nyuuzyou/wikis huggingface dataset:
43

== Number ==
$43$ (forty-three) is:
:The $14$th prime number, after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$
:The index of the $1$st non-integer term of Göbel's sequence.
:The lower end of the $4$th record-breaking gap between twin primes:
::$59 - 43 = 16$
:The $5$th of $11$ primes of the form $2 x^2 + 11$:
::$2 \times 4^2 + 11 = 43$ ()
:The $6$th prime $p$ after $11$, $23$, $29$, $37$, $41$ such that the Mersenne number $2^p - 1$ is composite
:The larger of the $6$th pair of twin primes, with $41$
:The $9$th left-truncatable prime after $2$, $3$, $5$, $7$, $13$, $17$, $23$, $37$
:The $12$th lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $\ldots$
:The $17$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
::$3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $\ldots$
:The $19$th positive integer which is not the sum of $1$ or more distinct squares:
::$2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $23$, $24$, $27$, $28$, $31$, $32$, $33$, $43$, $\ldots$
:The $21$st odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
::$1$, $3$, $5$, $7$, $\ldots$, $35$, $37$, $41$, $43$, $\ldots$
:The $26$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $26$, $29$, $30$, $31$, $32$, $33$, $37$, $38$, $42$ which cannot be expressed as the sum of distinct pentagonal numbers.
:The $30$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $27$, $30$, $31$, $32$, $35$, $36$, $37$, $38$, $42$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
== Also see ==
* Non-Integral Value of Göbel's Sequence
* 
* 
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* 
* 
* 
* 
* 
* 
== Sources ==
* : $43$
Category:Specific Numbers
Category:43
43,046,721

== Number ==
$43 \, 046 \, 721$ is:
:$3^{16}$
:The $8$th power of $9$ after $(1)$, $9$, $81$, $729$, $6561$, $59 \, 049$, $531 \, 441$, $4 \, 782 \, 969$:
::$43 \, 046 \, 721 = 9^8$
:The $9$th eighth power after $1$, $256$, $6561$, $65 \, 536$, $390 \, 625$, $1 \, 679 \, 616$, $5 \, 764 \, 801$, $16 \, 777 \, 216$:
::$43 \, 046 \, 721 = 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9$
:The $16$th power of $3$ after $(1)$, $3$, $9$, $27$, $81$, $243$, $729$, $2187$, $6561$, $19 \, 683$, $59 \, 049$, $177 \, 147$, $531 \, 441$, $1 \, 594 \, 323$, $4 \, 782 \, 969$, $14 \, 348 \, 907$:
::$43 \, 046 \, 721 = 3^{16}$
:The $81$st fourth power:
::$43 \, 046 \, 721 = 81 \times 81 \times 81 \times 81$
:The $6561$st square number:
::$43 \, 046 \, 721 = 6561 \times 6561$
== Also see ==
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:43,046,721
43,056

== Number ==
$43 \, 056$ (forty-three thousand and fifty-six) is:
:$2^4 \times 3^2 \times 13 \times 23$
:The $2$nd (with $1056$) of the only $2$ solutions $n$ to the equation $n = x \paren {x + 1} = y \paren {y + 5} \paren {y + 10} \paren {y + 15}$:
::$43 \, 056 = 207 \times 208 = 8 \times 13 \times 18 \times 23$
== Also see ==
* 
== Sources ==
* : $1056$
Category:Specific Numbers
Category:43,056
43,252,003,274,489,856,000

== Number ==
$43 \, 252 \, 003 \, 274 \, 489 \, 856 \, 000$ is:
:$2^{27} \times 3^{14} \times 5^3 \times 7^2 \times 11$
:The total number of reachable positions on Rubik's cube
== Also see ==
* Total Number of Reachable Positions on Rubik's Cube
== Sources ==
* : $43,252,003,274,489,856,000$
* : $43,252,003,274,489,856,000$
Category:Specific Numbers
Category:43,252,003,274,489,856,000
43,592

== Number ==
$43 \, 592$ (forty-three thousand, five hundred and ninety-two) is:
:$2^3 \times 5449$
:The $24$th integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$, $2653$, $3069$, $3943$, $4053$, $4998$, $8275$, $9158$, $11 \, 164$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$ is prime
== Also see ==
* 
Category:Specific Numbers
Category:43,592
43,744,839,742,282,591,947

== Number ==
$43 \, 744 \, 839 \, 742 \, 282 \, 591 \, 947$ is:
:$3 \times 283 \times 75 \, 767 \times 680 \, 047 \, 186 \, 109$
:The $2$nd of $5$ integers which have the property that the sum of any $3$ of them is square:
== Also see ==
* 
Category:Specific Numbers
Category:43,744,839,742,282,591,947
430

== Number ==
$430$ (four hundred and thirty) is:
:$2 \times 5 \times 43$
:The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $22$ different ways
:The $34$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $324$, $326$, $336$, $342$, $372$, $406$, $408$, $426$
:The $50$th sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $385$, $399$, $402$, $406$, $410$, $418$, $426$, $429$:
::$430 = 2 \times 5 \times 43$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:430
431

== Number ==
$431$ (four hundred and thirty-one) is:
:The $83$rd prime number
:The larger of the $7$th pair of primes whose prime gap is $10$:
::$431 - 421 = 10$
:The $23$rd Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$, $83$, $89$, $113$, $131$, $173$, $179$, $191$, $233$, $239$, $251$, $281$, $293$, $359$, $419$:
::$2 \times 431 + 1 = 863$, which is prime.
:The smaller of the $23$rd pair of twin primes:
::$433 - 431 = 2$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:431
432

== Number ==
$432$ (four hundred and thirty-two) is:
:$2^4 \times 3^3$
:The $7$th positive integer after $128$, $192$, $256$, $288$, $320$, $384$ with $7$ or more prime factors:
::$432 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3$
:The $20$th positive integer after $64$, $96$, $128$, $144$, $\ldots$, $320$, $324$, $336$, $352$, $360$, $384$, $400$, $416$ with $6$ or more prime factors:
::$432 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \paren {\times \, 3}$
:The $29$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $\ldots$, $135$, $144$, $175$, $212$, $216$, $224$, $312$, $315$, $384$:
::$432 = 18 \times 24 = 18 \times \paren {4 \times 3 \times 2}$
:The $35$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $289$, $324$, $343$, $361$, $392$, $400$:
::$432 = 2^4 \times 3^3$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:432
4324

== Number ==
$4324$ (four thousand, three hundred and twenty-four) is:
:$2^2 \times 23 \times 47$
:The $23$rd square pyramidal number after $1$, $5$, $14$, $30$, $55$, $\ldots$, $1015$, $1240$, $1496$, $1785$, $2109$, $2470$, $2870$, $3311$, $3795$:
::$4324 = \ds \sum_{k \mathop = 1}^{23} k^2 = \dfrac {23 \paren {23 + 1} \paren {2 \times 23 + 1} } 6$
== Also see ==
* 
Category:Specific Numbers
Category:4324
433

== Number ==
$433$ (four hundred and thirty-three) is:
:The $84$th prime number
:The $21$st near-repdigit prime after $101$, $113$, $131$, $151$, $181$, $191$, $199$, $211$, $223$, $227$, $229$, $233$, $277$, $311$, $313$, $331$, $337$, $353$, $373$, $383$
:The larger of the $23$rd pair of twin primes:
::$433 - 431 = 2$
:The $31$st long period prime after $7$, $17$, $19$, $23$, $29$, $\ldots$, $269$, $313$, $337$, $367$, $379$, $383$, $389$, $419$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:433
434

== Number ==
$434$ (four hundred and thirty-four) is:
:$2 \times 7 \times 31$
:The $51$st sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $385$, $399$, $402$, $406$, $410$, $418$, $426$, $429$, $430$:
::$434 = 2 \times 7 \times 31$
== Also see ==
* 
Category:Specific Numbers
Category:434
4347

== Number ==
$4347$ (four thousand, three hundred and forty-seven) is:
:$3^3 \times 7 \times 23$
:The $42$nd heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $\ldots$, $3010$, $3186$, $3367$, $3744$, $3940$, $4141$:
::$4347 = \ds \sum_{k \mathop = 1}^{42} \paren {5 k - 4} = \dfrac {42 \paren {5 \times 42 - 3} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:4347
435

== Number ==
$435$ (four hundred and thirty-five) is:
:$3 \times 5 \times 29$
:The $5$th Fermat pseudoprime to base $4$ after $15$, $85$, $91$, $341$:
::$4^{435} \equiv 4 \pmod {435}$
:The $15$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $120$, $153$, $190$, $231$, $276$, $325$, $378$:
::$435 = \ds \sum_{k \mathop = 1}^{15} \paren {4 k - 3} = 15 \paren {2 \times 15 - 1}$
:The $29$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $325$, $351$, $378$, $406$:
::$435 = \ds \sum_{k \mathop = 1}^{29} k = \dfrac {29 \times \paren {29 + 1} } 2$
:The $52$nd sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $385$, $399$, $402$, $406$, $410$, $418$, $426$, $429$, $430$, $434$:
::$435 = 3 \times 5 \times 29$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:435
4356

== Number ==
$4356$ (four thousand, three hundred and fifty-six) is:
:$2^2 \times 3^2 \times 11^2$
:The sum of the first $11$ cubes:
::$4356 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3 + 10^3 + 11^3$
:The $25$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $\ldots$, $1936$, $2304$, $2704$, $2916$, $3136$, $3600$, $3844$, $4096$ to be the divisor sum value of some (strictly) positive integer:
::$4356 = \map {\sigma_1} {1782} = \map {\sigma_1} {2410} = \map {\sigma_1} {2902} = \map {\sigma_1} {4097}$
:The $66$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $3249$, $3364$, $3481$, $3600$, $3721$, $3844$, $3969$, $4096$, $4225$:
::$4356 = 66 \times 66$
:$2/3$ times its reversal:
::$4356 \times \dfrac 3 2 = 6534$
== Also see ==
* 
* 
* 
== Sources ==
* : $4356$
* : $4356$
Category:Specific Numbers
Category:4356
4357

== Number ==
$4357$ (four thousand, three hundred and fifty-seven) is:
:The $595$th prime number
:The $15$th prime number of the form $n^2 + 1$ after $2$, $5$, $17$, $37$, $101$, $197$, $257$, $401$, $577$, $677$, $1297$, $1601$, $2917$, $3137$:
::$4357 = 66^2 + 1$
== Also see ==
* 
* 
Category:Specific Numbers
Category:4357
436

== Number ==
$436$ (four hundred and thirty-six) is:
:$2^2 \times 109$
:The $43$rd noncototient after $10$, $26$, $34$, $50$, $\ldots$, $344$, $346$, $362$, $366$, $372$, $386$, $394$, $404$, $412$:
::$\nexists m \in \Z_{>0}: m - \phi \left({m}\right) = 436$
:where $\phi \left({m}\right)$ denotes the Euler $\phi$ function
== Also see ==
* 
Category:Specific Numbers
Category:436
4369

== Number ==
$4369$ (four thousand, three hundred and sixty-nine) is:
:$17 \times 257$
:The $14$th Poulet number after $341$, $561$, $645$, $1105$, $1387$, $1729$, $1905$, $2047$, $2465$, $2701$, $2821$, $3277$, $4033$:
::$2^{4369} \equiv 2 \pmod {4369}$: $4369 = 17 \times 257$
== Also see ==
* 
Category:Specific Numbers
Category:4369
4371

== Number ==
$4371$ (four thousand, three hundred and seventy-one) is:
:$3 \times 31 \times 47$
:The $15$th Poulet number after $341$, $561$, $645$, $1105$, $1387$, $1729$, $1905$, $2047$, $2465$, $2701$, $2821$, $3277$, $4033$, $4369$:
::$2^{4371} \equiv 2 \pmod {4371}$: $4371 = 3 \times 31 \times 47$
:The $47$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $2145$, $2278$, $2415$, $2556$, $2701$, $2850$, $3003$, $3160$, $3321$, $3486$, $3655$, $3828$, $4005$, $4186$:
::$4371 = \ds \sum_{k \mathop = 1}^{47} \paren {4 k - 3} = 47 \paren {2 \times 47 - 1}$
:The $93$nd triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $3655$, $3741$, $3828$, $3916$, $4005$, $4095$, $4186$, $4278$:
::$4371 = \ds \sum_{k \mathop = 1}^{93} k = \dfrac {93 \times \paren {93 + 1} } 2$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:4371
4374

== Number ==
$4374$ (four thousand, three hundred and seventy-four) is:
:$2 \times 3^7$
:$35$ and $4374$ have the same prime factors between them as $36$ and $4375$:
::$35 = 5 \times 7$, $4374 = 2 \times 3^7$; $36 = 2^2 \times 3^2$, $4375 = 5^4 \times 7$
== Also see ==
* Prime Factors of 35, 36, 4734 and 4735
Category:Specific Numbers
Category:4374
4375

== Number ==
$4375$ (four thousand, three hundred and seventy-five) is:
:$5^4 \times 7$
:The $28$th trimorphic number after $1$, $4$, $5$, $6$, $9$, $\ldots$, $501$, $624$, $625$, $749$, $751$, $875$, $999$, $1249$, $3751$:
::$4375^3 = 83 \, 740 \, 23 \mathbf {4 \, 375}$
:$35$ and $4374$ have the same prime factors between them as $36$ and $4375$:
::$35 = 5 \times 7$, $4374 = 2 \times 3^7$; $36 = 2^2 \times 3^2$, $4375 = 5^4 \times 7$
== Also see ==
* Prime Factors of 35, 36, 4734 and 4735
* 
Category:Specific Numbers
Category:4375
438

== Number ==
$438$ (four hundred and thirty-eight) is:
:$2 \times 3 \times 73$
:The $18$th Smith number after $4$, $22$, $27$, $58$, $85$, $94$, $121$, $166$, $202$, $265$, $274$, $319$, $346$, $355$, $378$, $382$, $391$:
::$4 + 3 + 8 = 2 + 3 + 7 + 3 = 15$
:The $53$rd sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $385$, $399$, $402$, $406$, $410$, $418$, $426$, $429$, $430$, $434$, $435$:
::$438 = 2 \times 3 \times 73$
== Also see ==
* 
* 
Category:Specific Numbers
Category:438
438,579,088

== Number ==
$438 \, 579 \, 088$ is:
:$2^4 \times 23^2 \times 51 \, 817$
:The $4$th perfect digit-to-digit invariant after $0$, $1$, $3435$:
::$438 \, 579 \, 088 = 4^4 + 3^3 + 8^8 + 5^5 + 7^7 + 9^9 + 0^0 + 8^8 + 8^8$
== Also see ==
* 
== Sources ==
* : $438,579,088$
* : $438,579,088$
Category:Specific Numbers
Category:438,579,088
44

== Number ==
$44$ (forty-four) is:
:$2^2 \times 11$
:The $1$st of the $1$st ordered quadruple of consecutive integers that have divisor sums which are strictly decreasing:
::$\map {\sigma_1} {44} = 84$, $\map {\sigma_1} {45} = 78$, $\map {\sigma_1} {46} = 72$, $\map {\sigma_1} {47} = 48$
:The $5$th subfactorial after $0$, $1$, $2$, $9$:
::$44 = 5! \left({1 - \dfrac 1 {1!} + \dfrac 1 {2!} - \dfrac 1 {3!} + \dfrac 1 {4!} - \dfrac 1 {5!} }\right)$
:The $1$st of the $1$st pair of consecutive integers which both have $6$ divisors:
::$\map {\sigma_0} {44} = \map {\sigma_0} {45} = 6$
:The $10$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $28$, $31$, $32$:
::$44 \to 4^2 + 4^2 = 16 + 16 = 32 \to 3^2 + 2^2 = 9 + 4 = 13 \to 1^2 + 3^2 = 9 + 1 = 10 \to 1^2 + 0^2 = 1$
:The $20$th positive integer which is not the sum of $1$ or more distinct squares:
::$2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $23$, $24$, $27$, $28$, $31$, $32$, $33$, $43$, $44$, $\ldots$
:The $27$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $26$, $29$, $30$, $31$, $32$, $33$, $37$, $38$, $42$, $43$ which cannot be expressed as the sum of distinct pentagonal numbers.
:The $31$st (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $27$, $30$, $31$, $32$, $35$, $36$, $37$, $38$, $42$, $43$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
:The length of the shortest edge of the smallest cuboid whose edges and the diagonals of whose faces are all integers:
::The lengths of the edges are $44, 117, 240$
::The lengths of the diagonals of the faces are $125, 244, 267$.
:The largest integer $n$ such that the set of integers from $1$ to $n$ can be partitioned into $4$ subsets such that no integer in any of these subsets is the sum of $2$ other integers in the same subset:
::$\set {1, 3, 5, 15, 17, 19, 26, 28, 40, 42, 44}$
::$\set {2, 7, 8, 18, 21, 24, 27, 33, 37, 38, 43}$
::$\set {4, 6, 13, 20, 22, 23, 25, 30, 32, 39, 41}$
::$\set {9, 10, 11, 12, 14, 16, 29, 31, 34, 35, 36}$
== Also see ==
* Cuboid with Integer Edges and Face Diagonals
* Largest n such that 1 to n can be Partitioned for no Element to be Sum of 2 Elements in Same Set
* 
* 
* 
* 
* 
* 
* 
== Sources ==
* : $44$
* : $44$
Category:Specific Numbers
Category:44
44,488

== Number ==
$44 \, 488$ (forty-four thousand, four hundred and eighty-eight) is:
:$2^3 \times 67 \times 83$
:The $1$st term of the smallest sequence of $5$ consecutive integers which are all happy numbers:
== Also see ==
* 
== Sources ==
* : $44,488$
Category:Specific Numbers
Category:44,488
44,497

== Number ==
$44 \, 497$ (forty-four thousand, four hundred and ninety-seven) is:
:The $4624$th prime number
:The index of the $27$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $\ldots$, $2203$, $2281$, $3217$, $4253$, $4423$, $9689$, $9941$, $11 \, 213$, $19 \, 937$, $21 \, 701$, $23 \, 209$:
::$M_{44 \, 497} = 2^{44 \, 497} - 1 \approx 8 \cdotp 545 \times 10^{13 \, 394}$
== Also see ==
* 
* 
== Historical Note ==
== Sources ==
* : $2^{44497} - 1$
* : $2^{44,497} - 1$
Category:Specific Numbers
Category:44,497
44,497/Historical Note

== Historical Note on $44 \, 497$ ==
The Mersenne number $M_{44 \, 497} = 2^{44 \, 497} - 1$ was demonstrated to be a Mersenne prime on $8$ April $1979$ by and , using a CRAY-1 supercomputer.
== Sources ==
* : $2^{44497} - 1$
* : $2^{44,497} - 1$
Category:Historical Notes
44,899

== Number ==
$44 \, 899$ (forty-four thousand, eight hundred and ninety-nine) is:
:$59 \times 761$
:The $3$rd self-locating number in $\pi$ after $1$, $16 \, 470$
== Also see ==
* 
== Sources ==
* : Cool Numbers: Self-location and $\pi$
Category:44,899
Category:Specific Numbers
44,944

== Number ==
$44 \, 944$ (forty-four thousand, nine hundred and forty-four) is:
:$2^4 \times 53^2$
:The palindromic square of a palindromic number each using only $2$ distinct digits
::$44 \, 944 = 212 \times 212$
:The $2$nd after $484$ of the only $3$ square numbers which start and end with $n$ $4$s.
:The $20$th square after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $121$, $144$, $225$, $441$, $484$, $676$, $1444$, $7744$, $11 \, 881$, $29 \, 929$ which has no more than $2$ distinct digits and does not end in $0$:
::$44 \, 944 = 212^2$
:The $212$th square number:
::$44 \, 944 = 212 \times 212$
== Also see ==
* Square of Small-Digit Palindromic Number is Palindromic
* 
* 
* 
== Sources ==
* : $44,944$
Category:Specific Numbers
Category:44,944
441

== Number ==
$441$ (four hundred and forty-one) is:
:$3^2 \times 7^2$
:The sum of the first $6$ cubes:
::$441 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3$
:The $13$th square after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $121$, $144$, $225$ which has no more than $2$ distinct digits and does not end in $0$:
::$441 = 21^2$
:The $21$st square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $225$, $256$, $289$, $324$, $361$, $400$:
::$441 = 21 \times 21$
:The $36$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $289$, $324$, $343$, $361$, $392$, $400$, $432$:
::$441 = 3^2 \times 7^2$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:441
4416

== Number ==
$4416$ (four thousand, four hundred and sixteen) is:
:$2^6 \times 3 \times 23$
:The $14$th and last positive integer after $504$, $756$, $806$, $1008$, $1148$, $1209$, $1472$, $1512$, $2016$, $2208$, $2418$, $2924$, $3024$ 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:
::$4416 = 46 \times 96 = 69 \times 64$
== Also see ==
* 
Category:Specific Numbers
Category:4416
442

== Number ==
$442$ (four hundred and forty-two) is:
:$2 \times 13 \times 17$
:The $17$th second pentagonal number after $2$, $7$, $15$, $26$, $40$, $57$, $77$, $100$, $126$, $155$, $187$, $222$, $260$, $301$, $345$, $392$:
::$442 = \dfrac {17 \paren {3 \times 17 + 1} } 2$
:The $34$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $222$, $247$, $260$, $287$, $301$, $330$, $345$, $376$, $392$, $425$:
::$442 = \dfrac {17 \paren {3 \times 17 + 1} } 2$
== Also see ==
* 
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Category:Specific Numbers
Category:442
4421

== Number ==
$4421$ (four thousand, four hundred and twenty-one) is:
:The $601$st prime number
:The $5$th prime number after $5$, $19$, $101$, $619$ of the form $\ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$:
::$4421 = 7! - 6! + 5! - 4! + 3! - 2! + 1!$
== Also see ==
* 
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Category:Specific Numbers
Category:4421
4423

== Number ==
$4423$ (four thousand, four hundred and twenty-three) is:
:The $602$nd prime number
:The index of the $20$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $17$, $19$, $31$, $61$, $89$, $107$, $127$, $521$, $607$, $1279$, $2203$, $2281$, $3217$, $4253$:
::$M_{4423} = 2^{4423} - 1 \approx 2 \cdotp 855 \times 10^{1331}$
== Historical Note ==
== Also see ==
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Category:Specific Numbers
Category:4423
4423/Historical Note

== Historical Note on $4423$ ==
The Mersenne number $M_{4423} = 2^{4423} - 1$ was demonstrated to be a Mersenne prime by on $3$ November $1961$, using an IBM 7090, along with $M_{4253}$, whose primality was similarly demonstrated in the same computer run.
These were the first titanic primes ever discovered.
It is a moot question which one was actually discovered first.
Category:Historical Notes
443

== Number ==
$443$ (four hundred and forty-three) is:
:The $86$th prime number
:The $22$nd near-repdigit prime after $101$, $113$, $131$, $151$, $181$, $191$, $199$, $211$, $223$, $227$, $229$, $233$, $277$, $311$, $313$, $331$, $337$, $353$, $373$, $383$, $433$
:The $24$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$, $83$, $89$, $113$, $131$, $173$, $179$, $191$, $233$, $239$, $251$, $281$, $293$, $359$, $419$, $431$:
::$2 \times 443 + 1 = 887$, which is prime.
:The $32$nd left-truncatable prime after $2$, $3$, $5$, $7$, $\ldots$, $197$, $223$, $283$, $313$, $317$, $337$, $347$, $353$, $367$, $373$, $383$, $397$
== Also see ==
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Category:Specific Numbers
Category:443
443,372,888,629,441

== Number ==
$443 \, 372 \, 888 \, 629 \, 441$ is:
:$17 \times 31 \times 41 \times 43 \times 89 \times 97 \times 167 \times 331$
:The smallest strong Fibonacci pseudoprime of type I
== Also see ==
* Smallest Strong Fibonacci Pseudoprime of Type I
== Sources ==
* : $443,372,888,629,441$
Category:Specific Numbers
Category:443,372,888,629,441
444,171,597,444

== Number ==
$444 \, 171 \, 597 \, 444$ is:
:$2^2 \times 3^2 \times 277^2 \times 401^2$
:The $666 \, 462$nd square number:
::$444 \, 171 \, 597 \, 444 = 666 \, 462 \times 666 \, 462$
:The $3$rd after $484$, $44 \, 944$ of the only $3$ square numbers which start and end with $n$ $4$s.
== Also see ==
* 
* 
== Sources ==
* : $444,171,597,444$
Category:Specific Numbers
Category:444,171,597,444
4447

== Number ==
$4447$ (four thousand, four hundred and forty-seven) is:
:The $604$th prime number
:The $39$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $\ldots$, $2791$, $2977$, $3169$, $3367$, $3571$, $3781$, $3997$, $4219$:
::$4447 = \ds 1 + \sum_{k \mathop = 1}^{39 - 1} 6 k = 39^3 - 38^3$
== Also see ==
* 
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Category:Specific Numbers
Category:4447
4465

== Number ==
$4465$ (four thousand, four hundred and sixty-five) is:
:$5 \times 19 \times 47$
:The $94$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $3655$, $3741$, $3828$, $3916$, $4005$, $4095$, $4186$, $4278$, $4371$:
::$4465 = \ds \sum_{k \mathop = 1}^{94} k = \dfrac {94 \times \paren {94 + 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:4465
448

== Number ==
$448$ (four hundred and forty-eight) is:
:$2^6 \times 7$
:The $8$th positive integer after $128$, $192$, $256$, $288$, $320$, $384$, $432$ with $7$ or more prime factors:
::$448 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7$
:The $21$st positive integer after $64$, $96$, $128$, $144$, $\ldots$, $320$, $324$, $336$, $352$, $360$, $384$, $400$, $416$, $432$ with $6$ or more prime factors:
::$448 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \paren {\times \, 7}$
:The $35$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $324$, $326$, $336$, $342$, $372$, $406$, $408$, $426$, $430$
== Also see ==
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Category:Specific Numbers
Category:448
4485

== Number ==
$4485$ (four thousand, four hundred and eighty-five) is:
:$3 \times 5 \times 13 \times 23$
:The $39$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $3008$, $3201$, $3400$, $3605$, $3816$, $4033$, $4256$:
::$4485 = \ds \sum_{k \mathop = 1}^{39} \paren {6 k - 5} = 39 \paren {3 \times 39 - 2}$
== Also see ==
* 
Category:Specific Numbers
Category:4485
4489

== Number ==
$4489$ (four thousand, four hundred and eighty-nine) is:
:$67^2$
:The $67$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $3249$, $3364$, $3481$, $3600$, $3721$, $3844$, $3969$, $4096$, $4225$, $4356$:
::$4489 = 67 \times 67$
== Also see ==
* 
Category:Specific Numbers
Category:4489