nyuuzyou/wikis huggingface dataset:
182

== Number ==
$182$ (one hundred and eighty-two) is:
:$2 \times 7 \times 13$
:The $10$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 $16$th sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$, $114$, $130$, $138$, $154$, $165$, $170$, $174$:
::$182 = 2 \times 7 \times 13$
:The $25$th nontotient:
::$\nexists m \in \Z_{>0}: \map \phi m = 172$
:where $\map \phi m$ denotes the Euler $\phi$ function
== Also see ==
* 
* 
* 
Category:Specific Numbers
Category:182
1820

== Number ==
$1820$ (one thousand, eight hundred and twenty) is:
:$2^2 \times 5 \times 7 \times 13$
:The $13$th pentatope number after $1$, $5$, $15$, $35$, $70$, $126$, $210$, $330$, $495$, $715$, $1001$, $1365$:
::$1820 = \ds \sum_{k \mathop = 1}^{13} \dfrac {k \paren {k + 1} \paren {k + 2} } 6 = \dfrac {13 \paren {13 + 1} \paren {13 + 2} \paren {13 + 3} } {24}$
:The $35$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $925$, $1001$, $1080$, $1162$, $1247$, $1335$, $1426$, $1520$, $1617$, $1717$:
::$1820 = \ds \sum_{k \mathop = 1}^{35} \paren {3 k - 2} = \dfrac {35 \paren {3 \times 35 - 1} } 2$
:The $69$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $1335$, $1365$, $1426$, $1457$, $1520$, $1552$, $1617$, $1650$, $1717$, $1751$:
::$1820 = \ds \sum_{k \mathop = 1}^{35} \paren {3 k - 2} = \dfrac {35 \paren {3 \times 35 - 1} } 2$
== Also see ==
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Category:Specific Numbers
Category:1820
1825

== Number ==
$1825$ (one thousand, eight hundred and twenty-five) is:
:$5^2 \times 73$
:The $25$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $645$, $736$, $833$, $936$, $1045$, $1160$, $1281$, $1408$, $1541$, $1680$:
::$1825 = \ds \sum_{k \mathop = 1}^{25} \paren {6 k - 5} = 25 \paren {3 \times 25 - 2}$
== Also see ==
* 
Category:Specific Numbers
Category:1825
183,184

== Number ==
$183 \, 184$ (one hundred and eighty-three thousand, one hundred and eighty-four) is:
:$2^4 \times 107^2$
:The $428$th square number:
::$183 \, 184 = 428 \times 428$
:The $2$nd square number after $8281$ whose digits form $2$ consecutive integers:
::$183 \, 184 = 428^2$
:The $1$st square number whose digits form $2$ consecutive increasing integers:
::$183 \, 184 = 428^2$
== Also see ==
* 
* 
* 
== Sources ==
* : $183,184$
* : $183,184$
Category:Specific Numbers
Category:183,184
1830

== Number ==
$1830$ (one thousand, eight hundred and thirty) is:
:$2 \times 3 \times 5 \times 61$
:The $60$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $1326$, $1378$, $1431$, $1485$, $1540$, $1596$, $1653$, $1711$, $1770$:
::$1830 = \ds \sum_{k \mathop = 1}^{60} k = \dfrac {60 \times \paren {60 + 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:1830
1849

== Number ==
$1849$ (one thousand eight hundred and forty-nine) is:
:$43^2$
:The $37$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $1024$, $1089$, $1225$, $1255$, $1351$, $1414$, $1444$, $1521$, $1681$, $1849$, $\ldots$
:The $43$rd square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $1296$, $1369$, $1444$, $1521$, $1600$, $1681$, $1764$:
::$1849 = 43 \times 43$
== Also see ==
* 
* 
Category:Specific Numbers
Category:1849
185

== Number ==
$185$ (one hundred and eighty-five) is:
:$5 \times 37$
:The $8$th positive integer after $50$, $65$, $85$, $125$, $130$, $145$, $170$ which can be expressed as the sum of two square numbers in two or more different ways:
::$185 = 13^2 + 4^2 = 11^2 + 8^2$
:The $36$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:185
185,136

== Number ==
$185 \, 136$ (one hundred and eighty-five thousand, one hundred and thirty-six) is:
:$2^4 \times 3 \times 7 \times 19 \times 29$
:The $608$th triangular number:
::$185 \, 136 = \ds \sum_{k \mathop = 1}^{608} k = \dfrac {608 \times \left({608 + 1}\right)} 2$
:The $5$th triangular number after $6$, $120$, $210$, $990$ which can be expressed as the product of $3$ consecutive integers:
::$185 \, 136 = T_{608} = 56 \times 57 \times 58$
== Also see ==
* 
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Category:Specific Numbers
Category:185,136
1854

== Number ==
$1854$ (one thousand, eight hundred and fifty-four) is:
:$2 \times 3^2 \times 103$
:The $7$th subfactorial after $0$, $1$, $2$, $9$, $44$, $265$:
::$1854 = \, !7 = 7! \paren {1 - \dfrac 1 {1!} + \dfrac 1 {2!} - \dfrac 1 {3!} + \dfrac 1 {4!} - \dfrac 1 {5!} + \dfrac 1 {6!} - \dfrac 1 {7!} }$
== Also see ==
* 
== Sources ==
* : $1854$
* : $1854$
Category:Specific Numbers
Category:1854
1855

== Number ==
$1855$ (one thousand, eight hundred and fifty-five) is:
:$3 \times 5 \times 53$
:The $35$th second pentagonal number after $2$, $7$, $15$, $26$, $\ldots$, $1107$, $1190$, $1276$, $1365$, $1457$, $1552$, $1650$, $1751$:
::$1855 = \dfrac {35 \paren {3 \times 35 + 1} } 2$
:The $70$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $1335$, $1365$, $1426$, $1457$, $1520$, $1552$, $1617$, $1650$, $1717$, $1751$, $1820$:
::$1855 = \dfrac {35 \paren {3 \times 35 + 1}} 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:1855
186

== Number ==
$186$ (one hundred and eighty-six) is:
:$2 \times 3 \times 31$
:The $17$th sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$, $114$, $130$, $138$, $154$, $165$, $170$, $174$, $182$:
::$186 = 2 \times 3 \times 31$
:The $17$th noncototient after $10$, $26$, $34$, $50$, $52$, $58$, $86$, $100$, $116$, $122$, $130$, $134$, $146$, $154$, $170$, $172$:
::$\nexists m \in \Z_{>0}: m - \map \phi m = 186$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $26$th nontotient:
::$\nexists m \in \Z_{>0}: \map \phi m = 182$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $37$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:186
186,378,732,807,587,076,747

== Number ==
$186 \, 378 \, 732 \, 807 \, 587 \, 076 \, 747$ is:
:$3 \times 2207 \times 39 \, 373 \times 714 \, 947 \, 677 \, 859$
:The $4$th of $5$ integers which have the property that the sum of any $3$ of them is square:
== Also see ==
* 
Category:Specific Numbers
Category:186,378,732,807,587,076,747
187

== Number ==
$187$ (one hundred and eighty-seven) is:
:$11 \times 17$
:The $1$st of the $3$-digit integers $m$ which need the largest number of reverse-and-add process iterations ($23$) before reaching a palindromic number:
::$187$, $968$, $1837$, $\ldots$, $8713200023178$
:The $7$th positive integer after $1$, $7$, $102$, $110$, $142$, $159$ the sum of whose divisors is a cube:
::$\map {\sigma_1} {187} = 216 = 6^3$
:The $11$th second pentagonal number after $2$, $7$, $15$, $26$, $40$, $57$, $77$, $100$, $126$, $155$:
::$187 = \dfrac {11 \paren {3 \times 11 + 1} } 2$
:The $22$nd generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$, $57$, $70$, $77$, $92$, $100$, $117$, $126$, $145$, $155$, $176$:
::$187 = \dfrac {11 \paren {3 \times 11 + 1} } 2$
== Also see ==
* 
* 
* 
* 
== Sources ==
* : $187$
* : $187$
Category:Specific Numbers
Category:187
1873

== Number ==
$1873$ (one thousand, eight hundred and seventy-three) is:
:The $287$th prime number
:The $10$th prime $p$ such that $p \# - 1$, where $p \#$ denotes primorial (product of all primes up to $p$) of $p$, is prime:
::$3$, $5$, $11$, $13$, $41$, $89$, $317$, $337$, $991$, $1873$
:The larger of the $57$th pair of twin primes:
::$1873 - 1871 = 2$
== Also see ==
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Category:Specific Numbers
Category:1873
1879

== Number ==
$1879$ (one thousand, eight hundred and seventy-nine) is:
:The $289$th prime number
:The $9$th after $199$, $409$, $619$, $829$, $1039$, $1249$, $1459$, $1669$ of the smallest $10$ primes in arithmetic sequence:
::$1879 = 8 \times 210 + 199$
:The larger of the $58$th pair of twin primes:
::$1879 - 1877 = 2$
== Also see ==
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* 
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Category:Specific Numbers
Category:1879
188

== Number ==
$188$ (one hundred and eighty-eight) is:
:$2^2 \times 47$
:The $10$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $146$, $162$.
:The $27$th nontotient:
::$\nexists m \in \Z_{>0}: \map \phi m = 188$
:where $\map \phi m$ denotes the Euler $\phi$ function
:The $29$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $91$, $94$, $97$, $100$, $103$, $109$, $129$, $130$, $133$, $139$, $167$, $176$:
::$188 \to 1^2 + 8^2 + 8^2 = 1 + 64 + 64 = 129 \to 1^2 + 2^2 + 9^2 = 1 + 4 + 81 = 86 \to 8^2 + 6^2 = 64 + 36 = 100 \to 1^2 + 0^2 + 0^2 = 1$
== Also see ==
* 
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== Sources ==
* : $188$
Category:Specific Numbers
Category:188
1880

== Number ==
$1880$ (one thousand, eight hundred and eighty) is:
:$2^3 \times 5 \times 47$
:The $1$st term of the smallest triple of consecutive integers all of which are happy:
::$1880$, $1881$, $1882$
== Also see ==
* 
== Sources ==
* : $1880$
Category:Specific Numbers
Category:1880
1881

== Number ==
$1881$ (one thousand, eight hundred and eighty-one) is:
:$3^2 \times 11 \times 19$
:The $2$nd term of the smallest triple of consecutive integers all of which are happy:
::$1880$, $1881$, $1882$
== Also see ==
* 
== Sources ==
* : $1880$
Category:Specific Numbers
Category:1881
1882

== Number ==
$1882$ (one thousand, eight hundred and eighty-two) is:
:$2 \times 941$
:The $2$nd term of the smallest triple of consecutive integers all of which are happy:
::$1880$, $1881$, $1882$
== Also see ==
* 
== Sources ==
* : $1880$
Category:Specific Numbers
Category:1882
1885

== Number ==
$1885$ (one thousand, eight hundred and eighty-five) is:
:$5 \times 13 \times 29$
:The $1$st term of the $2$nd triplet of consecutive positive integers all of which are sphenic:
::$1885 = 5 \times 13 \times 29$, $1886 = 2 \times 23 \times 41$, $1887 = 3 \times 17 \times 37$
== Also see ==
* 
Category:Specific Numbers
Category:1885
1886

== Number ==
$1886$ (one thousand, eight hundred and eighty-six) is:
:$2 \times 23 \times 41$
:The $2$nd term of the $2$nd triplet of consecutive positive integers all of which are sphenic:
::$1885 = 5 \times 13 \times 29$, $1886 = 2 \times 23 \times 41$, $1887 = 3 \times 17 \times 37$
== Also see ==
* 
Category:Specific Numbers
Category:1886
1887

== Number ==
$1887$ (one thousand, eight hundred and eighty-seven) is:
:$3 \times 17 \times 37$
:The $3$rd term of the $2$nd triplet of consecutive positive integers all of which are sphenic:
::$1885 = 5 \times 13 \times 29$, $1886 = 2 \times 23 \times 41$, $1887 = 3 \times 17 \times 37$
== Also see ==
* 
Category:Specific Numbers
Category:1887
189

== Number ==
$189$ (one hundred and eighty-nine) is:
:$3^3 \times 7$
:The $9$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $148$:
::$189 = 1 + 7 + 11 + 16 + 21 + 26 + 31 + 36 + 41 = \dfrac {9 \left({5 \times 9 - 3}\right)} 2$
:The $36$th lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $133$, $135$, $141$, $151$, $159$, $163$, $169$, $171$, $189$, $\ldots$
== Also see ==
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Category:Specific Numbers
Category:189
1891

== Number ==
$1891$ (one thousand, eight hundred and ninety-one) is:
:$31 \times 61$
:The $8$th Fermat pseudoprime to base $5$ after $4$, $124$, $217$, $561$, $781$, $1541$, $1729$:
::$5^{1891} \equiv 5 \pmod {1891}$
:The $10$th Fermat pseudoprime to base $3$ after $91$, $121$, $286$, $671$, $703$, $949$, $1105$, $1541$, $1729$:
::$3^{1891} \equiv 3 \pmod {1891}$
:The $31$st hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$, $1035$, $1225$, $1326$, $1431$, $1540$, $1653$, $1770$:
::$1891 = \ds \sum_{k \mathop = 1}^{31} \paren {4 k - 3} = 31 \paren {2 \times 31 - 1}$
:The $61$st triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $1326$, $1378$, $1431$, $1485$, $1540$, $1596$, $1653$, $1711$, $1770$, $1830$:
::$1891 = \ds \sum_{k \mathop = 1}^{61} k = \dfrac {61 \times \paren {61 + 1} } 2$
== Also see ==
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Category:Specific Numbers
Category:1891
19,116

== Number ==
$19 \, 116$ (nineteen thousand, one hundred and sixteen) is:
:$2^2 \times 3^4 \times 59$
:The $2$nd 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:19,116
19,600

== Number ==
$19 \, 600$ (nineteen thousand, six hundred) is:
:$2^4 \times 5^2 \times 7^2$
:The $140$th square number:
::$19 \, 600 = 140 \times 140$
:The $48$th tetrahedral number:
::$19 \, 600 = \ds \sum_{k \mathop = 1}^{48} \frac {k \paren {k + 1} } 2 = \dfrac {48 \paren {48 + 1} \paren {48 + 2} } 6$
:The $3$rd and last after $1$, $4$ of the $3$ tetrahedral numbers which are also square
== Also see ==
* 
* 
* 
== Sources ==
* : $19,600$
* : $19,600$
Category:Specific Numbers
Category:19,600
19,683

== Number ==
$19 \, 683$ (nineteen thousand, six hundred and eighty-three) is:
:$3^9$
:The number of different binary operations that can be applied to a set with $3$ elements
:The $7$th and last cube after $0$, $1$, $512$, $4913$, $5832$, $17 \, 576$ whose digits add up to its root:
::$19 \, 683 = 27^3$, while $1 + 9 + 6 + 9 + 3 = 27$
:The $9$th power of $3$ after $(1)$, $3$, $9$, $27$, $81$, $243$, $729$, $2187$, $6561$:
::$19 \, 683 = 3^9$
:The $27$th cube number:
::$19 \, 683 = 27 \times 27 \times 27$
== Also see ==
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Category:Specific Numbers
Category:19,683
19,916

== Number ==
$19 \, 916$ (nineteen thousand, nine hundred and sixteen) is:
:$2^2 \times 13 \times 383$
:The $27$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:19,916
19,937

== Number ==
$19 \, 937$ (nineteen thousand, nine hundred and thirty-seven) is:
:The $2254$th prime number
:The index of the $24$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $\ldots$, $2203$, $2281$, $3217$, $4253$, $4423$, $9689$, $9941$, $11 \, 213$:
::$M_{19 \, 937} = 2^{19 \, 937} - 1 \approx 4 \cdotp 315 \times 10^{6001}$
== Also see ==
* 
* 
== Historical Note ==
== Sources ==
* : $2^{19937} - 1$
* : $2^{19,937} - 1$
Category:Specific Numbers
Category:19,937
19,937/Historical Note

== Historical Note on $19 \, 937$ ==
The Mersenne number $M_{19 \, 937} = 2^{19 \, 937} - 1$ was demonstrated to be a Mersenne prime by on $4$ March $1971$.
== Sources ==
* : $2^{19937} - 1$
* : $2^{19,937} - 1$
Category:Historical Notes
190

== Number ==
$190$ (one hundred and ninety) is:
:$2 \times 5 \times 19$
:The $10$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $120$, $153$:
::$190 = 1 + 5 + 9 + 13 + 17 + 21 + 25 + 29 + 33 + 37 = 10 \paren {2 \times 10 - 1}$
:The $11$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 $12$th integer $n$ after $1, 3, 15, 30, 35, 56, 70, 78, 105, 140, 168$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:
::$\map {\sigma_0} {190} = 8$, $\map \phi {190} = 72$, $\map {\sigma_1} {190} = 360$
:The $12$th integer after $7$, $13$, $19$, $35$, $38$, $41$, $57$, $65$, $70$, $125$, $130$ the decimal representation of whose square can be split into two parts which are each themselves square:
::$190^2 = 36 \, 100$; $36 = 6^2$, $100 = 10^2$
:The $18$th sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$, $114$, $130$, $138$, $154$, $165$, $170$, $174$, $182$, $186$:
::$190 = 2 \times 5 \times 19$
:The $19$th triangular number after $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$, $55$, $66$, $78$, $91$, $105$, $120$, $136$, $153$, $171$:
::$190 = \ds \sum_{k \mathop = 1}^{19} k = \dfrac {19 \times \paren {19 + 1} } 2$
:The $30$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $91$, $94$, $97$, $100$, $103$, $109$, $129$, $130$, $133$, $139$, $167$, $176$, $188$:
::$190 \to 1^2 + 9^2 + 0^2 = 1 + 81 + 0 = 82 \to 8^2 + 2^2 = 64 + 4 = 68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$
== Also see ==
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Category:Specific Numbers
Category:190
1905

== Number ==
$1905$ (one thousand, nine hundred and five) is:
:$3 \times 5 \times 127$
:The $7$th Poulet number after $341$, $561$, $645$, $1105$, $1387$, $1729$:
::$2^{1905} \equiv 2 \pmod {1905}$: $1905 = 3 \times 5 \times 127$
== Also see ==
* 
Category:Specific Numbers
Category:1905
1906

== Number ==
$1906$ (one thousand, nine hundred and six) is:
:$2 \times 953$
:The $17$th non-square positive integer which cannot be expressed as the sum of a square and a prime:
::$10$, $34$, $58$, $85$, $91$, $130$, $214$, $226$, $370$, $526$, $706$, $730$, $771$, $1255$, $1351$, $1414$, $1906$, $\ldots$
:The $38$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $1255$, $1351$, $1414$, $1444$, $1521$, $1681$, $1849$, $1906$, $\ldots$
== Also see ==
* 
* 
Category:Specific Numbers
Category:1849
191

== Number ==
$191$ (one hundred and ninety-one) is:
:The $43$rd prime number
:The larger of the $2$nd pair of primes whose prime gap is $10$:
::$191 - 181 = 10$
:The $6$th Thabit number after $(2)$, $5$, $11$, $23$, $47$, $95$:
::$191 = 3 \times 2^6 - 1$ 
:The $6$th Thabit prime after $2$, $5$, $11$, $23$, $47$:
::$191 = 3 \times 2^6 - 1$ 
:The $6$th near-repdigit prime after $101$, $113$, $131$, $151$, $181$
:The $10$th palindromic prime:
::$2$, $3$, $5$, $7$, $11$, $101$, $131$, $151$, $181$, $191$, $\ldots$
:The $10$th of $29$ primes of the form $2 x^2 + 29$:
::$2 \times 9^2 + 29 = 191$ ()
:The $13$th prime number after $53$, $71$, $103$, $107$, $109$, $149$, $151$, $157$, $163$, $167$, $173$, $181$ which cannot be expressed as either the sum of or the difference between a power of $2$ and a power of $3$
:The smaller of the $14$th pair of twin primes, with $193$
:The $15$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$, $83$, $89$, $113$, $131$, $173$, $179$:
::$2 \times 191 + 1 = 383$, which is prime
== Also see ==
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::No further elements of this sequence will be tabulated on .
Category:Specific Numbers
Category:191
191,918,080,818,091,909,090,909,190,818,080,819,191

== Number ==
$191 \, 918 \, 080 \, 818 \, 091 \, 909 \, 090 \, 909 \, 190 \, 818 \, 080 \, 819 \, 191$ is:
:A prime number
:A palindromic Sophie Germain prime $N$ such that $2 N + 1$ is also a palindromic Sophie Germain prime and $2 \left({2 N + 1}\right) + 1$ is also a palindromic prime number (but not a Sophie Germain prime)
== Also see ==
* Sequence of Palindromic Sophie Germain Primes
== Sources ==
* : $191,918,080,818,091,909,090,909,190,818,080,819,191$
Category:Specific Numbers
Category:191,918,080,818,091,909,090,909,190,818,080,819,191
1918

== Number ==
$1918$ (one thousand, nine hundred and eighteen) is:
:$2 \times 7 \times 137$
:The $28$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $\ldots$, $874$, $970$, $1071$, $1177$, $1288$, $1404$, $1525$, $1651$, $1782$:
::$\ds 1918 = \sum_{k \mathop = 1}^{28} \paren {5 k - 4} = \dfrac {28 \paren {5 \times 28 - 3} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:1918
192

== Number ==
$192$ (one hundred and ninety-two) is:
:$2^6 \times 3$
:The $1$st of $4$ integers $n$ such that $n + 2 n$ can be expressed as a sum using each of the digits $1$ to $9$ exactly once each:
::$192 + 384 = 576$
:The $2$nd positive integer after $128$ with $7$ or more prime factors:
::$192 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$
:The $2$nd element of the $1$st set of $3$ integers $T$ such that $m \map {\sigma_0} m$ is equal for each $m \in T$:
::$168 \times \map {\sigma_0} {168} = 192 \times \map {\sigma_0} {192} = 224 \times \map {\sigma_0} {224} = 2688$
:The $6$th positive integer after $64$, $96$, $128$, $144$, $160$ with $6$ or more prime factors:
::$192 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$
:The $31$st happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $91$, $94$, $97$, $100$, $103$, $109$, $129$, $130$, $133$, $139$, $167$, $176$, $188$, $190$:
::$192 \to 1^2 + 9^2 + 2^2 = 1 + 81 + 4 = 86 \to 8^2 + 6^2 = 64 + 36 = 100 \to 1^2 + 0^2 + 0^2 = 1$
:The $38$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.
== Also see ==
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== Sources ==
* : $168$
* : $192$
Category:Specific Numbers
Category:192
1924

== Number ==
$1924$ (one thousand nine hundred and twenty four) is:
:$2^2 \times 13 \times 37$
:One of the legs of the Pythagorean triangle $693-1924-2045$, whose area is $666 \, 666$.
== Also see ==
* Pythagorean Triangles whose Areas are Repdigit Numbers
Category:Specific Numbers
Category:1924
1925

== Number ==
$1925$ (one thousand nine hundred and twenty-five) is:
:$5^2 \times 7 \times 11$
:With $1050$, an element of the $3$rd quasiamicable pair:
::$\map {\sigma_1} {1050} = \map {\sigma_1} {1925} = 2976 = 1050 + 1925 + 1$
== Also see ==
* 
Category:Specific Numbers
Category:1925
1926

== Number ==
$1926$ (one thousand, nine hundred and twenty-six) is:
:$2 \times 3^2 \times 107$
:The $36$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $925$, $1001$, $1080$, $1162$, $1247$, $1335$, $1426$, $1520$, $1617$, $1717$, $1820$:
::$1926 = \ds \sum_{k \mathop = 1}^{36} \paren {3 k - 2} = \dfrac {36 \paren {3 \times 36 - 1} } 2$
:The $71$st generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $1335$, $1365$, $1426$, $1457$, $1520$, $1552$, $1617$, $1650$, $1717$, $1751$, $1820$, $1855$:
::$1926 = \ds \sum_{k \mathop = 1}^{36} \paren {3 k - 2} = \dfrac {36 \paren {3 \times 36 - 1} } 2$
== Also see ==
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Category:Specific Numbers
Category:1926
193

== Number ==
$193$ (one hundred and ninety-three) is:
:The $44$th prime number
:The $8$th Proth prime after $3$, $5$, $13$, $17$, $41$, $97$, $113$:
::$193 = 3 \times 2^6 + 1$
:The larger of the $14$th pair of twin primes, with $191$
:The $17$th long period prime after $7$, $17$, $19$, $23$, $29$, $47$, $59$, $61$, $97$, $109$, $113$, $131$, $149$, $167$, $179$, $181$
:The $32$nd happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $130$, $133$, $139$, $167$, $176$, $188$, $190$, $192$:
::$193 \to 1^2 + 9^2 + 3^2 = 1 + 81 + 9 = 91 \to 9^2 + 1^2 = 81 + 1 = 82 \to 8^2 + 2^2 = 64 + 4 = 68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$
:The $37$th lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $133$, $135$, $141$, $151$, $159$, $163$, $169$, $171$, $189$, $193$, $\ldots$
== Also see ==
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Category:Specific Numbers
Category:193
1936

== Number ==
$1936$ (one thousand nine hundred and thirty-six) is:
:$2^4 \times 11^2$
:The $17$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $324$, $400$, $576$, $784$, $900$, $961$, $1024$, $1296$, $1600$, $1764$ to be the divisor sum value of some (strictly) positive integer:
::$1936 = \map {\sigma_1} {1687}$
:The $39$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $1255$, $1351$, $1414$, $1444$, $1521$, $1681$, $1849$, $1906$, $1936$, $\ldots$
:The $44$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $1296$, $1369$, $1444$, $1521$, $1600$, $1681$, $1764$, $1849$:
::$1936 = 44 \times 44$
== Also see ==
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Category:Specific Numbers
Category:1936