nyuuzyou/wikis huggingface dataset:
2839

== Number ==
$2839$ (two thousand, eight hundred and thirty-nine) is:
:$17 \times 167$
:The $34$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $\ldots$, $2205$, $2356$, $2512$, $2673$:
::$2839 = \ds \sum_{k \mathop = 1}^{34} \paren {5 k - 4} = \dfrac {34 \paren {5 \times 34 - 3} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:2839
284

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== Number ==
$284$ (two hundred and eighty-four) is:
:$2^2 \times 71$
:The larger of the $1$st amicable pair, with $220$:
::$\map {\sigma_1} {220} = \map {\sigma_1} {284} = 504 = 220 + 284$
:which is also the first Thabit pair:
::$220 = 2^2 \times 11 \times 5 = 2^2 \paren {3 \times 2^2 - 1} \paren {3 \times 2^{2 - 1} - 1}, 284 = 2^2 \paren {9 \times 2^{2 \times 2 - 1} - 1}$
:The $3$rd integer solution to $\map {\sigma_1} n = \map {\sigma_1} {n + 2}$ after $33, 54$:
::$\map {\sigma_1} {284} = 504 = \map {\sigma_1} {286}$
:The $45$th nontotient:
::$\nexists m \in \Z_{>0}: \map \phi m = 284$
:where $\map \phi m$ denotes the Euler $\phi$ function
== Also see ==
* 
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* 
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== Sources ==
* : $220$
* : $284$
* : $220$
* : $284$
Category:Specific Numbers
Category:284
285

== Number ==
$285$ (two hundred and eighty-five) is:
:$3 \times 5 \times 19$
:The $9$th square pyramidal number after $1$, $5$, $14$, $30$, $55$, $91$, $140$, $204$:
::$285 = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 = \ds \sum_{k \mathop = 1}^9 k^2 = \dfrac {9 \paren {9 + 1} \paren {2 \times 9 + 1} } 6$
:The $16$th integer after $7$, $13$, $19$, $35$, $38$, $41$, $57$, $65$, $70$, $125$, $130$, $190$, $205$, $223$, $253$ the decimal representation of whose square can be split into two parts which are each themselves square:
::$285^2 = 81 \, 225$; $81 = 9^2$, $225 = 15^2$
:The $30$th sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $182$, $186$, $190$, $195$, $222$, $230$, $231$, $246$, $255$, $258$, $266$, $273$, $282$:
::$285 = 3 \times 5 \times 19$
:The $53$rd lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $219$, $223$, $231$, $235$, $237$, $241$, $259$, $261$, $267$, $273$, $283$, $285$, $\ldots$
:The $56$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.
== Also see ==
* 
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Category:Specific Numbers
Category:285
285,778

== Number ==
$285 \, 778$ (two hundred and eighty-five thousand, seven hundred and seventy-eight) is:
:$2 \times 43 \times 3323$
:The $19$th term of a sociable chain of order $28$ whose smallest term is $14 \, 316$:
::$14 \, 316$, $19 \, 116$, $31 \, 704$, $47 \, 616$, $83 \, 328$, $177 \, 792$, $295 \, 488$, $629 \, 072$, $589 \, 786$, $294 \, 896$, $358 \, 336$, $418 \, 904$, $366 \, 556$, $274 \, 924$, $275 \, 444$, $243 \, 760$, $376 \, 736$, $381 \, 028$, $285 \, 778$, $152 \, 990$, $122 \, 410$, $97 \, 946$, $48 \, 976$, $45 \, 946$, $22 \, 976$, $22 \, 744$, $19 \, 916$, $17 \, 716$, $14 \, 316$, $\ldots$
== Also see ==
* 
Category:Specific Numbers
Category:285,778
2850

== Number ==
$2850$ (two thousand, eight hundred and fifty) is:
:$2 \times 3 \times 5^2 \times 19$
:The $38$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $2145$, $2278$, $2415$, $2556$, $2701$:
::$2850 = \ds \sum_{k \mathop = 1}^{38} \paren {4 k - 3} = 38 \paren {2 \times 38 - 1}$
:The $75$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $2211$, $2278$, $2346$, $2415$, $2485$, $2556$, $2628$, $2701$, $2775$:
::$2850 = \ds \sum_{k \mathop = 1}^{75} k = \dfrac {75 \times \paren {75 + 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:2850
286

== Number ==
$286$ (two hundred and eighty-six) is:
:$2 \times 11 \times 13$
:The $2$nd of the $3$-digit integers $m$ which need the largest number of reverse-and-add process iterations ($23$) before reaching a palindromic number:
::$286$, $968$, $1837$, $\ldots$, $8713200023178$
:The $3$rd Fermat pseudoprime to base $3$ after $91$, $121$:
::$3^{286} \equiv 3 \pmod {286}$
:The $11$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $56$, $84$, $120$, $165$, $220$:
::$286 = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 = \dfrac {11 \paren {11 + 1} \paren {11 + 2} } 6$
:The $11$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $148$, $189$, $235$:
::$286 = 1 + 7 + 11 + 16 + 21 + 26 + 31 + 36 + 41 + 46 + 51 = \dfrac {11 \paren {5 \times 11 - 3} } 2$
:The $31$st sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $182$, $186$, $190$, $195$, $222$, $230$, $231$, $246$, $255$, $258$, $266$, $273$, $282$, $285$:
::$286 = 2 \times 11 \times 13$
:The $46$th nontotient:
::$\nexists m \in \Z_{>0}: \map \phi m = 286$
:where $\map \phi m$ denotes the Euler $\phi$ function
== Also see ==
* 
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Category:Specific Numbers
Category:286
287

== Number ==
$287$ (two hundred and eighty-seven) is:
:$7 \times 41$
:The $14$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $51$, $70$, $92$, $117$, $145$, $176$, $210$, $247$:
::$287 = \ds \sum_{k \mathop = 1}^{14} \paren {3 k - 2} = \dfrac {14 \paren {3 \times 14 - 1} } 2$
:The $27$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $126$, $145$, $176$, $187$, $210$, $222$, $247$, $260$:
::$287 = \dfrac {14 \paren {3 \times 14 - 1} } 2$
== Also see ==
* 
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Category:Specific Numbers
Category:287
2870

== Number ==
$2870$ (two thousand, eight hundred and seventy) is:
:$2 \times 5 \times 7 \times 41$
:The $20$th square pyramidal number after $1$, $5$, $14$, $30$, $55$, $\ldots$, $1015$, $1240$, $1496$, $1785$, $2109$, $2470$:
::$2870 = \ds \sum_{k \mathop = 1}^{20} k^2 = \dfrac {20 \paren {20 + 1} \paren {2 \times 20 + 1} } 6$
== Also see ==
* 
Category:Specific Numbers
Category:2870
2879

== Number ==
$2879$ (two thousand, eight hundred and seventy-nine) is:
:The $417$th prime number.
:The $6$th and last term after $89$, $179$, $359$, $719$, $1439$ of the smallest Cunningham chain of the first kind of length $6$:
::$\left({89, 179, 359, 719, 1439, 2879}\right)$
== Also see ==
* 
* 
Category:Specific Numbers
Category:2879
288

== Number ==
$288$ (two hundred and eighty-eight) is:
:$2^5 \times 3^2$
:The smallest integer multiple of $9$ all of whose digits are even:
::$288 = 32 \times 9$
:The product of the number of edges, edges per face and faces of a cube.
:The product of the number of edges, edges per face and faces of a regular octahedron.
:The smaller of the $2$nd pair of consecutive powerful numbers:
::$288 = 2^5 \times 3^2$, $289 = 17^2$
:The $4$th superfactorial after $1$, $2$, $12$:
::$288 = 4\$ = 4! \times 3! \times 2! \times 1!$
:The $4$th positive integer after $128$, $192$, $256$ with $7$ or more prime factors:
::$288 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$
:The $8$th pentagonal pyramidal number after $1$, $6$, $12$, $40$, $75$, $126$, $196$:
::$288 = 1 + 5 + 12 + 22 + 35 + 51 + 70 + 92 = \dfrac {8^2 \paren {8 + 1} } 2$
:The $11$th positive integer after $64$, $96$, $128$, $144$, $160$, $192$, $216$, $224$, $240$, $256$ with $6$ or more prime factors:
::$288 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \paren {\times \, 3}$
:The $20$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $146$, $162$, $188$, $206$, $210$, $216$, $238$, $246$, $248$, $262$, $268$, $276$
:The $28$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $144$, $169$, $196$, $200$, $216$, $225$, $243$, $256$
:The $30$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $\ldots$, $120$, $144$, $168$, $180$, $210$, $216$, $240$:
::$\map {\sigma_1} {288} = 819$
== Also see ==
* Product of Number of Edges, Edges per Face and Faces of Cube
* Product of Number of Edges, Edges per Face and Faces of Regular Octahedron
* Smallest Multiple of 9 with all Digits Even
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== Sources ==
* : $72$
* : $288$
Category:Specific Numbers
Category:288
288,230,376,151,711,745

== Number ==
$288 \, 230 \, 376 \, 151 \, 711 \, 745$ is:
:$5 \times 107 \, 367 \, 629 \times 536 \, 903 \, 681$
:$2^{58} + 1$
== Also see ==
* Prime Decomposition of $2^{58} + 1$
== Sources ==
* : $2^{58} + 1$
* : $2^{58} + 1$
Category:Specific Numbers
Category:288,230,376,151,711,745
2882

== Number ==
$2882$ (two thousand, eight hundred and eighty-two) is:
:$2 \times 11 \times 131$
:The $5$th pentagonal number after $1$, $5$, $22$, $1001$ which is also palindromic:
::$2882 = \ds \sum_{k \mathop = 1}^{44} \paren {3 k - 2} = \dfrac {44 \paren {3 \times 44 - 1} } 2$
:The $44$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $1820$, $1926$, $2035$, $2147$, $2262$, $2380$, $2501$, $2625$, $2752$:
::$2882 = \ds \sum_{k \mathop = 1}^{44} \paren {3 k - 2} = \dfrac {44 \paren {3 \times 44 - 1} } 2$
:The $87$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $2380$, $2420$, $2501$, $2542$, $2625$, $2667$, $2752$, $2795$:
::$2882 = \ds \sum_{k \mathop = 1}^{44} \paren {3 k - 2} = \dfrac {44 \paren {3 \times 44 - 1} } 2$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:2882
289

== Number ==
$289$ (two hundred and eighty-nine) is:
:$17^2$
:The larger of the $2$nd pair of consecutive powerful numbers:
::$288 = 2^5 \times 3^2$, $289 = 17^2$
:The $6$th square lucky number:
::$1$, $9$, $25$, $49$, $169$, $289$, $\ldots$
:The $9$th Friedman number base $10$ after $25$, $121$, $125$, $126$, $127$, $128$, $153$, $216$:
::$289 = \paren {8 + 9}^2$
:The $15$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $214$, $226$, $289$, $\ldots$
:The $17$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $100$, $121$, $144$, $169$, $196$, $225$, $256$:
::$289 = 17 \times 17$
:The $29$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $144$, $169$, $196$, $200$, $216$, $225$, $243$, $256$, $288$
:The $54$th lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $237$, $241$, $259$, $261$, $267$, $273$, $283$, $285$, $289$, $\ldots$
== Also see ==
* 
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== Sources ==
* : $288$
Category:Specific Numbers
Category:289
29

== Number ==
$29$ (twenty-nine) is:
:The $10$th prime number, after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$, $23$
:The smaller of the $5$th pair of twin primes, with $31$
:The $1$st of $29$ primes of the form $2 x^2 + 29$:
::$2 \times 0^2 + 29 = 29$ ()
:The $2$nd of the $1$st pair of consecutive prime numbers which differ by $6$:
::$29 - 23 = 6$
:The $2$nd primorial prime after $5$:
::$29 = p_3 \# - 1 = 5 \# - 1 = 2 \times 3 \times 5 - 1$
:The $2$nd after $21$ of the $5$ $2$-digit positive integers which can occur as a $5$-fold repetition at the end of a square number
:The $3$rd number such that $2 n^2 - 1$ is square, after $1$, $5$:
::$2 \times 29^2 - 1 = 2 \times 841 - 1 = 1681 = 41^2$
:The $3$rd prime $p$ after $11$, $23$ such that the Mersenne number $2^p - 1$ is composite
:The upper end of the $3$rd record-breaking gap between twin primes:
::$29 - 19 = 10$
:The $4$th of $11$ primes of the form $2 x^2 + 11$:
::$2 \times 3^2 + 11 = 29$ ()
:The $5$th Lucas prime after $2$, $3$, $7$, $11$.
:The $5$th positive integer $n$ after $5$, $11$, $17$, $23$ such that no factorial of an integer can end with $n$ zeroes.
:The $5$th positive integer $n$ after $0$, $1$, $5$, $25$ such that the Fibonacci number $F_n$ ends in $n$
:The $5$th long period prime after $7$, $17$, $19$, $23$:
::$\dfrac 1 {29} = 0 \cdotp \dot 03448 \, 27586 \, 20689 \, 65517 \, 24137 \, 93 \dot 1$
:The $6$th right-truncatable prime after $2$, $3$, $5$, $7$, $23$
:The $6$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$:
::$2 \times 29 + 1 = 59$, which is prime.
:The $7$th Lucas number after $(2)$, $1$, $3$, $4$, $7$, $11$, $18$:
::$29 = 11 + 18$
:The $12$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
::$3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $\ldots$
:The $15$th odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
::$1$, $3$, $5$, $7$, $9$, $11$, $13$, $15$, $17$, $19$, $21$, $23$, $25$, $27$, $29$, $\ldots$
:The $18$th positive integer after $2$, $3$, $4$, $7$, $8$, $9$, $10$, $11$, $14$, $15$, $16$, $19$, $20$, $21$, $24$, $25$, $26$ which cannot be expressed as the sum of distinct pentagonal numbers.
== Also see ==
* Hilbert-Waring Theorem: Cubes
* Smallest Integer not Sum of Two Ulam Numbers
* Square-Bracing Problem: Non-Crossing Rods
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== Sources ==
* : $29$
* : $29$
Category:Specific Numbers
Category:29
29,341

== Number ==
$29 \, 341$ (twenty-nine thousand, three hundred and forty-one) is:
:$13 \times 37 \times 61$
:The smallest Fermat pseudoprime to each of the bases $2$, $3$, $5$ and $7$:
::$2^{29 \, 341} \equiv 2 \pmod {29 \, 341}$, $3^{29 \, 341} \equiv 3 \pmod {29 \, 341}$, $5^{29 \, 341} \equiv 5 \pmod {29 \, 341}$, $7^{29 \, 341} \equiv 7 \pmod {29 \, 341}$
:The $10$th Carmichael number after $561$, $1105$, $1729$, $2465$, $2821$, $6601$, $8911$, $10 \, 585$, $15 \, 841$:
::$\forall a \in \Z: a \perp 29 \, 341: a^{29 \, 340} \equiv 1 \pmod {29 \, 341}$
== Also see ==
* Smallest Fermat Pseudoprime to Bases 2, 3, 5 and 7
* 
== Sources ==
* : $29,351$
Category:Specific Numbers
Category:29,341
29,660

== Number ==
$29 \, 660$ (twenty-nine thousand, six hundred and sixty) is:
:$2^2 \times 5 \times 1483$
:The number of different ways to colour the faces of a cube with $5$ given colours, one colour per face.
== Also see ==
* Number of Different Ways to Colour the Faces of Cube with 5 Colours‎
== Sources ==
* : $114$
Category:Specific Numbers
Category:29,660
29,912,035,725

== Number ==
$29 \, 912 \, 035 \, 725$ is:
:$3^3 \times 5^2 \times 11 \times 13 \times 431 \times 719$
:The smaller of the $1$st of a set of $3$ amicable pairs whose sum is $64 \, 795 \, 852 \, 800$:
::$\map {\sigma_1} {29 \, 912 \, 035 \, 725} = \map {\sigma_1} {34 \, 883 \, 817 \, 075} = 64 \, 795 \, 852 \, 800 = 29 \, 912 \, 035 \, 725 + 34 \, 883 \, 817 \, 075$
== Also see ==
* 
Category:Specific Numbers
Category:29,912,035,725
29,929

== Number ==
$29 \, 929$ (twenty-nine thousand, nine hundred and twenty-nine) is:
:$173^2$
:The $19$th square after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $121$, $144$, $225$, $441$, $484$, $676$, $1444$, $7744$, $11 \, 881$ which has no more than $2$ distinct digits and does not end in $0$:
::$29 \, 929 = 173^2$
:The $173$rd square number:
::$29 \, 929 = 173 \times 173$
== Also see ==
* 
* 
Category:Specific Numbers
Category:29,929
290

== Number ==
$290$ (two hundred and ninety) is:
:$2 \times 5 \times 29$
:The $21$st untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $262$, $268$, $276$
:The $28$th noncototient after $10$, $26$, $34$, $50$, $\ldots$, $244$, $260$, $266$, $268$, $274$:
::$\nexists m \in \Z_{>0}: m - \map \phi m = 290$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $32$nd sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $246$, $255$, $258$, $266$, $273$, $282$, $285$, $286$:
::$290 = 2 \times 5 \times 29$
:The $47$th nontotient:
::$\nexists m \in \Z_{>0}: \map \phi m = 290$
:where $\map \phi m$ denotes the Euler $\phi$ function
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:290
291

== Number ==
$291$ (two hundred and ninety-one) is:
:$3 \times 97$
:The $43$rd happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $188$, $190$, $192$, $193$, $203$, $208$, $219$, $226$, $230$, $236$, $239$, $262$, $263$, $280$:
::$291 \to 2^2 + 9^2 + 1^2 = 4 + 81 + 1 = 86 \to 8^2 + 6^2 = 64 + 36 = 100 \to 1^2 + 0^2 + 0^2 = 1$
== Also see ==
* 
Category:Specific Numbers
Category:291
2915

== Number ==
$2915$ (two thousand, nine hundred and fifteen) is:
:$5 \times 11 \times 53$
:The $4$th Lucas-Carmichael number after $399$, $935$, $2015$:
::$\paren {5 + 1} \divides \paren {2915 + 1}$, $\paren {11 + 1} \divides \paren {2915 + 1}$, $\paren {53 + 1} \divides \paren {2915 + 1}$
== Also see ==
* 
Category:Specific Numbers
Category:2915
2916

== Number ==
$2916$ (two thousand, nine hundred and sixteen) is:
:$2^2 \times 3^6$
:The $20$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $324$, $400$, $576$, $784$, $900$, $961$, $1024$, $1296$, $1600$, $1764$, $1936$, $2304$, $2704$ to be the divisor sum value of some (strictly) positive integer:
::$2916 = \map {\sigma_1} {1802} = \map {\sigma_1} {1942}$
:The $54$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $1936$, $2025$, $2116$, $2209$, $2304$, $2401$, $2500$, $2601$, $2704$, $2809$:
::$2916 = 54 \times 54$
== Also see ==
* 
* 
Category:Specific Numbers
Category:2916
2917

== Number ==
$2917$ (two thousand, nine hundred and seventeen) is:
:The $422$nd prime number
:The $13$th prime number of the form $n^2 + 1$ after $2$, $5$, $17$, $37$, $101$, $197$, $257$, $401$, $577$, $677$, $1297$, $1601$:
::$2917 = 54^2 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:2917
292

== Number ==
$292$ (two hundred and ninety-two) is:
:$2^2 \times 73$
:The $22$nd untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $262$, $268$, $276$, $290$
:The $29$th noncototient after $10$, $26$, $34$, $50$, $\ldots$, $244$, $260$, $266$, $268$, $274$, $290$:
::$\nexists m \in \Z_{>0}: m - \map \phi m = 292$
:where $\map \phi m$ denotes the Euler $\phi$ function
== Also see ==
* 
* 
Category:Specific Numbers
Category:292
2924

== Number ==
$2924$ (two thousand, nine hundred and twenty-four) is:
:$2^2 \times 17 \times 43$
:The larger of the $3$rd amicable pair, with $2620$:
::$\map {\sigma_1} {2620} = \map {\sigma_1} {2924} = 5544 = 2620 + 2924$
:The $12$th positive integer after $504$, $756$, $806$, $1008$, $1148$, $1209$, $1472$, $1512$, $2016$, $2208$, $2418$ which can be expressed as the product of $2$ two-digit numbers in $2$ ways such that the factors in one of those pairs is the reversal of each of the factors in the other:
::$2924 = 34 \times 86 = 68 \times 43$
== Also see ==
* 
* 
== Sources ==
* : $2620$
* : $2620$
Category:Specific Numbers
Category:2924
2925

== Number ==
$2925$ (two thousand, nine hundred and twenty-five) is:
:$3^2 \times 5^2 \times 13$
:The $25$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $\ldots$, $816$, $969$, $1140$, $1330$, $1540$, $1771$, $2024$, $2300$, $2600$:
::$2925 = \ds \sum_{k \mathop = 1}^{25} \frac {k \paren {k + 1} } 2 = \dfrac {25 \paren {25 + 1} \paren {25 + 2} } 6$
:The magic constant of a magic square of order $18$, after $1$, $(5)$, $15$, $34$, $\ldots$, $870$, $1105$, $1379$, $1695$, $2056$, $2465$:
::$2925 = \ds \dfrac 1 {18} \sum_{k \mathop = 1}^{18^2} k = \dfrac {18 \paren {18^2 + 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:2925
2926

== Number ==
$2926$ (two thousand, nine hundred and twenty-six) is:
:$2 \times 7 \times 11 \times 19$
:The $4$th triangular number after $28$, $91$, $351$ which is the sum of $2$ cubes:
::$2926 = 729 + 2197 = 9^3 + 13^3$
:The $44$th second pentagonal number after $2$, $7$, $15$, $26$, $\ldots$, $1962$, $2072$, $2185$, $2301$, $2420$, $2542$, $2667$, $2795$:
::$2926 = \dfrac {44 \paren {3 \times 44 + 1} } 2$
:The $76$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $2211$, $2278$, $2346$, $2415$, $2485$, $2556$, $2628$, $2701$, $2775$, $2850$:
::$2926 = \ds \sum_{k \mathop = 1}^{76} k = \dfrac {76 \times \paren {76 + 1} } 2$
:The $88$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $2380$, $2420$, $2501$, $2542$, $2625$, $2667$, $2752$, $2795$, $2882$:
::$2926 = \dfrac {44 \paren {3 \times 44 + 1} } 2$
== Also see ==
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Category:Specific Numbers
Category:2926
293

== Number ==
$293$ (two hundred and ninety-three) is:
:The $62$nd prime number
:The smaller of the $2$nd pair of primes whose prime gap is $14$:
::$307 - 293 = 14$
:The larger of the $4$th pair of primes whose prime gap is $10$:
::$293 - 283 = 10$
:The $16$th right-truncatable prime after $2$, $3$, $5$, $7$, $23$, $29$, $31$, $37$, $53$, $59$, $71$, $73$, $79$, $233$, $239$
:The $20$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$, $83$, $89$, $113$, $131$, $173$, $179$, $191$, $233$, $239$, $251$, $281$:
::$2 \times 293 + 1 = 587$, which is prime.
:The $44$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $188$, $190$, $192$, $193$, $203$, $208$, $219$, $226$, $230$, $236$, $239$, $262$, $263$, $280$, $291$:
::$293 \to 2^2 + 9^2 + 3^2 = 4 + 81 + 9 = 94 \to 9^2 + 4^2 = 81 + 16 = 97 \to 9^2 + 7^2 = 81 + 49 = 130 \to 1^2 + 3^2 + 0^2 = 1 + 9 + 0 = 10 \to 1^2 + 0^2 = 1$
== Also see ==
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Category:Specific Numbers
Category:293
294,409

== Number ==
$294 \, 409$ is:
:$37 \times 73 \times 109$
:The $25$th Carmichael number:
::$\forall a \in \Z: a \perp 294 \, 409: a^{294 \, 408} \equiv 1 \pmod {294 \, 409}$
== Also see ==
* 
Category:Specific Numbers
Category:294,409
294,896

== Number ==
$294 \, 896$ (two hundred and ninety-four thousand, eight hundred and ninety-six) is:
:$2^4 \times 7 \times 2633$
:The $10$th term of a sociable chain of order $28$ whose smallest term is $14 \, 316$:
::$14 \, 316$, $19 \, 116$, $31 \, 704$, $47 \, 616$, $83 \, 328$, $177 \, 792$, $295 \, 488$, $629 \, 072$, $589 \, 786$, $294 \, 896$, $358 \, 336$, $418 \, 904$, $366 \, 556$, $274 \, 924$, $275 \, 444$, $243 \, 760$, $376 \, 736$, $381 \, 028$, $285 \, 778$, $152\, 990$, $122 \, 410$, $97 \, 946$, $48 \, 976$, $45 \, 946$, $22 \, 976$, $22 \, 744$, $19 \, 916$, $17 \, 716$, $14 \, 316$, $\ldots$
== Also see ==
* 
Category:Specific Numbers
Category:294,896
295

== Number ==
$295$ (two hundred and ninety-five) is:
:$5 \times 59$
:The $2$nd candidate Lychrel number.
:The $2$nd term of the smallest triplet of integers in arithmetic sequence which have the same divisor sum:
::$\map {\sigma_1} {267} = \map {\sigma_1} {295} = \map {\sigma_1} {323} = 360$
== Also see ==
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== Sources ==
* : $267$
Category:Specific Numbers
Category:295
295,488

== Number ==
$295 \, 488$ (two hundred and ninety-five thousand, four hundred and eighty-eight) is:
:$2^6 \times 3^5 \times 19$
:The $7$th term of a sociable chain of order $28$ whose smallest term is $14 \, 316$:
::$14 \, 316$, $19 \, 116$, $31 \, 704$, $47 \, 616$, $83 \, 328$, $177 \, 792$, $295 \, 488$, $629 \, 072$, $589 \, 786$, $294 \, 896$, $358 \, 336$, $418 \, 904$, $366 \, 556$, $274 \, 924$, $275 \, 444$, $243 \, 760$, $376 \, 736$, $381 \, 028$, $285 \, 778$, $152\, 990$, $122 \, 410$, $97 \, 946$, $48 \, 976$, $45 \, 946$, $22 \, 976$, $22 \, 744$, $19 \, 916$, $17 \, 716$, $14 \, 316$, $\ldots$
== Also see ==
* 
Category:Specific Numbers
Category:295,488
2961

== Number ==
$2961$ (two thousand, nine hundred and sixty-one) is:
:$3^2 \times 7 \times 47$
: The $3$rd integer after $954$, $1980$ whose digits are unchanged when subtracting its reversal:
::$2961 - 1692 = 1269$
== Also see ==
* 
Category:Specific Numbers
Category:2961
297

== Number ==
$297$ (two hundred and ninety-seven) is:
:$3^3 \times 11$
:The $4$th Kaprekar triple after $1$, $8$, $45$:
::$297^3 = 26 \, 198 \, 073 \to 26 + 198 + 073 = 297$
:The $6$th Kaprekar number after $1$, $9$, $45$, $55$, $99$:
::$297^2 = 88 \, 209 \to 88 + 209 = 297$
:The number of integer partitions for $17$:
::$\map p {17} = 297$
:The $55$th lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $237$, $241$, $259$, $261$, $267$, $273$, $283$, $285$, $289$, $297$, $\ldots$
== Also see ==
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== Sources ==
* : $297$
* : $297$
Category:Specific Numbers
Category:297
297/Mistake

== Source Work ==
:
:The Dictionary
::$297$
:
:The Dictionary
::$297$
== Mistake ==
:[$297$ is] the $5$th Kaprekar number.
== Correction ==
In fact it is the $6$th, if you include the trivial case of $1$:
:$1, 9, 45, 55, 99, 297$
It might be argued that meant to omit $1$ in his count, but this is then inconsistent with his entry on $45$:
:The $3$rd smallest Kaprekar number, after $1$ and $9$.
== Sources ==
* : $297$
* : $297$
Category:Mistakes/Curious and Interesting Numbers