100,000,000,000,000: Difference between revisions

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100,000,000,000,000 (hundred trillion on the short scale; hundred billion on the long scale; hundred thousand billion; hundred million million) is the natural number following 99,999,999,999,999 and preceding 100,000,000,000,001. It is known as 1 lakh arab, 1000 kharab, 1 crore crore, or 10 nil in the Indian numbering system.

Properties and usage

100,000,000,000,000 has the following properties and usage:

In mathematics

It is even, composite, abundant, polite, practical, frugal, and regular. It is also a perfect power and a harshad number.
It is written in scientific notation as 1 × 10¹⁴ or 10¹⁴ (1E+14 or simply 1E14 in E notation).
It has a total of 225 divisors (210 even, 15 odd). All divisors are displayed below:

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2048, 2500, 2560, 3125, 3200, 4000, 4096, 5000, 5120, 6250, 6400, 8000, 8192, 10000, 10240, 12500, 12800, 15625, 16000, 16384, 20000, 20480, 25000, 25600, 31250, 32000, 40000, 40960, 50000, 51200, 62500, 64000, 78125, 80000, 81920, 100000, 102400, 125000, 128000, 156250, 160000, 200000, 204800, 250000, 256000, 312500, 320000, 390625, 400000, 409600, 500000, 512000, 625000, 640000, 781250, 800000, 1000000, 1024000, 1250000, 1280000, 1562500, 1600000, 1953125, 2000000, 2048000, 2500000, 2560000, 3125000, 3200000, 3906250, 4000000, 5000000, 5120000, 6250000, 6400000, 7812500, 8000000, 9765625, 10000000, 10240000, 12500000, 12800000, 15625000, 16000000, 19531250, 20000000, 25000000, 25600000, 31250000, 32000000, 39062500, 40000000, 48828125, 50000000, 51200000, 62500000, 64000000, 78125000, 80000000, 97656250, 100000000, 125000000, 128000000, 156250000, 160000000, 195312500, 200000000, 244140625, 250000000, 256000000, 312500000, 320000000, 390625000, 400000000, 488281250, 500000000, 625000000, 640000000, 781250000, 800000000, 976562500, 1000000000, 1220703125, 1250000000, 1280000000, 1562500000, 1600000000, 1953125000, 2000000000, 2441406250, 2500000000, 3125000000, 3200000000, 3906250000, 4000000000, 4882812500, 5000000000, 6103515625, 6250000000, 6400000000, 7812500000, 8000000000, 9765625000, 10000000000, 12207031250, 12500000000, 15625000000, 16000000000, 19531250000, 20000000000, 24414062500, 25000000000, 31250000000, 32000000000, 39062500000, 40000000000, 48828125000, 50000000000, 62500000000, 78125000000, 80000000000, 97656250000, 100000000000, 125000000000, 156250000000, 160000000000, 195312500000, 200000000000, 250000000000, 312500000000, 390625000000, 400000000000, 500000000000, 625000000000, 781250000000, 800000000000, 1000000000000, 1250000000000, 1562500000000, 2000000000000, 2500000000000, 3125000000000, 4000000000000, 5000000000000, 6250000000000, 10000000000000, 12500000000000, 20000000000000, 25000000000000, 50000000000000, 100000000000000

The sum of all its divisors, including itself, is 249,992,370,597,277.
It has an Euler totient of 40,000,000,000,000, and an aliquot sum of 149,992,370,597,277.
There are a total of 3,204,941,750,802 positive primes less than it.^[1]
Below is the list of basic calculations of 100,000,000,000,000:

	Multiplication <math>\scriptstyle{\text{100,000,000,000,000 }\times\text{ x}}</math>	Division <math>\scriptstyle{\text{100,000,000,000,000 }\div\text{ x}}</math>	Exponentiation <math>\scriptstyle{\text{100,000,000,000,000}^\text{x}}</math>	[[nth root\|Template:Mvarth root]] <math>\scriptstyle{\sqrt[\text{x}]{\text{100,000,000,000,000}}}</math>
2	200,000,000,000,000	50,000,000,000,000	10²⁸	10,000,000
3	300,000,000,000,000	33,333,333,333,333.Template:Overline	10⁴²	≈46,415.8883
4	400,000,000,000,000	25,000,000,000,000	10⁵⁶	≈3,162.2776
5	500,000,000,000,000	20,000,000,000,000	10⁷⁰	≈630.9573
6	600,000,000,000,000	16,666,666,666,666.Template:Overline	10⁸⁴	≈215.4434
7	700,000,000,000,000	14,285,714,285,714.Template:Overline	10⁹⁸	100
8	800,000,000,000,000	12,500,000,000,000	10¹¹²	≈56.2341
9	900,000,000,000,000	11,111,111,111,111.Template:Overline	10¹²⁶	≈35.9381
10	1,000,000,000,000,000	10,000,000,000,000	10¹⁴⁰	≈25.1188

Selected 15-digit numbers (100,000,000,000,001–999,999,999,999,999)

100,000,000,000,001 to 199,999,999,999,999

100,000,000,000,031 : smallest 15-digit prime number^[2]
100,000,012,392,316 : smallest 15-digit triangular number, 14,142,136th triangular number^[3]^[4]
100,169,256,075,517 : 202nd Markov number^[5]
106,974,698,806,081 : 203rd Markov number
111,111,111,111,111 : repunit
117,669,030,460,994 : 204th Markov number
127,353,146,734,466 : 205th Markov number
145,624,636,022,689 : 206th Markov number
148,135,740,183,017 : 207th Markov number
151,620,880,341,401 : 208th Markov number
180,995,342,924,521 : 209th Markov number
187,611,224,490,881 : 210th Markov number

200,000,000,000,000 to 299,999,999,999,999

217,774,440,785,026 : 211th Markov number
222,222,222,222,222 : repdigit
238,763,690,000,642 : 212th Markov number
262,229,286,072,101 : 213th Markov number
299,713,796,309,065 : 214th Markov number

300,000,000,000,000 to 399,999,999,999,999

308,061,521,170,129 : 215th Markov number
316,141,040,381,993 : 216th Markov number
332,380,318,337,465 : 217th Markov number
333,333,333,333,333 : repdigit
379,325,837,704,445 : 218th Markov number
381,249,713,544,034 : 219th Markov number

400,000,000,000,000 to 499,999,999,999,999

426,776,599,819,081 : 220th Markov number
444,444,444,444,444 : repdigit
459,789,046,174,429 : 221st Markov number
473,638,416,248,177 : 222nd Markov number

500,000,000,000,000 to 599,999,999,999,999

542,557,456,311,485 : 223rd Markov number
554,510,738,235,029 : 224th Markov number
555,555,555,555,555 : repdigit

600,000,000,000,000 to 699,999,999,999,999

666,666,666,666,666 : repdigit
668,746,232,531,714 : 225th Markov number
686,480,075,504,546 : 226th Markov number

700,000,000,000,000 to 799,999,999,999,999

767,465,181,141,553 : 227th Markov number
777,777,777,777,777 : repdigit

800,000,000,000,000 to 899,999,999,999,999

806,515,533,049,393 : 228th Markov number
867,493,136,119,153 : 229th Markov number
888,888,888,888,888 : repdigit

900,000,000,000,000 to 999,999,999,999,999

971,341,527,703,714 : 230th Markov number
998,123,312,425,769 : 231st Markov number
999,999,999,999,989 : largest 15-digit prime number^[6]
999,999,999,999,999 : largest 15-digit number, repdigit

References

Template:Large numbers Template:Integers Template:Portal bar

[A006880-1] Template:Cite OEIS

[A003617-2] Template:Cite OEIS

[A068093-3] Template:Cite OEIS

[A068092-4] Template:Cite OEIS

[A002559-5] Template:Cite OEIS

[A003618-6] Template:Cite OEIS

[1]

[2]

[3]

[4]

[5]

[6]

@@ Line 53: / Line 53: @@
 *'''100,000,000,000,031''' : smallest 15-digit [[prime number]]<ref name="A003617">{{Cite OEIS|A003617|Smallest n-digit prime}}</ref>
 *'''100,000,012,392,316''' : smallest 15-digit [[triangular number]], 14,142,136th triangular number<ref name="A068093">{{Cite OEIS|A068093|Smallest n-digit triangular number}}</ref><ref name="A068092">{{Cite OEIS|A068092|Index of smallest triangular number with n digits}}</ref>
+*'''100,169,256,075,517''' : 202nd [[Markov number]]<ref name="A002559">{{Cite OEIS|A002559|Markoff (or Markov) numbers}}</ref>
+*'''106,974,698,806,081''' : 203rd Markov number
 *'''111,111,111,111,111''' : [[repunit]]
+*'''117,669,030,460,994''' : 204th Markov number
+*'''127,353,146,734,466''' : 205th Markov number
+*'''145,624,636,022,689''' : 206th Markov number
+*'''148,135,740,183,017''' : 207th Markov number
+*'''151,620,880,341,401''' : 208th Markov number
+*'''180,995,342,924,521''' : 209th Markov number
+*'''187,611,224,490,881''' : 210th Markov number
 === 200,000,000,000,000 to 299,999,999,999,999 ===
-*'''202,222,222,222,222''' : [[repdigit]]
+*'''217,774,440,785,026''' : 211th Markov number
+*'''222,222,222,222,222''' : [[repdigit]]
+*'''238,763,690,000,642''' : 212th Markov number
+*'''262,229,286,072,101''' : 213th Markov number
+*'''299,713,796,309,065''' : 214th Markov number
 === 300,000,000,000,000 to 399,999,999,999,999 ===
+*'''308,061,521,170,129''' : 215th Markov number
+*'''316,141,040,381,993''' : 216th Markov number
+*'''332,380,318,337,465''' : 217th Markov number
 *'''333,333,333,333,333''' : repdigit
+*'''379,325,837,704,445''' : 218th Markov number
+*'''381,249,713,544,034''' : 219th Markov number
 === 400,000,000,000,000 to 499,999,999,999,999 ===
+*'''426,776,599,819,081''' : 220th Markov number
 *'''444,444,444,444,444''' : repdigit
+*'''459,789,046,174,429''' : 221st Markov number
+*'''473,638,416,248,177''' : 222nd Markov number
 === 500,000,000,000,000 to 599,999,999,999,999 ===
+*'''542,557,456,311,485''' : 223rd Markov number
+*'''554,510,738,235,029''' : 224th Markov number
 *'''555,555,555,555,555''' : repdigit
 === 600,000,000,000,000 to 699,999,999,999,999 ===
 *'''666,666,666,666,666''' : repdigit
+*'''668,746,232,531,714''' : 225th Markov number
+*'''686,480,075,504,546''' : 226th Markov number
 === 700,000,000,000,000 to 799,999,999,999,999 ===
+*'''767,465,181,141,553''' : 227th Markov number
 *'''777,777,777,777,777''' : repdigit
 === 800,000,000,000,000 to 899,999,999,999,999 ===
+*'''806,515,533,049,393''' : 228th Markov number
+*'''867,493,136,119,153''' : 229th Markov number
 *'''888,888,888,888,888''' : repdigit
 === 900,000,000,000,000 to 999,999,999,999,999 ===
+*'''971,341,527,703,714''' : 230th Markov number
+*'''998,123,312,425,769''' : 231st Markov number
 *'''999,999,999,999,989''' : largest 15-digit prime number<ref name="A003618">{{Cite OEIS|A003618|Largest n-digit prime}}</ref>
 *'''999,999,999,999,999''' : largest 15-digit number, repdigit