff">
* ... is the smallest known number in a Friedman<sub>14</sub> loop<ref name="friedmanpair"/>:
:: 2<sup>6</sup>=64
:: 8<sup>4</sup>=4096
:: 6×(12×8-1)=570
:: 2×12+10=34
</div>

===35===
<div style="border:2px solid #ff00ff">
* ... is in a Friedman<sub>14</sub> loop<ref name="friedmanpair"/>:
:: 7<sup>3</sup>=343
:: (1+10)×7=77
:: 5×7=35
:: 7<sup>2</sup>=49
</div>

===36===
<div style="border:2px solid #ff00ff">

</div>

===37===
<div style="border:2px solid blue">
* ... is an RDI<sub>14</sub><ref name="rdi"/> of order 2.
</div>

===38===
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</div>

===39===
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</div>

===40===
<div style="border:2px solid #ff00ff">
* ... is in a Friedman<sub>14</sub> pair<ref name="friedmanpair"/>:
:: 12<sup>2</sup>=144
:: 4&times;10=40
</div>

===41===
<div style="border:2px solid blue">
* ... is the sum of all the one-digit<sub>14</sub><ref name="digit"/> prime numbers.
</div>

===42===
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</div>

===43===
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</div>

===44===
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</div>

===45===
<div style="border:2px solid #ff00ff">
* ... is the number of letters in the [[Shidinn alphabet]].
* ... is a narcissistic<sub>7</sub><ref name="narcissistic"/> number.
* ... is the third smallest<sup>&#91;lɤ ɛyuə iq<small><small>8</small></small> q<small><small>6</small></small>&#93;</sup> positive integer whose tesseractic is a happy<sub>7</sub><ref name="happy"/> number.
</div>

===46===
<div style="border:2px solid #ff00ff">

</div>

===47===
<div style="border:2px solid blue">
* ... is the largest two-digit<sub>7</sub><ref name="digit"/> prime number.
* ... is the [[平原素数系统|representative prime number]] of [[User:Rachel1211]].
* ... is featured on [http://www.zhihu.com/question/12695389890 this website]. You can submit entries there.
</div>

===48===
<div style="border:2px solid #ff00ff">
* ... is the largest two-digit<sub>7</sub><ref name="digit"/> number.
</div>

===49===
<div style="border:2px solid #ff00ff">
* ... is the smallest three-digit<sub>7</sub><ref name="digit"/> number.
* ... is the sum of all the one-digit<sub>14</sub><ref name="digit"/> composite numbers.
</div>

===50===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive palindromic<sub>7</sub><ref name="palindromic"/> number that is not repdigit<sub>7</sub><ref name="repdigit"/>.
</div>

===51===
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</div>

===52===
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</div>

===53===
<div style="border:2px solid blue">
* ... is the smallest three-digit<sub>7</sub><ref name="digit"/> prime number.
</div>

===54===
<div style="border:2px solid #ff00ff">

</div>

===55===
<div style="border:2px solid #ff00ff">
* ... is the second smallest positive integer that is both square pyramidal and triangular, as mentioned by a Shidinn enthusiast.
</div>

===56===
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</div>

===57===
<div style="border:2px solid #ff00ff">
* ... is the third smallest repunit<sub>7</sub><ref name="repunit"/> number.
</div>

===58===
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</div>

===59===
<div style="border:2px solid blue">
* ... is the smallest three-digit<sub>7</sub><ref name="digit"/> twin prime.
* ... is the smallest prime number that can be expressed as 8 times a square number plus 27 times a square number. This property of prime numbers was mentioned by a Shidinn enthusiast as an "unfortunate" property.
</div>

===60===
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===61===
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===62===
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===63===
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===64===
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===65===
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* ..., as [http://mathworld.wolfram.com/ExpandedNotation.html 4×14+9], is a Cyclic<sub>14</sub> number<ref name="cyclic"/>. 
</div>

===66===
<div style="border:2px solid #ff00ff">
* ... is the third smallest Smarandache<sub>7</sub><ref name="smarandache"/> number.
</div>

===67===
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</div>

===68===
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===69===
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===70===
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===71===
<div style="border:2px solid blue">
* ... is the largest known positive integer whose square can be written as one plus the factorial of another positive integer.
* ... is the smallest positive palindromic<sub>7</sub><ref name="palindromic"/> prime number that is not repdigit<sub>7</sub><ref name="repdigit"/>.
* ... is featured on [http://www.zhihu.com/question/14793120356 this website]. You can submit entries there.
</div>

===72===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive integer that is not a perfect power but can be written as the product of perfect powers.
</div>

===73===
<div style="border:2px solid blue">
* ... is the third smallest repunit<sub>8</sub><ref name="repunit"/> number.
* ... is the third smallest positive integer that is both palindromic<sub>2</sub><ref name="palindromic"/> and palindromic<sub>b3<ref name="balancedternary"/></sub>.
* ... is the number of cards in the [[Seven elements]] poker game. The pack has 7 suits of 10 cards each, along with three extra cards (INF, 7UT and blank).
* ... is a number worshipped in Shidinn culture.
* ... is featured on [http://www.zhihu.com/question/8988346680 this website]. You can submit entries there.
</div>

===74===
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===75===
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</div>

===76===
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* ... is the sum of the first three Smarandache<sub>7</sub><ref name="smarandache"/> numbers.
</div>

===77===
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===78===
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===79===
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===80===
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===81===
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* ... is the third smallest positive tesseractic number.
* ... is in the username of [[User:DGCK81LNN]].
</div>

===82===
<div style="border:2px solid #ff00ff">
* ... is a strobogrammatic<sub>[[希顶字母数字|xdi8]]</sub> number.
</div>

===83===
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===84===
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===85===
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* ... is the largest known index of a square pyramidal number that is also triangular. Its index in the triangular sequence is 645.
</div>

===86===
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===87===
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===88===
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===89===
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* ... is the total number of letters in the [[Shidinn alphabet]] and the Extended Shidinn alphabet, including the "number zero" letter.
</div>

===90===
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===91===
<div style="border:2px solid #ff00ff">
* ... is the sum of all the one-digit<sub>14</sub><ref name="digit"/> numbers.
* ... is the third smallest repunit<sub>9</sub><ref name="repunit"/> number.
* ... is the third smallest positive integer that is both square pyramidal and triangular, as mentioned by a Shidinn enthusiast.
</div>

===92===
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===93===
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===94===
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===95===
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===96===
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===97===
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===98===
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===99===
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===100===
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===101===
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===102===
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===103===
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===104===
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===105===
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===106===
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===107===
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===108===
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===109===
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===110===
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===111===
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===112===
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===113===
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===114===
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===115===
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===116===
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===117===
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===118===
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===119===
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===120===
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===121===
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===122===
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===123===
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===124===
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===125===
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===126===
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===127===
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* ... is a number worshipped in Shidinn culture.<sup>&#91;lɤ ɛyuə iq<small><small>8</small></small> q<small><small>6</small></small>&#93;</sup>
</div>

===128===
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===129===
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===130===
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===131===
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===132===
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===133===
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===135===
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===136===
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===137===
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===138===
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===139===
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===140===
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===141===
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===142===
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===143===
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===144===
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===145===
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===146===
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===147===
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===148===
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* ... is the largest two-digit<sub>14</sub><ref name="digit"/> number.
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* ... is the smallest three-digit<sub>14</sub><ref name="digit"/> number.
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* ... is the smallest three-digit<sub>14</sub><ref name="digit"/> prime number.
* ... is the smallest positive palindromic<sub>14</sub><ref name="palindromic"/> number that is not repdigit<sub>14</sub><ref name="repdigit"/>.
* ... is the smallest positive palindromic<sub>14</sub><ref name="palindromic"/> prime number that is not repdigit<sub>14</sub><ref name="repdigit"/>.
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* ... is the smallest three-digit<sub>14</sub><ref name="digit"/> squarefree<ref name="squarefree"/> composite number.
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* ... is the third smallest repunit<sub>14</sub><ref name="repunit"/> number.
* ... is the smallest repunit<sub>14</sub><ref name="repunit"/> prime number.
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* ... is the second smallest three-digit<sub>14</sub><ref name="digit"/> square number.
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* ... is the third smallest Smarandache<sub>14</sub><ref name="smarandache"/> number, as well as the smallest Smarandache<sub>14</sub> prime number.
* ... is the second smallest prime number that can be expressed as 8 times a square number plus 27 times a square number. This property of prime numbers was mentioned by a Shidinn enthusiast as an "unfortunate" property.
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==See also==

==Notes==
<references group="note">
</references>

==References==
<references><ref name="digit">[http://mathworld.wolfram.com/Digit.html Digit] on Wolfram Mathworld</ref>
<ref name="concatenation">[http://mathworld.wolfram.com/Concatenation.html Concatenation] on Wolfram Mathworld</ref>
<ref name="reversal">[http://mathworld.wolfram.com/Reversal.html Reversal] on Wolfram Mathworld</ref>
<ref name="palindromic">[http://mathworld.wolfram.com/PalindromicNumber.html Palindromic] on Wolfram Mathworld</ref>
<ref name="repdigit">[http://mathworld.wolfram.com/Repdigit.html Repdigit] on Wolfram Mathworld</ref>
<ref name="repunit">[http://mathworld.wolfram.com/Repunit.html Repunit] on Wolfram Mathworld</ref>
<ref name="pandigital">[http://mathworld.wolfram.com/PandigitalNumber.html Pandigital] on Wolfram Mathworld</ref>
<ref name="smarandache">[http://mathworld.wolfram.com/SmarandacheNumber.html Smarandache number] on Wolfram Mathworld</ref>
<ref name="harshad">[http://mathworld.wolfram.com/HarshadNumber.html Harshad number] on Wolfram Mathworld</ref>
<ref name="a185186">[http://oeis.org/A185186 "Kind" number] on OEIS</ref>
<ref name="repfigit">[http://mathworld.wolfram.com/KeithNumber.html Repfigit] on Wolfram Mathworld</ref>
<ref name="rdi">[http://mathworld.wolfram.com/RecurringDigitalInvariant.html Recurring digial invariant] on Wolfram Mathworld</ref>
<ref name="happy">[http://mathworld.wolfram.com/HappyNumber.html Happy number] on Wolfram Mathworld</ref>
<!--<ref name="unhappy">[http://mathworld.wolfram.com/UnhappyNumber.html Unhappy number] on Wolfram Mathworld</ref>-->
<ref name="narcissistic">[http://mathworld.wolfram.com/NarcissisticNumber.html Narcissistic number] on Wolfram Mathworld</ref>
<ref name="disarium">[http://oeis.org/A032799 Disarium number] on OEIS</ref>
<ref name="automorphic">[http://mathworld.wolfram.com/AutomorphicNumber.html Automorphic number] on Wolfram Mathworld</ref>
<ref name="cyclic">[http://mathworld.wolfram.com/CyclicNumber.html Cyclic number] on Wolfram Mathworld</ref>
<ref name="frp">[http://mathworld.wolfram.com/FullReptendPrime.html Full Reptend Prime] on Wolfram Mathworld</ref>
<ref name="balancedternary">[http://simple.wikipedia.org/wiki/Balanced_ternary Balanced ternary] on Simple Wikipedia</ref>
<!--<ref name="friedman">[http://erich-friedman.github.io/mathmagic/0800.html Friedman numbers, Nice Friedman numbers]</ref>-->
<!--<ref name="almostfriedman">[http://erich-friedman.github.io/mathmagic/0713.html Fractional Friedman numbers, Redundant Friedman numbers, Almost Friedman numbers, Non-integral Friedman numbers]</ref>-->
<ref name="friedmanpair">[http://erich-friedman.github.io/mathmagic/0619.html Anti-Friedman number, Shifted Friedman number, Friedman pair, Friedman loop]</ref>
<!-- Non-digit related properties -->
<ref name="squarefree">[http://mathworld.wolfram.com/Squarefree.html Squarefree number] on Wolfram Mathworld</ref>
</references>

==External links==
* [http://www.archimedes-lab.org/numbers/Num1_69.html Numbers] on Archimedes Lab