nyuuzyou/wikis huggingface dataset:
206

== Number ==
$206$ (two hundred and six) is:
:$2 \times 103$
:The $2$nd positive integer solution after $14$ to $\map {\sigma_1} n = \map {\sigma_1} {n + 1}$:
::$\map {\sigma_1} {206} = 312 = \map {\sigma_1} {207}$
:The $5$th positive integer after $200$, $202$, $204$, $205$ that cannot be made into a prime number by changing just $1$ digit
:The $11$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $146$, $162$, $188$.
:The $19$th noncototient after $10$, $26$, $34$, $50$, $52$, $58$, $86$, $100$, $116$, $122$, $130$, $134$, $146$, $154$, $170$, $172$, $186$, $202$:
::$\nexists m \in \Z_{>0}: m - \map \phi m = 206$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $30$th nontotient:
::$\nexists m \in \Z_{>0}: \map \phi m = 206$
:where $\map \phi m$ denotes the Euler $\phi$ function
== Also see ==
* 
* 
* 
* 
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Category:Specific Numbers
Category:206
207,622,273

== Number ==
$207 \, 622 \, 273$ is:
:The $11 \, 477 \, 482$nd prime number
:The $1$st of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 273 = 4 \times 51 \, 905 \, 568 + 1$
== Also see ==
* 
* 
== Sources ==
* : $207,622,273$
Category:Specific Numbers
Category:207,622,273
207,622,297

== Number ==
$207 \, 622 \, 297$ is:
:The $11 \, 477 \, 483$rd prime number
:The $2$nd of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 297 = 4 \times 51 \, 905 \, 574 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,297
207,622,301

== Number ==
$207 \, 622 \, 301$ is:
:The $11 \, 477 \, 484$th prime number
:The $3$rd of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 301 = 4 \times 51 \, 905 \, 575 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,301
207,622,313

== Number ==
$207 \, 622 \, 313$ is:
:The $11 \, 477 \, 485$th prime number
:The $4$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 313 = 4 \times 51 \, 905 \, 578 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,313
207,622,321

== Number ==
$207 \, 622 \, 321$ is:
:The $11 \, 477 \, 486$th prime number
:The $5$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 321 = 4 \times 51 \, 905 \, 580 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,321
207,622,381

== Number ==
$207 \, 622 \, 381$ is:
:The $11 \, 477 \, 487$th prime number
:The $6$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 381 = 4 \times 51 \, 905 \, 595 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,381
207,622,409

== Number ==
$207 \, 622 \, 409$ is:
:The $11 \, 477 \, 488$th prime number
:The $7$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 409 = 4 \times 51 \, 905 \, 602 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,409
207,622,417

== Number ==
$207 \, 622 \, 417$ is:
:The $11 \, 477 \, 489$th prime number
:The $8$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 417 = 4 \times 51 \, 905 \, 604 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,417
207,622,421

== Number ==
$207 \, 622 \, 421$ is:
:The $11 \, 477 \, 490$th prime number
:The $9$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 421 = 4 \times 51 \, 905 \, 605 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,421
207,622,489

== Number ==
$207 \, 622 \, 489$ is:
:The $11 \, 477 \, 491$st prime number
:The $10$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 489 = 4 \times 51 \, 905 \, 622 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,489
207,622,501

== Number ==
$207 \, 622 \, 501$ is:
:The $11 \, 477 \, 492$nd prime number
:The $11$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 501 = 4 \times 51 \, 905 \, 625 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,501
207,622,517

== Number ==
$207 \, 622 \, 517$ is:
:The $11 \, 477 \, 493$rd prime number
:The $12$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 517 = 4 \times 51 \, 905 \, 629 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,517
207,622,537

== Number ==
$207 \, 622 \, 537$ is:
:The $11 \, 477 \, 494$th prime number
:The $13$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 537 = 4 \times 51 \, 905 \, 634 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,537
207,622,549

== Number ==
$207 \, 622 \, 549$ is:
:The $11 \, 477 \, 495$th prime number
:The $14$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 549 = 4 \times 51 \, 905 \, 637 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,549
207,622,553

== Number ==
$207 \, 622 \, 553$ is:
:The $11 \, 477 \, 496$th prime number
:The $15$th of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 553 = 4 \times 51 \, 905 \, 638 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,553
207,622,561

== Number ==
$207 \, 622 \, 561$ is:
:The $11 \, 477 \, 497$th prime number
:The $16$th and last of a sequence of $16$ consecutive prime numbers of the form $4 n + 1$:
::$207 \, 622 \, 561 = 4 \times 51 \, 905 \, 640 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:207,622,561
2072

== Number ==
$2072$ (two thousand and seventy-two) is:
:$2^3 \times 7 \times 37$
:The $37$th second pentagonal number after $2$, $7$, $15$, $26$, $\ldots$, $1107$, $1190$, $1276$, $1365$, $1457$, $1552$, $1650$, $1751$, $1855$, $1962$:
::$2072 = \dfrac {37 \paren {3 \times 37 + 1} } 2$
:The $74$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $1617$, $1650$, $1717$, $1751$, $1820$, $1855$, $1926$, $1962$, $2035$:
::$2072 = \dfrac {37 \paren {3 \times 37 + 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:2072
208

== Number ==
$208$ (two hundred and eight) is:
:$2^4 \times 13$
:The $5$th after $4$, $13$, $38$, $87$ in the sequence formed by adding the squares of the first $n$ primes:
::$208 = \ds \sum_{i \mathop = 1}^5 {p_i}^2 = 2^2 + 3^2 + 5^2 + 7^2 + 11^2$
:The $6$th positive integer after $200$, $202$, $204$, $205$, $206$ that cannot be made into a prime number by changing just $1$ digit
:The $34$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $130$, $133$, $139$, $167$, $176$, $188$, $190$, $192$, $193$, $203$:
::$208 \to 2^2 + 0^2 + 8^2 = 4 + 0 + 64 = 68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:208
208,003

== Number ==
$208 \, 003$ (two hundred and eight thousand and three) is:
:The $18 \, 636$th prime number
:The $27$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
::$3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$, $94$, $166$, $324$, $379$, $469$, $546$, $974$, $1963$, $3507$, $3610$, $6917$, $21 \, 480$, $34 \, 790$, $94 \, 550$, $103 \, 040$, $147 \, 855$, $208 \, 003$
== Also see ==
* 
* 
Category:Specific Numbers
Category:208,003
208,012

== Number ==
$208 \, 012$ (two hundred and eight thousand and twelve) is:
:$2^2 \times 7 \times 17 \times 19 \times 23$
:The $12$th Catalan number after $(1)$, $1$, $2$, $5$, $14$, $42$, $132$, $429$, $1430$, $4862$, $16 \, 796$, $58 \, 786$:
::$208 \, 012 = \dfrac 1 {12 + 1} \dbinom {2 \times 12} {12} = \dfrac 1 {13} \times 2 \, 704 \, 156$
== Also see ==
* 
Category:Specific Numbers
Category:208,012
208,335

== Number ==
$208 \, 335$ is:
:$3 \times 5 \times 17 \times 19 \times 43$
:The $4$th and last after $1$, $55$, $91$ of the $4$ square pyramidal numbers which are also triangular.
:The $85$th square pyramidal number:
::$208 \, 335 = \ds \sum_{k \mathop = 1}^{85} k^2 = \dfrac {85 \paren {85 + 1} \paren {2 \times 85 + 1} } 6$
:The $645$th triangular number:
::$208 \, 335 = \ds \sum_{k \mathop = 1}^{645} k = \dfrac {645 \times \paren {645 + 1} } 2$
== Also see ==
* 
* 
* 
== Sources ==
* : $208,335$
* : $208,335$
Category:Specific Numbers
Category:208,335
2080

== Number ==
$2080$ (two thousand and eighty) is:
:$2^5 \times 5 \times 13$
:The total of all the entries in a magic cube of order $4$, after $1$, $36$, $378$:
::$2080 = \ds \sum_{k \mathop = 1}^{4^3} k = \dfrac {4^3 \paren {4^3 + 1} } 2$
:The total of all the entries in a magic square of order $8$, after $1$, $(10)$, $45$, $136$, $325$, $666$, $1225$:
::$2080 = \ds \sum_{k \mathop = 1}^{8^2} k = \dfrac {8^2 \paren {8^2 + 1} } 2$
:The $64$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $1326$, $1378$, $1431$, $1485$, $1540$, $1596$, $1653$, $1711$, $1770$, $1770$, $1830$, $1891$, $1953$, $2016$:
::$2080 = \ds \sum_{k \mathop = 1}^{64} k = \dfrac {64 \times \paren {64 + 1} } 2$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:2080
2089

== Number ==
$2089$ (two thousand and eighty-nine) is:
:The $316$rd prime number
:The $10$th, and last, after $199$, $409$, $619$, $829$, $1039$, $1249$, $1459$, $1669$, $1879$, of the smallest $10$ primes in arithmetic sequence:
::$2089 = 9 \times 210 + 199$
== Also see ==
* 
* 
Category:Specific Numbers
Category:2089
21

== Number ==
$21$ (twenty-one) is:
:$3 \times 7$
:The smallest integer with $2$ distinct prime factors neither of which is a divisor of $10$
:The number of parts in the smallest perfect square dissection of an integer square
:The $1$st of the $5$ $2$-digit positive integers which can occur as a $5$-fold repetition at the end of a square number, for example:
::$508 \, 853 \, 989^2 = 258 \, 932 \, 382 \, 121 \, 212 \, 121$
:The second of the $1$st pair of triangular numbers whose sum and difference are also both triangular:
::$15 = T_5$, $21 = T_6$, $15 + 21 = T_8$, $21 - 15 = T_3$
:The $3$rd octagonal number after $1$, $8$:
::$21 = 1 + 7 + 13 = 3 \paren {3 \times 3 - 2}$
:The smallest number which can be expressed as the sum of at most $3$ triangular numbers in $4$ ways:
::$21 = 15 + 6 = 15 + 3 + 3 = 10 + 10 + 1$
:The $4$th positive integer $n$ after $4$, $7$, $15$ such that $n - 2^k$ is prime for all $k$
:The $4$th after $0$, $1$, $3$ of the $5$ Fibonacci numbers which are also triangular
:The $6$th triangular number, after $1$, $3$, $6$, $10$, $15$:
::$21 = 1 + 2 + 3 + 4 + 5 + 6 = \dfrac {6 \times \paren {6 + 1} } 2$
:Thus $21$ is the number of pips on a die
:The $7$th semiprime after $4$, $6$, $9$, $10$, $14$, $15$:
::$21 = 3 \times 7$
:The $7$th lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$
:The $7$th odd positive integer after $1$, $3$, $5$, $7$, $9$, $15$ such that all smaller odd integers greater than $1$ which are coprime to it are prime
:The $8$th Fibonacci number, after $1$, $1$, $2$, $3$, $5$, $8$, $13$:
::$21 = 8 + 13$
:The $11$th odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
::$1$, $3$, $5$, $7$, $9$, $11$, $13$, $15$, $17$, $19$, $21$, $\ldots$
:The $14$th harshad number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $10$, $12$, $18$, $20$:
::$21 = 7 \times 3 = 7 \times \paren {2 + 1}$
:The $14$th positive integer after $2$, $3$, $4$, $7$, $8$, $9$, $10$, $11$, $14$, $15$, $16$, $19$, $20$ which cannot be expressed as the sum of distinct pentagonal numbers
:The $17$th (strictly) positive integer after $1$, $2$, $3$, $4$, $6$, $7$, $8$, $9$, $10$, $12$, $13$, $14$, $18$, $19$, $20$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
== Also see ==
* Smallest Number Expressible as Sum of at most Three Triangular Numbers in 4 ways
* Smallest Perfect Square Dissection
* Square of Reversal of Small-Digit Number
* 
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== Historical Note ==
== Sources ==
* : $21$
* : $47,619$
* : $21$
* : $47,619$
Category:Specific Numbers
Category:21
21,000

== Number ==
$21 \, 000$ (twenty-one thousand) is:
:$2^3 \times 3 \times 5^3 \times 7$
:The smallest integer which uses exactly $3$ words in its (British) English description:
::twenty-one thousand
== Also see ==
* Smallest Integer using Three Words in English Description
== Sources ==
* : $21,000$
* : $21,000$
Category:Specific Numbers
Category:21,000
21,147

== Number ==
$21 \, 147$ (twenty-one thousand, one hundred and forty-seven) is:
:$3 \times 7 \times 19 \times 53$
:The $9$th Bell number after $(1)$, $1$, $2$, $5$, $15$, $52$, $203$, $877$, $4140$
== Also see ==
* 
Category:Specific Numbers
Category:21,147
21,480

== Number ==
$21 \, 480$ (twenty-one thousand, four hundred and eighty) is:
:$2^3 \times 3 \times 5 \times 179$
:The $22$nd integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
::$3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$, $94$, $166$, $324$, $379$, $469$, $546$, $974$, $1963$, $3507$, $3610$, $6917$, $21 \, 480$
== Also see ==
* 
Category:Specific Numbers
Category:21,480
21,576

== Number ==
$21 \, 576$ (twenty-one thousand, five hundred and seventy-six) is:
:$2^3 \times 3 \times 29 \times 31$
:The area of The smallest Pythagorean quadrilateral in which the sides of the $4$ right triangles formed by its sides and perpendicular diagonals are all integers
== Also see ==
* Smallest Pythagorean Quadrilateral with Integer Sides
== Sources ==
* : $21,576$
Category:Specific Numbers
Category:21,576
21,679

== Number ==
$21 \, 679$ (twenty-one thousand, six hundred and seventy-nine) is:
:$7 \times 19 \times 163$
:The $21$st non-square positive integer, and largest known, which cannot be expressed as the sum of a square and a prime:
::$10$, $34$, $58$, $85$, $91$, $130$, $214$, $226$, $370$, $526$, $706$, $730$, $771$, $1255$, $1351$, $1414$, $1906$, $2986$, $3676$, $9634$, $21 \, 679$
== Also see ==
* 
Category:Specific Numbers
Category:21,679
21,701

== Number ==
$21 \, 701$ (twenty-one thousand, seven hundred and one) is:
:The $2435$th prime number
:The index of the $25$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $\ldots$, $2203$, $2281$, $3217$, $4253$, $4423$, $9689$, $9941$, $11 \, 213$, $19 \, 937$:
::$M_{21 \, 701} = 2^{21 \, 701} - 1 \approx 4 \cdotp 487 \times 10^{6532}$
== Also see ==
* 
* 
== Historical Note ==
== Sources ==
* : $2^{21701} - 1$
* : $2^{21,701} - 1$
Category:Specific Numbers
Category:21,701
21,701/Historical Note

== Historical Note on $21 \, 701$ ==
The Mersenne number $M_{21 \, 701} = 2^{21 \, 701} - 1$ was demonstrated to be a Mersenne prime on $30$ October $1978$, by two $18$-year-old school students: and .
== Sources ==
* : $2^{21701} - 1$
* : $2^{21,701} - 1$
Category:Historical Notes
21,952

== Number ==
$21 \, 952$ (twenty-one thousand, nine hundred and fifty-two) is:
:$2^6 \times 7^3$
:The $2$nd after $1$ of the $3$ positive integers whose divisor count equals its cube root:
::$\map {\sigma_0} {21 \, 952} = 28$
:The $28$th cube number:
::$21 \, 952 = 28 \times 28 \times 28$
== Also see ==
* 
* 
== Sources ==
* : $21,952$
Category:Specific Numbers
Category:21,952
210

== Number ==
$210$ (two hundred and ten) is:
:$2 \times 3 \times 5 \times 7$
:The $2$nd pentagonal number after $1$ which is also triangular:
::$210 = \dfrac {12 \paren {3 \times 12 - 1} } 2 = \dfrac {20 \times \paren {20 + 1} } 2$
:The $3$rd triangular number after $6$, $120$ which can be expressed as the product of $3$ consecutive integers:
::$210 = T_{20} = 5 \times 6 \times 7$
:The $4$th primorial after $1$, $2$, $6$, $30$ (counting $1$ as the zeroth):
::$210 = p_4 \# = 7 \# = 2 \times 3 \times 5 \times 7$
:Hence the smallest positive integer with $4$ distinct prime factors.
:The $4$th primorial after $2$, $6$, $30$ which can be expressed as the product of consecutive integers:
::$210 = 7 \# = 14 \times 15$
:The $7$th pentatope number after $1$, $5$, $15$, $35$, $70$, $126$:
::$210 = 1 + 4 + 10 + 20 + 35 + 56 + 84 = \dfrac {7 \paren {7 + 1} \paren {7 + 2} \paren {7 + 3} } {24}$
:The $11$th number after $1$, $3$, $22$, $66$, $70$, $81$, $94$, $115$, $119$, $170$ whose divisor sum is square:
:
:The $12$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $51$, $70$, $92$, $117$, $145$, $176$:
::$210 = 1 + 4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 + 31 + 34 = \dfrac {12 \paren {3 \times 12 - 1} } 2$
:The $12$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $146$, $162$, $188$, $206$.
:The $13$th integer $n$ after $1, 3, 15, 30, 35, 56, 70, 78, 105, 140, 168, 190$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:
::$\map {\sigma_0} {210} = 16$, $\map \phi {210} = 48$, $\map {\sigma_1} {210} = 576$
:The $20$th triangular number after $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$, $55$, $66$, $78$, $91$, $105$, $120$, $136$, $153$, $171$, $190$:
::$210 = \ds \sum_{k \mathop = 1}^{20} k = \dfrac {20 \times \paren {20 + 1} } 2$
:The $21$st and last of $21$ integers which can be represented as the sum of two primes in the maximum number of ways
::$1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $10$, $12$, $14$, $16$, $18$, $24$, $30$, $36$, $42$, $48$, $60$, $90$, $210$
:The $23$rd generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $100$, $117$, $126$, $145$, $155$, $176$, $187$:
::$210 = \dfrac {12 \paren {3 \times 12 - 1} } 2$
:The $27$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$, $16$, $18$, $20$, $24$, $30$, $36$, $42$, $48$, $60$, $72$, $84$, $90$, $96$, $108$, $120$, $144$, $168$, $180$:
::$\map {\sigma_1} {210} = 576$
:The $41$st positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.
== Also see ==
* 
* 
* 
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* 
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== Sources ==
* : $30$
* : $210$
* : $30$
* : $210$
Category:Specific Numbers
Category:210
2107

== Number ==
$2107$ (two thousand, one hundred and seven) is:
:$7^2 \times 43$
:The $27$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $\ldots$, $817$, $919$, $1027$, $1141$, $1261$, $1387$, $1519$, $1657$, $1801$, $1951$:
::$2107 = \ds 1 + \sum_{k \mathop = 1}^{27 - 1} 6 k = 27^3 - 26^3$
== Also see ==
* 
Category:Specific Numbers
Category:2107
2109

== Number ==
$2109$ (two thousand, one hundred and nine) is:
:$3 \times 19 \times 37$
:The $18$th square pyramidal number after $1$, $5$, $14$, $30$, $55$, $91$, $140$, $204$, $285$, $385$, $506$, $650$, $819$, $1015$, $1240$, $1496$, $1785$:
::$2109 = \ds \sum_{k \mathop = 1}^{18} k^2 = \dfrac {18 \paren {18 + 1} \paren {2 \times 18 + 1} } 6$
== Also see ==
* 
Category:Specific Numbers
Category:2109
211

== Number ==
$211$ (two hundred and eleven) is:
:The $47$th prime number
:The $4$th Euclid number after $3$, $7$, $31$:
::$211 = p_4\# + 1 = 2 \times 3 \times 5 \times 7 + 1$
:The $5$th Euclid prime after $2$, $3$, $7$, $31$:
::$211 = p_4\# + 1 = 2 \times 3 \times 5 \times 7 + 1$
:The $5$th balanced prime after $5$, $53$, $157$, $173$:
::$211 = \dfrac {199 + 223} 2$
:The $8$th near-repdigit prime after $101$, $113$, $131$, $151$, $181$, $191$, $199$
:The $11$th of $11$ primes of the form $2 x^2 + 11$:
::$2 \times 10^2 + 11 = 211$ ()
:The $41$st lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $163$, $169$, $171$, $189$, $193$, $195$, $201$, $205$, $211$, $\ldots$
== Also see ==
* 
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:211
2112

== Number ==
$2112$ (two thousand one hundred and twelve) is:
:$2^6 \times 3 \times 11$
:The $52$nd Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $\ldots$, $1176$, $1184$, $1197$, $1212$, $1296$, $1311$, $1332$, $1344$, $1416$, $1575$, $1715$:
::$2112 = 528 \times 4 = 528 \times \left({2 \times 1 \times 1 \times 2}\right)$
== Also see ==
* 
Category:Specific Numbers
Category:2112
2116

== Number ==
$2116$ (two thousand, one hundred and sixteen) is:
:$2^2 \times 23^2$
:The $40$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $1024$, $1089$, $1225$, $1255$, $1351$, $1414$, $1444$, $1521$, $1681$, $1849$, $1906$, $1936$, $2116$, $\ldots$
:The $46$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $1296$, $1369$, $1444$, $1521$, $1600$, $1681$, $1764$, $1849$, $1936$, $2025$:
::$2116 = 46 \times 46$
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Category:Specific Numbers
Category:2116
212

== Number ==
$212$ (two hundred and twelve) is:
:$2^2 \times 53$
:The $8$th integer after $0$, $1$, $2$, $4$, $8$, $121$, $151$ which is palindromic in both decimal and ternary:
::$212_{10} = 12 \, 121_3$
:The $11$th palindromic integer after $0$, $1$, $2$, $3$, $11$, $22$, $101$, $111$, $121$, $202$ whose square is also palindromic integer
::$212^2 = 44 \, 944$
:The $23$rd Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $15$, $24$, $36$, $111$, $112$, $115$, $128$, $132$, $135$, $144$, $175$:
::$212 = 53 \times 4 = 53 \times \paren {2 \times 1 \times 2}$
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== Historical Note ==
Category:Specific Numbers
Category:212
212,890,625

== Number ==
$212 \, 890 \, 625$ is:
:$5^9 \times 109$
:The $16$th automorphic number after $1$, $5$, $6$, $25$, $76$, $376$, $625$, $9376$, $90 \, 625$, $109 \, 376$, $890 \, 625$, $2 \, 890 \, 625$, $7 \, 109 \, 376$, $12 \, 890 \, 625$, $87 \, 109 \, 376$:
::$212 \, 890 \, 625^2 = 45 \, 322 \, 418 \, \mathbf {212 \, 890 \, 625}$
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Category:Specific Numbers
Category:212,890,625
2133

== Number ==
$2133$ (two thousand, one hundred and thirty-three) is:
:$3^3 \times 79$
:The $27$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $645$, $736$, $833$, $936$, $1045$, $1160$, $1281$, $1408$, $1541$, $1680$, $1825$, $1976$:
::$2133 = \ds \sum_{k \mathop = 1}^{27} \paren {6 k - 5} = 27 \paren {3 \times 27 - 2}$
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Category:Specific Numbers
Category:2133
214

== Number ==
$214$ (two hundred and fourteen) is:
:$2 \times 107$
:The $7$th non-square positive integer which cannot be expressed as the sum of a square and a prime:
::$10$, $34$, $58$, $85$, $91$, $130$, $214$, $\ldots$
:The $12$th number after $1$, $3$, $22$, $66$, $70$, $81$, $94$, $115$, $119$, $170$, $210$ whose divisor sum is square:
:
:The $13$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $214$, $\ldots$
:The $31$st nontotient:
::$\nexists m \in \Z_{>0}: \map \phi m = 214$
:where $\map \phi m$ denotes the Euler $\phi$ function
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Category:Specific Numbers
Category:214
2144

== Number ==
$2144$ (two thousand one hundred and forty-four) is:
:$2^5 \times 67$
:The $53$rd Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $\ldots$, $1296$, $1311$, $1332$, $1344$, $1416$, $1575$, $1715$, $2112$:
::$2144 = 67 \times 32 = 67 \times \left({2 \times 1 \times 4 \times 4}\right)$
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Category:Specific Numbers
Category:2144
2145

== Number ==
$2145$ (two thousand, one hundred and forty-five) is:
:$3 \times 5 \times 11 \times 13$
:The $1$st of the $6$th pair of triangular numbers whose sum and difference are also both triangular:
::$2145 = T_{65}$, $3741 = T_{86}$, $3741 + 2145 = T_{108}$, $3741 - 2145 = T_{56}$
:The $33$rd hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$, $1035$, $1225$, $1326$, $1431$, $1540$, $1653$, $1770$, $1891$, $2016$:
::$2145 = \ds \sum_{k \mathop = 1}^{33} \paren {4 k - 3} = 33 \paren {2 \times 33 - 1}$
:The $65$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $1326$, $1378$, $1431$, $1485$, $1540$, $1596$, $1653$, $1711$, $1770$, $1770$, $1830$, $1891$, $1953$, $2016$, $2080$:
::$2145 = \ds \sum_{k \mathop = 1}^{65} k = \dfrac {65 \times \paren {65 + 1} } 2$
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Category:Specific Numbers
Category:2145