nyuuzyou/wikis huggingface dataset:
77

== Number ==
$77$ (seventy-seven) is:
:$7 \times 11$
:The smallest positive integer having a multiplicative persistence of $4$
:The $6$th palindromic integer after $0$, $1$, $2$, $3$, $11$ which is the index of a palindromic triangular number
::$T_{77} = 3003$
:The $7$th second pentagonal number after $2$, $7$, $15$, $26$, $40$, $57$:
::$77 = \dfrac {7 \left({3 \times 7 + 1}\right)} 2$
:The $10$th integer $m$ such that $m! + 1$ (its factorial plus $1$) is prime:
::$0$, $1$, $2$, $3$, $11$, $27$, $37$, $41$, $73$, $77$
:The number of integer partitions for $12$:
::$\map p {12} = 77$
:The $14$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$, $57$, $70$:
::$77 = \dfrac {7 \left({3 \times 7 + 1}\right)} 2$
:The $26$th semiprime:
::$77 = 7 \times 11$
:The $32$nd odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
::$1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $73$, $77$, $\ldots$
:The $34$th integer $n$ such that $2^n$ contains no zero in its decimal representation:
::$2^{77} = 151 \, 115 \, 727 \, 451 \, 828 \, 646 \, 838 \, 272$
:The $41$st positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $50$, $54$, $55$, $59$, $60$, $61$, $65$, $66$, $67$, $72$ which cannot be expressed as the sum of distinct pentagonal numbers
:The $44$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $55$, $60$, $61$, $65$, $66$, $67$, $72$, $73$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
:The smallest (positive) integer which requires $5$ syllables to say it in the English language:
::sev-en-ty-sev-en
:The largest positive integer which cannot be expressed as the sum of positive integers whose reciprocals add up to $1$
== Also see ==
* Positive Integers Expressible by Sum of Integers whose Reciprocals Sum to 1
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
* 
== Sources ==
* : $77$
Category:Specific Numbers
Category:77
77,777,400,996

== Number ==
$77 \, 777 \, 400 \, 996$ is:
:$2^2 \times 3^2 \times 53^2 \times 877^2$
The $278 \, 886$th square number:
::$77 \, 777 \, 400 \, 996 = 278 \, 886 \times 278 \, 886$
:Starts with a remarkably long string of $7$s. Nothing to see here, move along now.
== Also see ==
* 
== Sources ==
* : $278,886$
* : $278,886$
Category:Specific Numbers
Category:77,777,400,996
770

== Number ==
$770$ (seven hundred and seventy) is:
:$2 \times 5 \times 7 \times 11$
:The $11$th positive integer after $1$, $7$, $102$, $110$, $142$, $159$, $187$, $381$, $690$, $714$ the sum of whose divisors is a cube:
::$\map {\sigma_1} {770} = 1728 = 12^3$
:The $17$th primitive semiperfect number after $6$, $20$, $28$, $88$, $104$, $272$, $304$, $350$, $368$, $464$, $490$, $496$, $550$, $572$, $650$, $748$:
::$770 = 1 + 5 + 7 + 11 + 14 + 35 + 55 + 70 + 77 + 110 + 385$
== Also see ==
* 
* 
Category:Specific Numbers
Category:770
7701

== Number ==
$7701$ (seven thousand, seven hundred and one) is:
:$3 \times 17 \times 151$
:The $51$st octagonal number, after $1$, $8$, $21$, $40$, $65$, $\ldots$, $5985$, $6256$, $6533$, $6816$, $7105$, $7400$:
::$7701 = \ds \sum_{k \mathop = 1}^{51} \paren {6 k - 5} = 51 \paren {3 \times 51 - 2}$
== Also see ==
* 
Category:Specific Numbers
Category:7701
771

== Number ==
$730$ (seven hundred and thirty) is:
:$2 \times 5 \times 73$
:The $13$th non-square positive integer which cannot be expressed as the sum of a square and a prime:
::$10$, $34$, $58$, $85$, $91$, $130$, $214$, $226$, $370$, $526$, $706$, $730$, $771$, $\ldots$
:The $25$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $214$, $226$, $289$, $324$, $370$, $400$, $526$, $529$, $625$, $676$, $706$, $730$, $771$, $\ldots$
== Also see ==
* 
* 
Category:Specific Numbers
Category:771
7714

== Number ==
$7714$ (seven thousand, seven hundred and fourteen) is:
:$2 \times 7 \times 19 \times 29$
:The $28$th square pyramidal number after $1$, $5$, $14$, $30$, $55$, $\ldots$, $3311$, $3795$, $4324$, $4900$, $5525$, $6201$, $6930$:
::$7714 = \ds \sum_{k \mathop = 1}^{28} k^2 = \dfrac {28 \paren {28 + 1} \paren {2 \times 28 + 1} } 6$
== Also see ==
* 
Category:Specific Numbers
Category:7714
773

== Number ==
$773$ (seven hundred and seventy-three) is:
:The $137$th prime number
:The smaller of the $4$th pair of primes whose prime gap is $14$:
::$787 - 773 = 14$
:The $33$rd near-repdigit prime after $101$, $113$, $131$, $151$, $\ldots$, $353$, $373$, $383$, $433$, $443$, $449$, $499$, $557$, $577$, $599$, $661$, $677$, $727$, $733$, $757$
:The $44$th left-truncatable prime after $2$, $3$, $5$, $7$, $\ldots$, $443$, $467$, $523$, $547$, $613$, $617$, $643$, $647$, $653$, $673$, $683$, $743$
== Also see ==
* 
* 
* 
* 
Category:Specific Numbers
Category:773
7744

== Number ==
$7744$ (seven thousand, seven hundred and forty-four) is:
:$2^6 \times 11^2$
:The $17$th square after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $121$, $144$, $225$, $441$, $484$, $676$, $1444$ which has no more than $2$ distinct digits and does not end in $0$:
::$7744 = 88^2$
:The $33$rd square number after $1$, $4$, $36$, $121$, $144$, $256$, $\ldots$, $5184$, $5776$, $6084$, $6400$, $7056$ to be the divisor sum value of some (strictly) positive integer:
::$7744 = \map {\sigma_1} {5061} = \map {\sigma_1} {6769} = \map {\sigma_1} {7471}$
:The $88$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $6084$, $6241$, $6400$, $6561$, $6724$, $6889$, $7056$, $7225$, $7396$, $7569$:
::$7744 = 88 \times 88$
== Also see ==
* 
* 
* 
== Sources ==
* : $7744$
* : $7744$
Category:Specific Numbers
Category:7744
7750

== Number ==
$7750$ (seven thousand, seven hundred and fifty) is:
:$2 \times 5^3 \times 31$
:The $124$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $6786$, $6903$, $7021$, $7140$, $7260$, $7381$, $7503$, $7626$:
::$7750 = \ds \sum_{k \mathop = 1}^{124} k = \dfrac {124 \times \paren {124 + 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:7750
777

== Number ==
$777$ (seven hundred and seventy-seven) is:
:$3 \times 7 \times 37$
:The $16$th palindromic lucky number:
::$1$, $3$, $7$, $9$, $33$, $99$, $111$, $141$, $151$, $171$, $303$, $393$, $535$, $717$, $727$, $777$, $\ldots$
== Also see ==
* 
Category:Specific Numbers
Category:777
7770

== Number ==
$7770$ (seven thousand, seven hundred and seventy) is:
:$2 \times 3 \times 5 \times 7 \times 37$
:The $35$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $\ldots$, $3276$, $3276$, $4060$, $4495$, $4960$, $5456$, $5984$, $6545$, $7140$:
::$7770 = \ds \sum_{k \mathop = 1}^{35} \frac {k \paren {k + 1} } 2 = \dfrac {35 \paren {35 + 1} \paren {35 + 2} } 6$
== Also see ==
* 
Category:Specific Numbers
Category:7770
7776

== Number ==
$7776$ (seven thousand, seven hundred and seventy-six) is:
:$2^5 \times 3^5$
:The $5$th power of $6$ after $(1)$, $6$, $36$, $216$, $1296$:
::$7776 = 6^5$
:The $6$th fifth power after $1$, $32$, $243$, $1024$, $3125$:
::$7776 = 6 \times 6 \times 6 \times 6 \times 6$
== Also see ==
* 
* 
Category:Specific Numbers
Category:7776
7777

== Number ==
$7777$ (seven thousand, seven hundred and seventy-seven) is:
:$7 \times 11 \times 101$
:The $16$th Kaprekar number after $1$, $9$, $45$, $55$, $99$, $297$, $703$, $999$, $2223$, $2728$, $4879$, $4950$, $5050$, $5292$, $7272$:
::$7777^2 = 60 \, 481 \, 729 \to 6048 + 1729 = 7777$
== Also see ==
* 
== Sources ==
* : $6666$
* : $6666$
Category:Specific Numbers
Category:7777
778

== Number ==
$778$ (seven hundred and seventy-eight) is:
:$2 \times 389$
:The $40$th Smith number after $4$, $22$, $27$, $58$, $\ldots$, $648$, $654$, $663$, $666$, $690$, $706$, $728$, $729$, $762$:
::$7 + 7 + 8 = 2 + 3 + 8 + 9 = 22$
== Also see ==
* 
Category:Specific Numbers
Category:778
78

== Number ==
$78$ (seventy-eight) is:
:$2 \times 3 \times 13$
:The $2$nd element of the $1$st set of $4$ positive integers which form an arithmetic sequence which all have the same Euler $\phi$ value:
::$\map \phi {72} = \map \phi {78} = \map \phi {84} = \map \phi {90} = 24$
:The $5$th sphenic number after $30$, $42$, $66$, $70$:
::$78 = 2 \times 3 \times 13$
:The smallest positive integer which can be expressed as the sum of $2$ odd primes in $7$ ways.
:The $8$th integer $n$ after $1$, $3$, $15$, $30$, $35$, $56$, $70$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:
::$\map {\sigma_0} {78} = 8$, $\map \phi {78} = 24$, $\map {\sigma_1} {78} = 168$
:The $12$th triangular number after $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$, $55$, $66$:
::$78 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = \dfrac {12 \times \paren {12 + 1} } 2$
:The $17$th semiperfect number after $6$, $12$, $18$, $20$, $24$, $28$, $30$, $36$, $40$, $42$, $48$, $54$, $56$, $60$, $66$, $72$:
::$78 = 13 + 26 + 39$
:The $45$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $55$, $60$, $61$, $65$, $66$, $67$, $72$, $73$, $77$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
== Also see ==
* 
* 
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:78
78,125

== Number ==
$78 \, 125$ (seventy-eight thousand, one hundred and twenty-five) is:
:$5^7$
:The $5$th seventh power after $1$, $128$, $2187$, $16 \, 384$:
::$78 \, 125 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5$
:The $7$th power of $5$ after $(1)$, $5$, $25$, $125$, $625$, $3125$, $15 \, 625$:
::$78 \, 125 = 5^7$
== Also see ==
* 
* 
Category:Specific Numbers
Category:78,125
78,498

== Number ==
$78 \, 498$ (seventy-eight thousand, four hundred and ninety-eight) is:
:$2 \times 3^2 \times 7^2 \times 89$
:The number of primes with no more than $6$ digits:
::$2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$, $23$, $\ldots$, $999 \, 959$, $999 \, 961 $, $999 \, 979$, $999 \, 983$
== Also see ==
* 
Category:Specific Numbers
Category:78,498
78,557

== Number ==
$78 \,557$ (seventy-eight thousand, five hundred and fifty-seven) is:
:$17 \times 4621$
:The $1$st known Sierpiński number of the second kind, although there may exist smaller
== Also see ==
* 
== Sources ==
* : $78,557$
* : $78,557$
Category:Specific Numbers
Category:78,557
78,557 is Sierpiński

== Theorem ==
$78 \, 557$ is a Sierpiński number of the second kind.
== Proof ==
When considering $\bmod {36}$, every positive integer $n$ can be written in one of the forms:
:$2 k, 4 k + 1, 3 k + 1, 12 k + 11, 18 k + 15, 36 k + 27, 9 k + 3$
$\begin{array}{|c|c|}
\hline n \bmod {36} & \text { Form } \\
\hline 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34 & 2 k \\
\hline 1, 5, 9, 13, 17, 21, 25, 29, 33 & 4 k + 1 \\
\hline 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 & 3 k + 1 \\
\hline 11, 23, 35 & 12 k + 11 \\
\hline 15, 33 & 18 k + 15 \\
\hline 27 & 36 k + 27 \\
\hline 3, 12, 21, 30 & 9 k + 3\\
\hline
\end{array}$
As seen by inspection, every number less than $36$ is included in the table.
And we have:
Therefore $78557 \times 2^n + 1$ is always divisible by one of $\set {3, 5, 7, 13, 19, 37, 73}$.
Hence they are composite for every $n$.
== Historical Note ==
Category:Sierpiński Numbers of the Second Kind
Category:78,557
78,901

== Number ==
$78 \, 901$ (seventy-eight thousand, nine hundred and one) is:
:The $7814$th prime number
:The $9$th prime number after $2$, $3$, $5$, $7$, $23$, $67$, $89$, $4567$ consisting of a string of consecutive ascending digits (allowing $0$ to follow $9$)
== Also see ==
* 
* 
Category:Specific Numbers
Category:78,901
780

== Number ==
$780$ (seven hundred and eighty) is:
:$2^2 \times 3 \times 5 \times 13$
:The side length of the smallest square with integer sides that can be inscribed within two different Pythagorean triangles so that one side of the square lies on the hypotenuse:
::$\tuple {1443, 1924, 2405}$ and $\tuple {1145, 2748, 2977}$ are the side lengths.
:The first of the $4$th pair of triangular numbers whose sum and difference are also both triangular:
::$780 = T_{39}$, $990 = T_{44}$, $780 + 990 = T_{59}$, $990 - 780 = T_{20}$
:The $20$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $378$, $435$, $496$, $561$, $630$, $703$:
::$780 = \ds \sum_{k \mathop = 1}^{20} \paren {4 k - 3} = 20 \paren {2 \times 20 - 1}$
:The $39$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $325$, $351$, $378$, $406$, $435$, $465$, $496$, $528$, $561$, $595$, $630$, $666$, $703$, $741$:
::$780 = \ds \sum_{k \mathop = 1}^{39} k = \dfrac {39 \times \paren {39 + 1} } 2$
== Also see ==
* Smallest Square Inscribed in Two Pythagorean Triangles
* 
* 
* 
== Sources ==
* : $780$
* : $780$
Category:Specific Numbers
Category:780
781

== Number ==
$781$ (seven hundred and eighty-one) is:
:$11 \times 71$
:The $5$th Fermat pseudoprime to base $5$ after $4$, $124$, $217$, $561$:
::$5^{781} \equiv 5 \pmod {781}$
:The $6$th of the $3$-digit integers $m$ which need the largest number of reverse-and-add process iterations ($23$) before reaching a palindromic number:
::$781$, $968$, $1837$, $\ldots$, $8713200023178$
== Also see ==
* 
* 
Category:Specific Numbers
Category:781
7810

== Number ==
$7810$ (seven thousand, eight hundred and ten) is:
:$2 \times 5 \times 11 \times 71$
:The $6$th integer after $91$, $428$, $573$, $727$, $846$ whose square has a decimal representation consisting of the concatenation of $2$ consecutive integers:
::$7810^2 = 60 \, 996 \, 100$
:The $5$th integer after $428$, $573$, $727$, $846$ whose square has a decimal representation consisting of the concatenation of $2$ consecutive increasing integers:
::$7810^2 = 60 \, 996 \, 100$
== Also see ==
* 
* 
Category:Specific Numbers
Category:7810
782

== Number ==
$782$ (seven hundred and eighty-two) is:
:$2 \times 17 \times 23$
:The $23$rd pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $477$, $532$, $590$, $651$, $715$:
::$782 = \ds \sum_{k \mathop = 1}^{23} \paren {3 k - 2} = \dfrac {23 \paren {3 \times 23 - 1} } 2$
:The $45$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $392$, $425$, $442$, $477$, $495$, $532$, $551$, $590$, $610$, $651$, $672$, $715$, $737$:
::$782 = \ds \sum_{k \mathop = 1}^{23} \paren {3 k - 2} = \dfrac {23 \paren {3 \times 23 - 1} } 2$
== Also see ==
* 
* 
Category:Specific Numbers
Category:782
7825

== Number ==
$7825$ (seven thousand, eight hundred and twenty-five) is:
:$5^2 \times 313$
:The magic constant of a magic square of order $25$, after $1$, $(5)$, $15$, $34$, $\ldots$, $2465$, $2925$, $3439$, $4010$, $4641$, $5335$, $6095$, $6924$:
::$\ds 7825 = \dfrac 1 {25} \sum_{k \mathop = 1}^{25^2} k = \dfrac {25 \paren {25^2 + 1} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:7825
783

== Number ==
$783$ (seven hundred and eighty-three) is:
:$3^3 \times 29$
:The $18$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $148$, $189$, $235$, $286$, $342$, $403$, $469$, $540$, $616$, $697$:
::$783 = \ds \sum_{k \mathop = 1}^{18} \paren {5 k - 4} = \dfrac {18 \paren {5 \times 18 - 3} } 2$
== Also see ==
* 
Category:Specific Numbers
Category:783
784

== Number ==
$784$ (seven hundred and eighty-four) is:
:$2^4 \times 7^2$
:The sum of the first $7$ cubes:
::$784 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3$
:The $10$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $324$, $400$, $576$ to be the divisor sum value of some (strictly) positive integer:
::$784 = \map {\sigma_1} {364}$
:The $12$th even integer after $2$, $4$, $94$, $96$, $98$, $400$, $402$, $404$, $514$, $516$, $518$ that cannot be expressed as the sum of $2$ prime numbers which are each one of a pair of twin primes
:The $26$th positive integer which cannot be expressed as the sum of a square and a prime:
::$1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $214$, $226$, $289$, $324$, $370$, $400$, $526$, $529$, $625$, $676$, $706$, $730$, $771$, $784$, $\ldots$
:The $28$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $361$, $400$, $441$, $484$, $529$, $57$, $625$, $676$, $729$:
::$784 = 28 \times 28$
:The $47$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $400$, $432$, $441$, $484$, $500$, $512$, $529$, $576$, $625$, $648$, $675$, $676$, $729$:
::$784 = 2^4 \times 7^2$
== Also see ==
* 
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:784
786

== Number ==
$786$ (seven hundred and eighty-six) is:
:$2 \times 3 \times 131$
:The $13$th even integer after $2$, $4$, $94$, $96$, $98$, $400$, $402$, $404$, $514$, $516$, $518$, $784$ that cannot be expressed as the sum of $2$ prime numbers which are each one of a pair of twin primes
== Also see ==
* 
Category:Specific Numbers
Category:786
787

== Number ==
$787$ (seven hundred and eighty-seven) is:
:The $138$th prime number
:The larger of the $4$th pair of primes whose prime gap is $14$:
::$787 - 773 = 14$
:The smaller of the $13$th pair of primes whose prime gap is $10$:
::$797 - 787 = 10$
:The $17$th palindromic prime:
::$2$, $3$, $5$, $7$, $11$, $101$, $131$, $151$, $181$, $191$, $313$, $353$, $373$, $383$, $727$, $757$, $787$, $\ldots$
:The $17$th palindromic lucky number:
::$1$, $3$, $7$, $9$, $33$, $99$, $111$, $141$, $151$, $171$, $303$, $393$, $535$, $717$, $727$, $777$, $787$, $\ldots$
:The $34$th near-repdigit prime after $101$, $113$, $131$, $151$, $\ldots$, $353$, $373$, $383$, $433$, $443$, $449$, $499$, $557$, $577$, $599$, $661$, $677$, $727$, $733$, $757$, $773$
== Also see ==
* 
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:787
787,109,376

== Number ==
$787 \, 109 \, 376$ is:
:$2^9 \times 3 \times 47 \times 10 \, 903$
:The $17$th automorphic number after $1$, $5$, $6$, $25$, $76$, $376$, $625$, $9376$, $\ldots$, $12 \, 890 \, 625$, $87 \, 109 \, 376$, $212 \, 890 \, 625$:
::$787 \, 109 \, 376^2 = 619 \, 541 \, 169 \, \mathbf {787 \, 109 \, 376}$
== Also see ==
* 
Category:Specific Numbers
Category:787,109,376
7875

== Number ==
$7875$ (seven thousand, eight hundred and seventy-five) is:
:$3^2 \times 5^3 \times 7$
:The total of all the entries in a magic cube of order $5$, after $1$, $36$, $378$, $2080$:
::$7875 = \ds \sum_{k \mathop = 1}^{5^3} k = \dfrac {5^3 \paren {5^3 + 1} } 2$
:The $1$st of the $8$th pair of triangular numbers whose sum and difference are also both triangular:
::$7875 = T_{125}$, $8778 = T_{132}$, $8778 + 7875 = T_{182}$, $8778 - 7875 = T_{42}$
:The $16$th odd abundant number after $945$, $1575$, $2205$, $2835$, $3465$, $4095$, $4725$, $5355$, $5775$, $5985$, $6435$, $6615$, $6825$, $7245$, $7425$:
::$\map {\sigma_1} {7875} - 7875 = 8349 > 7875$
:The $63$rd hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $5565$, $5778$, $5995$, $6216$, $6441$, $6670$, $6903$, $7140$, $7381$, $7626$:
::$7875 = \ds \sum_{k \mathop = 1}^{63} \paren {4 k - 3} = 63 \paren {2 \times 63 - 1}$
:The $125$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $6786$, $6903$, $7021$, $7140$, $7260$, $7381$, $7503$, $7626$, $7750$:
::$7875 = \ds \sum_{k \mathop = 1}^{125} k = \dfrac {125 \times \paren {125 + 1} } 2$
== Also see ==
* 
* 
* 
* 
* 
Category:Specific Numbers
Category:7875
788

== Number ==
$788$ (seven hundred and eighty-eight) is:
:$2^2 \times 197$
:The $1$st in a sequence of $6$ consecutive integers which are divisible by the corresponding term in the sequence of the first $6$ primes:
::$788 = 2 \times 394$
:The $8$th candidate Lychrel number
:The $14$th even integer after $2$, $4$, $94$, $96$, $98$, $400$, $402$, $404$, $514$, $516$, $518$, $784$, $786$ that cannot be expressed as the sum of $2$ prime numbers which are each one of a pair of twin primes
== Also see ==
* 
* 
* 
== Sources ==
* : $788$
Category:Specific Numbers
Category:788
789

== Number ==
$789$ (seven hundred and eighty-nine) is:
:$3 \times 263$
:The $2$nd in a sequence of $6$ consecutive integers which are divisible by the corresponding term in the sequence of the first $6$ primes:
::$789 = 3 \times 263$
== Also see ==
* 
== Sources ==
* : $788$
Category:Specific Numbers
Category:789
79

== Number ==
$79$ (seventy-nine) is:
:The $22$nd prime number.
:The $1$st positive integer which cannot be expressed as the sum of fewer than $19$ fourth powers:
::$79 = 15 \times 1^4 + 4 \times 2^4$
:The $6$th of $29$ primes of the form $2 x^2 + 29$:
::$2 \times 5^2 + 29 = 79$ ()
:The $7$th emirp after $13$, $17$, $31$, $37$, $71$, $73$
:The $12$th permutable prime after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $31$, $37$, $71$, $73$
:The $13$th prime $p$ after $11$, $23$, $29$, $37$, $41$, $43$, $47$, $53$, $59$, $67$, $71$, $73$ such that the Mersenne number $2^p - 1$ is composite
:The $13$th right-truncatable prime after $2$, $3$, $5$, $7$, $23$, $29$, $31$, $37$, $53$, $59$, $71$, $73$
:The $14$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $28$, $31$, $32$, $44$, $49$, $68$, $70$:
::$79 \to 7^2 + 9^2 = 49 + 81 = 130 \to 1^2 + 3^2 + 0^2 = 1 + 9 + 0 = 10 \to 1^2 + 0^2 = 1$
:The $15$th positive integer $n$ after $5$, $11$, $17$, $23$, $29$, $30$, $36$, $42$, $48$, $54$, $60$, $61$, $67$, $73$ such that no factorial of an integer can end with $n$ zeroes
:The $19$th lucky number:
::$1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $63$, $67$, $73$, $75$, $79$, $\ldots$
:The $30$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
::$3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $53$, $55$, $61$, $62$, $64$, $66$, $68$, $69$, $74$, $75$, $79$, $\ldots$
:The $46$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $55$, $60$, $61$, $65$, $66$, $67$, $72$, $73$, $77$, $78$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
== Also see ==
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== Sources ==
* : $79$
* : $79$
Category:Specific Numbers
Category:79
79,873,884

== Number ==
$79 \, 873 \, 884$ (seventy-nine million, eight hundred and seventy-three thousand, eight hundred and eighty-four) is:
:$2^2 \times 3^3 \times 383 \times 1931$
:The $4$th self-locating number in $\pi$ after $1$, $16 \, 470$, $44 \, 899$
== Also see ==
* 
Category:79,873,884
Category:Specific Numbers
790

== Number ==
$790$ (seven hundred and ninety) is:
:$2 \times 5 \times 79$
:The $9$th candidate Lychrel number.
:The $3$rd in a sequence of $6$ consecutive integers which are divisible by the corresponding term in the sequence of the first $6$ primes:
::$790 = 5 \times 158$
== Also see ==
* 
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== Sources ==
* : $788$
Category:Specific Numbers
Category:790
791

== Number ==
$791$ (seven hundred and ninety-one) is:
:$7 \times 113$
:The $4$th in a sequence of $6$ consecutive integers which are divisible by the corresponding term in the sequence of the first $6$ primes:
::$791 = 7 \times 113$
== Also see ==
* 
== Sources ==
* : $788$
Category:Specific Numbers
Category:791
7912

== Number ==
$7912$ (seven thousand, nine hundred and twelve) is:
:$2^3 \times 23 \times 43$
:The $6$th weird number after $70$, $836$, $4030$, $5830$, $7192$:
::$\map {\sigma_1} {7912} - 7912 = 7928$: $7912$ cannot be made from its aliquot parts
== Also see ==
* 
Category:Specific Numbers
Category:7912
792

== Number ==
$792$ (seven hundred and ninety-two) is:
:$2^3 \times 3^2 \times 11$
:The $5$th in a sequence of $6$ consecutive integers which are divisible by the corresponding term in the sequence of the first $6$ primes:
::$792 = 11 \times 72$
:The $8$th tri-automorphic number after $2$, $5$, $7$, $67$, $75$, $92$, $667$:
::$792^2 \times 3 = 1 \, 881 \, \mathbf {792}$
:The number of integer partitions for $21$:
::$\map p {21} = 792$
== Also see ==
* 
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== Sources ==
* : $788$
Category:Specific Numbers
Category:792
7921

== Number ==
$7921$ (seven thousand, nine hundred and twenty-one) is:
:$89^2$
:The $89$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $6084$, $6241$, $6400$, $6561$, $6724$, $6889$, $7056$, $7225$, $7396$, $7569$, $7744$
::$7921 = 89 \times 89$
== Also see ==
* 
Category:Specific Numbers
Category:7921
793

== Number ==
$793$ (seven hundred and ninety-three) is:
:$13 \times 61$
:The $6$th and last in a sequence of $6$ consecutive integers which are divisible by the corresponding term in the sequence of the first $6$ primes:
::$793 = 13 \times 61$
== Also see ==
* 
== Sources ==
* : $788$
Category:Specific Numbers
Category:793