nyuuzyou/wikis huggingface dataset:
1431

== Number ==
$1431$ (one thousand, four hundred and thirty-one) is:
:$3^3 \times 53$
:The $27$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$, $1035$, $1225$, $1326$:
::$1431 = \ds \sum_{k \mathop = 1}^{27} \paren {4 k - 3} = 27 \paren {2 \times 27 - 1}$
:The $53$rd triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $990$, $1035$, $1081$, $1128$, $1176$, $1225$, $1275$, $1326$, $1378$:
::$1431 = \ds \sum_{k \mathop = 1}^{53} k = \dfrac {53 \times \paren {53 + 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:1431
1439

== Number ==
$1439$ (one thousand, four hundred and thirty-nine) is:
:The $228$th prime number.
:The smaller of the $20$th pair of primes whose prime gap is $8$:
::$1447 - 1439 = 8$
:The $32$nd safe prime after $5$, $7$, $11$, $23$, $47$, $\ldots$, $839$, $863$, $887$, $983$, $1019$, $1187$, $1283$, $1307$, $1319$, $1367$:
::$1439 = 2 \times 719 + 1$
:The $47$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $1031$, $1049$, $1103$, $1223$, $1229$, $1289$, $1409$:
::$2 \times 1439 + 1 = 2879$, which is prime.
:The $5$th term after $89$, $179$, $359$, $719$ of the smallest Cunningham chain of the first kind of length $6$:
::$\tuple {89, 179, 359, 719, 1439, 2879}$
== Also see ==
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:1439
144

== Number ==
$144$ (one hundred and forty-four) is:
:$2^4 \times 3^2$
:The $2$nd power of $12$ after $(1)$, $12$:
::$144 = 12^2$
:The $3$rd and last Square Fibonacci Number after $0$ and $1$
::$144 = F_{12} = 55 + 89 = 12^2$
:The $3$rd and last Fibonacci number after $0$, $1$ which equals the square of its index
::$144 = F_{12} = 12^2 = 55 + 89$
:The $4$th positive integer after $64$, $96$, $128$ with $6$ or more prime factors:
::$144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3$
:The $5$th square number after $1$, $4$, $36$, $121$ to be the divisor sum value of some (strictly) positive integer:
::$144 = \map {\sigma_1} {66} = \map {\sigma_1} {70} = \map {\sigma_1} {94} = \map {\sigma_1} {115} = \map {\sigma_1} {119}$
:The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $6$ different ways
:The $11$th square after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $121$ which has no more than $2$ distinct digits and does not end in $0$:
::$144 = 12^2$
:The smallest positive integer which can be expressed as the sum of $2$ odd primes in $11$ ways.
:The $12$th Fibonacci number, after $1$, $1$, $2$, $3$, $5$, $8$, $13$, $21$, $34$, $55$, $89$:
::$144 = 55 + 89$
:The $12$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $100$, $121$:
::$144 = 12 \times 12 = \paren {2^2 \times 3}^2$
:Hence in duodecimal notation:
::$100$
:The $20$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $27$, $32$, $36$, $49$, $64$, $72$, $81$, $100$, $108$, $121$, $125$, $128$
:The $21$st Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $15$, $24$, $36$, $111$, $112$, $115$, $128$, $132$, $135$:
::$144 = 9 \times 16 = 9 \times \paren {1 \times 4 \times 4}$
:The $24$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$, $16$, $18$, $20$, $24$, $30$, $36$, $42$, $48$, $60$, $72$, $84$, $90$, $96$, $108$, $120$:
::$\map {\sigma_1} {144} = 403$
== Also see ==
* Square Fibonacci Number
* Fibonacci Numbers which equal the Square of their Index
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
== Historical Note ==
== Sources ==
* : $144$
* : $144$
Category:Specific Numbers
Category:144
144,648

== Number ==
$144 \, 648$ is:
:$2^3 \times 3^2 \times 7^2 \times 41$
:An EPORN which is not a multiple of $10$:
::$144,648 = 861 \times 168 = 492 \times 294 = \paren {3 \times 7 \times 41} \times \paren {2^3 \times 3 \times 7} = \paren {2^3 \times 3 \times 41} \times \paren {2 \times 3 \times 7^2}$
== Also see ==
* EPORN/Examples/144,648
== Sources ==
* : $63,504$
Category:Specific Numbers
Category:144,648
1444

== Number ==
$1444$ (one thousand four hundred and forty-four) is:
:$2^2 \times 19^2$
:The $5$th square after $49$, $169$, $361$, $1225$ whose decimal representation can be split into two parts which are each themselves square:
::$1444 = 38^2$; $144 = 12^2$, $4 = 2^2$
:The $16$th square after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $121$, $144$, $225$, $441$, $484$, $676$ which has no more than $2$ distinct digits and does not end in $0$:
::$1444 = 38^2$
:The $34$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $706$, $730$, $771$, $784$, $841$, $1024$, $1089$, $1225$, $1255$, $1351$, $1414$, $1444$, $\ldots$
:The $38$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $625$, $676$, $729$, $784$, $841$, $900$, $961$, $1024$, $1089$, $1156$, $1225$, $1296$, $1369$:
::$1444 = 38 \times 38$
== Also see ==
* Squares Ending in Repeated Digits
* Integers whose Squares end in 444
* 
* 
* 
* 
== Sources ==
* : $1444$
* : $1444$
Category:Specific Numbers
Category:1444
145

== Number ==
$145$ (one hundred and forty-five) is:
:$5 \times 29$
:The $1$st term of the $3$rd $5$-tuple of consecutive integers have the property that they are not values of the divisor sum function $\map {\sigma_1} n$ for any $n$:
::$\tuple {145, 146, 147, 148, 149}$
:The $3$rd factorion base $10$ after $1$, $2$:
::$145 = 1! + 4! + 5!$
:The $6$th positive integer after $50$, $65$, $85$, $125$, $130$ which can be expressed as the sum of two square numbers in two or more different ways:
::$145 = 12^2 + 1^2 = 9^2 + 8^2$
:The $10$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $51$, $70$, $92$, $117$:
::$145 = 1 + 4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 = \dfrac {10 \paren {3 \times 10 - 1} } 2$
:The $14$th positive integer $n$ after $0$, $1$, $5$, $25$, $29$, $41$, $49$, $61$, $65$, $85$, $89$, $101$, $125$ such that the Fibonacci number $F_n$ ends in $n$
:The $19$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$, $57$, $70$, $77$, $92$, $100$, $117$, $126$:
::$145 = \dfrac {10 \paren {3 \times 10 - 1} } 2$
== Also see ==
* 
* 
* 
* 
* 
* 
== Sources ==
* : $145$
* : $145$
Category:Specific Numbers
Category:145
1451

== Number ==
$1451$ (one thousand, four hundred and fifty-one) is:
:The $230$th prime number.
:The smaller of the $48$th pair of twin primes:
::$1453 - 1451 = 2$
:The $48$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $1031$, $1049$, $1103$, $1223$, $1229$, $1289$, $1409$, $1439$:
::$2 \times 1451 + 1 = 2903$, which is prime.
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:1451
1457

== Number ==
$1457$ (one thousand, four hundred and fifty-seven) is:
:$31 \times 47$
:The $31$st second pentagonal number after $2$, $7$, $15$, $26$, $\ldots$, $610$, $672$, $737$, $805$, $876$, $950$, $1027$, $1107$, $1190$, $1276$, $1365$:
::$1457 = \dfrac {31 \paren {3 \times 31 + 1} } 2$
:The $62$nd generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $925$, $950$, $1001$, $1027$, $1080$, $1107$, $1162$, $1190$, $1247$, $1276$, $1335$, $1365$, $1426$:
::$1457 = \dfrac {31 \paren {3 \times 31 + 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:1457
1458

== Number ==
$1458$ (one thousand, four hundred and fifty-eight) is:
:$2 \times 3^6$
:A harshad number:
::$1458 = 81 \times 18 = 81 \times \paren {1 + 4 + 5 + 8}$
:The $3$rd, after $1$, $81$, of the $4$ harshad numbers which can each be expressed as the product of the sum of its digits and the reversal of the sum of its digits:
::$1458 = 81 \times 18 = 81 \times \paren {1 + 4 + 5 + 8}$
== Also see ==
* 
Category:Specific Numbers
Category:1458
1459

== Number ==
$1459$ (one thousand, four hundred and fifty-nine) is:
:The $232$nd prime number
:The $7$th after $199$, $409$, $619$, $829$, $1039$, $1249$ of the smallest $10$ primes in arithmetic sequence:
::$1459 = 6 \times 210 + 199$
== Also see ==
* 
* 
Category:Specific Numbers
Category:1459
146

== Number ==
$146$ (one hundred and forty-six) is:
:$2 \times 73$
:The $2$nd term of the $3$rd $5$-tuple of consecutive integers have the property that they are not values of the divisor sum function $\map {\sigma_1} n$ for any $n$:
::$\tuple {145, 146, 147, 148, 149}$
:The $7$th of the $17$ positive integers for which the value of the Euler $\phi$ function is $72$:
::$73$, $91$, $95$, $111$, $117$, $135$, $146$, $148$, $152$, $182$, $190$, $216$, $222$, $228$, $234$, $252$, $270$
:The $8$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$.
:The $13$th noncototient after $10$, $26$, $34$, $50$, $52$, $58$, $86$, $100$, $116$, $122$, $130$, $134$:
::$\nexists m \in \Z_{>0}: m - \map \phi m = 146$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $19$th nontotient after $14$, $26$, $34$, $38$, $50$, $62$, $68$, $74$, $76$, $86$, $90$, $94$, $98$, $114$, $118$, $122$, $124$, $134$, $142$:
::$\nexists m \in \Z_{>0}: \map \phi m = 146$
:where $\map \phi m$ denotes the Euler $\phi$ function
== Also see ==
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:146
146,361,946,186,458,562,560,000

== Number ==
$146 \, 361 \, 946 \, 186 \, 458 \, 562 \, 560 \, 000$ is:
:$2^{18} \times 3 \times 5^4 \times 7 \times 11 \times 13 \times 19 \times 37 \times 79 \times 109 \times 157 \times 313$
:The $5$th and largest known unitary perfect number after $6$, $60$, $90$, $87 \, 360$:
== Also see ==
* 
== Sources ==
* : $87,360$
Category:Specific Numbers
Category:146,361,946,186,458,562,560,000
146,511,208

== Number ==
$146 \, 511 \, 208$ is:
:$2^3 \times 31 \times 590 \, 771$
:The $28$th pluperfect digital invariant after $1$, $2$, $3$, $4$, $5$, $6$, $\ldots$, $9 \, 926 \, 315$, $24 \, 678 \, 050$, $24 \, 678 \, 051$, $88 \, 593 \, 477$:
== Also see ==
* 
Category:Specific Numbers
Category:146,511,208
147

== Number ==
$147$ (one hundred and forty-seven) is:
:$3 \times 7^2$
:The $3$rd term of the $3$rd $5$-tuple of consecutive integers have the property that they are not values of the divisor sum function $\map {\sigma_1} n$ for any $n$:
::$\tuple {145, 146, 147, 148, 149}$
:The number of different representations of $1$ as the sum of $5$ unit fractions.
:The $1$st of the $5$th pair of consecutive integers which both have $6$ divisors:
::$\map {\sigma_0} {147} = \map {\sigma_0} {148} = 6$
:The $28$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.
:The $60$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $95$, $96$, $100$, $101$, $102$, $107$, $112$, $116$, $124$, $136$, $137$, $141$, $142$ which cannot be expressed as the sum of distinct pentagonal numbers.
:$42 \times 147 = 6174$ which is Kaprekar's Constant
== Also see ==
* 
* 
* 
* 
* 
== Historical Note ==
== Sources ==
* : $147$
Category:Specific Numbers
Category:147
147,573,952,589,676,412,927

== Number ==
$147 \, 573 \, 952 \, 589 \, 676 \, 412 \, 927$ is:
:$193 \, 707 \, 721 \times 761 \, 838 \, 257 \, 287$
:The $67$th Mersenne number:
::$147 \, 573 \, 952 \, 589 \, 676 \, 412 \, 927 = 2^{67} - 1$
:Mistakenly reported as prime in $1644$ by .
:Proven composite by in $1903$.
== Also see ==
* Factors of Mersenne Number M67
== Sources ==
* : $2^{67} - 1$
* : $2^{67} - 1$
Category:Specific Numbers
Category:147,573,952,589,676,412,927
147,852

== Number ==
$147 \, 852$ (one hundred and forty-seven thousand, eight hundred and fifty-two) is:
:$2^2 \times 3^3 \times 37^2$
:Equal to $333 \times 444$, and an anagram of $142 \, 857$
:The digits $147852$ in various orders that are not cyclic permutations of the period of $1/7$ occur in several other products also.''
== Sources ==
* : $147,852$
* : $147,852$
Category:Specific Numbers
Category:147,852
147,852/Mistake

== Source Work ==
:
:The Dictionary
::$147,852$
:
:The Dictionary
::$147,852$
== Mistake ==
:The digits $147852$ in various orders that are not permutations of the period of $1/7$ occur in several other products also.
== Correction ==
Technically, $147852$ is a permutation of the period of $1/7$ -- just not a cyclic permutation of it.
So this should read:
:The digits $147852$ in various orders that are not cyclic permutations of the period of $1/7$ occur in several other products also.
== Sources ==
* : $147,852$
* : $147,852$
Category:Mistakes/Curious and Interesting Numbers
147,855

== Number ==
$147 \, 855$ (one hundred and forty-seven thousand, eight hundred and fifty-five) is:
:$3 \times 5 \times 9857$
:The $26$th integer $m$ such that $m! - 1$ (its factorial minus $1$) is prime:
::$3$, $4$, $6$, $7$, $12$, $14$, $30$, $32$, $33$, $38$, $94$, $166$, $324$, $379$, $469$, $546$, $974$, $1963$, $3507$, $3610$, $6917$, $21 \, 480$, $34 \, 790$, $94 \, 550$, $103 \, 040$, $147 \, 855$
== Also see ==
* 
Category:Specific Numbers
Category:147,855
1470

== Number ==
$1470$ (one thousand, four hundred and seventy) is:
:$2 \times 3 \times 5 \times 7^2$
:The $14$th pentagonal pyramidal number after $1$, $6$, $12$, $40$, $75$, $126$, $196$, $288$, $405$, $550$, $726$, $936$, $1183$:
::$1470 = \ds \sum_{k \mathop = 1}^{14} \dfrac {k \paren {3 k - 1} } 2 = \dfrac {14^2 \paren {14 + 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:1470
1472

== Number ==
$1472$ (one thousand, four hundred and seventy-two) is:
:$2^6 \times 23$
:The $7$th positive integer after $504$, $756$, $806$, $1008$, $1148$, $1209$ 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:
::$1472 = 23 \times 64 = 46 \times 32$
== Also see ==
* 
Category:Specific Numbers
Category:1472
1477

== Number ==
$1477$ (one thousand, four hundred and seventy-seven) is:
:$7 \times 211$
:The $18$th integer $m$ such that $m! + 1$ (its factorial plus $1$) is prime:
::$0$, $1$, $2$, $3$, $11$, $27$, $37$, $41$, $73$, $77$, $116$, $154$, $320$, $340$, $399$, $427$, $872$, $1477$
== Also see ==
* 
== Sources ==
* : $1477$
* : $1477! + 1$
Category:Specific Numbers
Category:1477
1477/Mistake

== Source Work ==
:
:The Dictionary
::$1477$
== Mistake ==
:$1477! + 1$ is prime. $n! + 1$ is also prime for $1$, $2$, $3$, $11$, $27$, $37$, $41$, $73$, $77$, $116$, $154$, $320$, $340$, $399$, $427$, $872$, $1477 \ldots$
$0! + 1 = 1 + 1 = 2$ is mistakenly omitted here.
The same mistake is repeated on the page $1477! + 1$.
== Sources ==
* : $1477$
Category:Mistakes/Curious and Interesting Numbers
148

== Number ==
$148$ (one hundred and forty-eight) is:
:$2^2 \times 37$
:The $4$th term of the $3$rd $5$-tuple of consecutive integers have the property that they are not values of the divisor sum function $\map {\sigma_1} n$ for any $n$:
::$\tuple {145, 146, 147, 148, 149}$
:The $2$nd of the $5$th pair of consecutive integers which both have $6$ divisors:
::$\map {\sigma_0} {147} = \map {\sigma_0} {148} = 6$
:The $8$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$:
::$148 = 1 + 7 + 11 + 16 + 21 + 26 + 31 + 36 = \dfrac {8 \paren {5 \times 8 - 3} } 2$
:The $8$th of the $17$ positive integers for which the value of the Euler $\phi$ function is $72$:
::$73$, $91$, $95$, $111$, $117$, $135$, $146$, $148$, $152$, $182$, $190$, $216$, $222$, $228$, $234$, $252$, $270$
:The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $10$ different ways
== Also see ==
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:148
148,349

== Number ==
$148 \, 349$ (one hundred and forty-eight thousand, three hundred and forty-nine) is:
:$109 \times 1361$
:The only integer which is the sum of the subfactorials of its digits:
::$148 \, 349 = \mathop !1 + \mathop !4 + \mathop !8 + \mathop !3 \mathop + \mathop !4 \mathop + \mathop !9$
== Also see ==
* Number which is Sum of Subfactorials of Digits
== Sources ==
* : $148,349$
* : $148,349$
Category:Specific Numbers
Category:148,349
1481

== Number ==
$1481$ (one thousand, four hundred and eighty-one) is:
:The $234$th prime number.
:The larger of the $25$th pair of primes whose prime gap is $10$:
::$1481 - 1471 = 10$
:The smaller of the $49$th pair of twin primes:
::$1483 - 1481 = 2$
:The $49$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $1031$, $1049$, $1103$, $1223$, $1229$, $1289$, $1409$, $1439$, $1451$:
::$2 \times 1481 + 1 = 2963$, which is prime.
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:1481
1485

== Number ==
$1485$ (one thousand, four hundred and eighty-six) is:
:$3^3 \times 5 \times 11$
:The first of the $5$th pair of triangular numbers whose sum and difference are also both triangular:
::$1485 = T_{54}$, $4186 = T_{91}$, $1485 + 4186 = T_{106}$, $4186 - 1485 = T_{73}$
:The $9$th integer after $1$, $14$, $30$, $105$, $248$, $264$, $418$, $714$ whose divisor sum divided by its Euler $\phi$ value is a square:
::$\dfrac {\map {\sigma_1} {1485} } {\map \phi {1485} } = \dfrac {2880} {720} = 4 = 2^2$
:The $54$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $990$, $1035$, $1081$, $1128$, $1176$, $1225$, $1275$, $1326$, $1378$, $1431$:
::$1485 = \ds \sum_{k \mathop = 1}^{54} k = \dfrac {54 \times \paren {54 + 1} } 2$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:1485
1487

== Number ==
$1487$ (one thousand four hundred and eighty-seven) is:
:The $236$th prime number
:The $28$th of $29$ primes of the form $2 x^2 + 29$:
::$2 \times 27^2 + 29 = 1487$ ()
:The $33$rd safe prime after $5$, $7$, $11$, $23$, $47$, $\ldots$, $839$, $863$, $887$, $983$, $1019$, $1187$, $1283$, $1307$, $1319$, $1367$, $1439$:
::$1487 = 2 \times 743 + 1$
:The smaller of the $50$th pair of twin primes:
::$1489 - 1487 = 2$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:1487
149

== Number ==
$149$ (one hundred and forty-nine) is:
:The $35$th prime number
:The larger of the $1$st pair of primes whose prime gap is $10$:
::$149 - 139 = 10$
:The $3$rd obstinate number after $1$, $127$
:The $5$th term of the $3$rd $5$-tuple of consecutive integers have the property that they are not values of the divisor sum function $\map {\sigma_1} n$ for any $n$:
::$\tuple {145, 146, 147, 148, 149}$
:The $6$th prime number after $53$, $71$, $103$, $107$, $109$ which cannot be expressed as either the sum of or the difference between a power of $2$ and a power of $3$.
:The $11$th emirp after $13$, $17$, $31$, $37$, $71$, $73$, $79$, $97$, $107$, $113$
:The smaller of the $12$th pair of twin primes, with $151$
:The $13$th long period prime after $7$, $17$, $19$, $23$, $29$, $47$, $59$, $61$, $97$, $109$, $113$, $131$
:The $15$th positive integer $n$ after $0$, $1$, $5$, $25$, $29$, $41$, $49$, $61$, $65$, $85$, $89$, $101$, $125$, $145$ such that the Fibonacci number $F_n$ ends in $n$
== Also see ==
* 
* 
* 
* 
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:149
1493

== Number ==
$1493$ (one thousand, four hundred and ninety-three) is:
:The $238$th prime number
:The $8$th Stern number after $1$, $3$, $17$, $137$, $227$, $977$, $1187$
:The $8$th (and highest known) Stern prime after $1$, $3$, $17$, $137$, $227$, $977$, $1187$
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:1493
1496

== Number ==
$1496$ (one thousand, four hundred and ninety-six) is:
:$2^3 \times 11 \times 17$
:The $16$th square pyramidal number after $1$, $5$, $14$, $30$, $55$, $91$, $140$, $204$, $285$, $385$, $506$, $650$, $819$, $1015$, $1240$:
::$1496 = \ds \sum_{k \mathop = 1}^{16} k^2 = \dfrac {16 \paren {16 + 1} \paren {2 \times 16 + 1} } 6$
== Also see ==
* 
Category:Specific Numbers
Category:1496
1499

== Number ==
$1499$ (one thousand, four hundred and ninety-nine) is:
:The $239$th prime number.
:The $50$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $1031$, $1049$, $1103$, $1223$, $1229$, $1289$, $1409$, $1439$, $1451$, $1481$:
::$2 \times 1499 + 1 = 2999$, which is prime.
== Also see ==
* 
* 
Category:Specific Numbers
Category:1499
15,051

== Number ==
$15 \, 051$ (fifteen thousand and fifty-one) is:
:$3 \times 29 \times 173$
:The $13$th palindromic triangular number after $0$, $1$, $3$, $6$, $55$, $66$, $171$, $595$, $666$, $3003$, $5995$, $8778$
:The $173$rd triangular number:
::$15 \, 051 = \ds \sum_{k \mathop = 1}^{173} k = \dfrac {173 \times \paren {173 + 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:15,051
15,251

== Number ==
$15 \, 251$ (fifteen thousand, two hundred and fifty-one) is:
:$101 \times 151$
:The $6$th pentagonal number after $1$, $5$, $22$, $1001$, $2882$ which is also palindromic:
::$15 \, 251 = \ds \sum_{k \mathop = 1}^{101} \paren {3 k - 2} = \dfrac {101 \paren {3 \times 101 - 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:15,251
15,351

== Number ==
$15 \, 351$ (fifteen thousand, three hundred and fifty-one) is:
:$3 \times 7 \times 17 \times 43$
:The $13$th integer after $0$, $1$, $3$, $5$, $7$, $9$, $33$, $99$, $313$, $585$, $717$, $7447$ which is palindromic in both decimal and binary:
::$15 \, 351_{10} = 11 \, 101 \, 111 \, 110 \, 111_2$
== Also see ==
* 
Category:Specific Numbers
Category:15,351
15,472

== Number ==
$15 \, 472$ (fifteen thousand, four hundred and seventy-two) is:
:$2^4 \times 967$
:The $3$rd term of a sociable chain of order $5$ whose smallest term is $12 \, 496$:
::$12 \, 496 \to 14 \, 288 \to 15 \, 472 \to 14 \, 536 \to 14 \, 264 \to 12 \, 496$
== Also see ==
* 
Category:Specific Numbers
Category:15,472
15,527,402,881

== Number ==
$15 \, 527 \, 402 \, 881$ is:
:$353^4$
:The $353$rd fourth power:
::$15 \, 527 \, 402 \, 881 = 353^4$
:The smallest fourth power which can be expressed as the sum of $4$ fourth powers:
::$15 \, 527 \, 402 \, 881 = 353^4 = 30^4 + 120^4 + 272^4 + 315^4$
== Also see ==
* Smallest Fourth Power expressible as Sum of 4 Fourth Powers
* 
== Sources ==
* : $15,527,402,881$
* : $15,527,402,881$
Category:Specific Numbers
Category:15,527,402,881
15,625

== Number ==
$15 \, 625$ (fifteen thousand, six hundred and twenty-five) is:
:$5^6$
:The $5$th $6$th power after $1$, $64$, $729$, $4096$:
::$15 \, 625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5$
:The $6$th power of $5$ after $(1)$, $5$, $25$, $125$, $625$, $3125$:
::$15 \, 625 = 5^6$
:The $10$th square after $49$, $169$, $361$, $1225$, $1444$, $1681$, $3249$, $4225$, $4900$ whose decimal representation can be split into two parts which are each themselves square:
::$15 \, 625 = 125^2$; $1 = 1^2$, $5625 = 75^2$
:The $25$th cube number:
::$15 \, 625 = 25 \times 25 \times 25$
:The $125$th square number:
::$15 \, 625 = 125 \times 125$
== Also see ==
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:15,625
15,760,091

== Number ==
$15 \, 760 \, 091$ is:
:The $1 \, 016 \, 626$th prime number
:The $1$st of a sequence of $8$ prime numbers which have the same prime gaps as the $8$ primes starting at $11$
== Also see ==
* 
* 
== Sources ==
* : $15,760,091$
Category:Specific Numbers
Category:15,760,091
15,760,093

== Number ==
$15 \, 760 \, 093$ is:
:The $1 \, 016 \, 627$th prime number
:The $2$nd of a sequence of $8$ prime numbers which have the same prime gaps as the $8$ primes starting at $11$
== Also see ==
* 
* 
Category:Specific Numbers
Category:15,760,093
15,760,097

== Number ==
$15 \, 760 \, 097$ is:
:The $1 \, 016 \, 628$th prime number
:The $3$rd of a sequence of $8$ prime numbers which have the same prime gaps as the $8$ primes starting at $11$
== Also see ==
* 
* 
Category:Specific Numbers
Category:15,760,097
15,760,099

== Number ==
$15 \, 760 \, 099$ is:
:The $1 \, 016 \, 629$th prime number
:The $4$th of a sequence of $8$ prime numbers which have the same prime gaps as the $8$ primes starting at $11$
== Also see ==
* 
* 
Category:Specific Numbers
Category:15,760,099
15,760,103

== Number ==
$15 \, 760 \, 103$ is:
:The $1 \, 016 \, 630$th prime number
:The $5$th of a sequence of $8$ prime numbers which have the same prime gaps as the $8$ primes starting at $11$
== Also see ==
* 
* 
Category:Specific Numbers
Category:15,760,103
15,760,109

== Number ==
$15 \, 760 \, 109$ is:
:The $1 \, 016 \, 631$st prime number
:The $6$th of a sequence of $8$ prime numbers which have the same prime gaps as the $8$ primes starting at $11$
== Also see ==
* 
* 
Category:Specific Numbers
Category:15,760,109