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{{Portal|Mathematics}}
{{Portal|Mathematics}}
'''100,000,000,000,000''' ('''hundred trillion''' on the short scale; '''hundred billion''' on the long scale; hundred thousand [[1,000,000,000|billion]]; hundred million [[1,000,000|million]]) is the [[natural number]] following [[10,000,000,000,000#99,000,000,000,000 to 99,999,999,999,999|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.
'''100,000,000,000,000''' ('''hundred trillion''' on the short scale;<ref name=":1">{{Cite web |title=100000000000000 (Number) |url=https://metanumbers.com/100000000000000 |access-date=2026-09-27 |website=metanumbers.com |language=en}}</ref> '''hundred billion''' on the long scale; hundred thousand [[1,000,000,000|billion]]; hundred million [[1,000,000|million]]) is the [[natural number]] following [[10,000,000,000,000#99,000,000,000,000 to 99,999,999,999,999|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.
 
== In mathematics ==
 
=== Divisors ===
100,000,000,000,000 has a total of 225 [[divisor]]s (210 even, 15 odd). All divisors are displayed below:<ref name=":1" />
:<small>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</small>


== Selected 15-digit numbers (100,000,000,000,001–999,999,999,999,999) ==
== 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 ===
=== 100,000,000,000,001 to 199,999,999,999,999 ===
*'''100,000,000,000,031''' : smallest 15-digit [[prime number]]<ref name="A003617">{{Cite OEIS|A003617|Smallest n-digit prime}}</ref>
*'''100,000,000,000,031''' : smallest 15-digit [[prime number]]<ref name="A003617">{{Cite OEIS|A003617|Smallest n-digit prime}}</ref><ref>{{Cite web |last=Weisstein |first=Eric W. |title=Next Prime |url=https://mathworld.wolfram.com/NextPrime.html |access-date=2026-09-27 |website=mathworld.wolfram.com |publisher=Wolfram Research, Inc. |language=en}}</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>
*'''100,000,012,392,316''' : smallest 15-digit [[triangular number]], 14,142,136th triangular number<ref>{{cite web |last=Gupta |first=Shyam Sunder |date=2002-10-26 |title=Fascinating Triangular Numbers |url=https://www.shyamsundergupta.com/triangle.htm |website=shyamsundergupta.com |access-date=2026-09-26}}</ref><ref>{{Cite web |last=Samojluk |first=Artur |last2=Siemaszko |first2=Artur |date=2026-06-30 |title=An Efficient Algorithm for Estimating Prime Counts |url=https://arxiv.org/abs/2606.31761v2 |access-date=2026-09-27 |website=arXiv.org |language=en}}</ref>
*'''100,169,256,075,517''' : 202nd [[Markov number]]<ref name="A002559">{{Cite OEIS|A002559|Markoff (or Markov) numbers}}</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
*'''106,974,698,806,081''' : 203rd Markov number
Line 45: Line 45:
*'''195,643,523,275,200''' : 84th superabundant number, 20th [[superior highly composite number]]<ref name=A002201>{{Cite OEIS|A002201|Superior highly composite numbers}}</ref>
*'''195,643,523,275,200''' : 84th superabundant number, 20th [[superior highly composite number]]<ref name=A002201>{{Cite OEIS|A002201|Superior highly composite numbers}}</ref>
=== 200,000,000,000,000 to 299,999,999,999,999 ===
=== 200,000,000,000,000 to 299,999,999,999,999 ===
*'''213,458,046,676,875''' = 27[[double factorial|!!]]
*'''213,458,046,676,875''' = 27[[double factorial|!!]]. There are 213,458,046,676,875 total [[unrooted tree]]s for 16 [[taxa]]<ref>{{Cite web |last=Kong |first=Yibo |last2=Tiley |first2=George P. |last3=Solis-Lemus |first3=Claudia |date=2023-12-26 |title=Unsupervised Learning of Phylogenetic Trees via Split-Weight Embedding |url=https://arxiv.org/abs/2312.16074v2 |access-date=2026-09-27 |website=arXiv.org |language=en}}</ref><ref>{{cite journal |last1=Perretto |first1=Mauricio |last2=Lopes |first2=Heitor Silvério |date=2005-09-30 |title=Reconstruction of phylogenetic trees using the ant colony optimization paradigm |url=http://silverio.net.br/heitor/publicacoes/2005/gmr43.pdf |journal=Genetics and Molecular Research |volume=4 |issue=3 |pages=581–589 |issn=1676-5680}}</ref>
*'''215,440,028,338,359''' : number of secondary structures of RNA molecules with 40 nucleotides<ref name=A004148>{{Cite OEIS|A004148|Generalized Catalan numbers}}</ref>
*'''215,440,028,338,359''' : number of secondary structures of RNA molecules with 40 nucleotides<ref name=A004148>{{Cite OEIS|A004148|Generalized Catalan numbers}}</ref>
*'''217,774,440,785,026''' : 211th Markov number
*'''217,774,440,785,026''' : 211th Markov number
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*'''288,807,105,787,200''' : 85th superabundant number
*'''288,807,105,787,200''' : 85th superabundant number
*'''299,713,796,309,065''' : 214th Markov number, 39th Pell number
*'''299,713,796,309,065''' : 214th Markov number, 39th Pell number
=== 300,000,000,000,000 to 399,999,999,999,999 ===
=== 300,000,000,000,000 to 399,999,999,999,999 ===
*'''308,061,521,170,129''' : 215th Markov number, 71st Fibonacci number
*'''308,061,521,170,129''' : 215th Markov number, 71st Fibonacci number
*'''314,159,265,358,979''' : the first 15 decimal digits of [[pi]]<ref>{{Cite journal |last=Galperin |first=G. |date=2003 |title=Playing Pool With π (The number π from a billard point of view) |url=http://rcd.ics.org.ru/RD2003v008n04ABEH000252 |journal=Regular and Chaotic Dynamics |language=en |volume=8 |issue=4 |pages=375 |doi=10.1070/RD2003v008n04ABEH000252 |issn=1560-3547}}</ref><ref>{{cite OEIS|A011545|a(n) is the integer whose decimal digits are the first n+1 decimal digits of Pi}}</ref>
*'''316,141,040,381,993''' : 216th Markov number
*'''316,141,040,381,993''' : 216th Markov number
*'''321,685,824,284,100''' : number of 56-bead necklaces (turning over is allowed) where complements are equivalent
*'''321,685,824,284,100''' : number of 56-bead necklaces (turning over is allowed) where complements are equivalent
Line 74: Line 76:
*'''381,249,713,544,034''' : 219th Markov number
*'''381,249,713,544,034''' : 219th Markov number
*'''382,745,902,953,654''' : number of (unordered, unlabeled) rooted trimmed trees with 42 nodes
*'''382,745,902,953,654''' : number of (unordered, unlabeled) rooted trimmed trees with 42 nodes
=== 400,000,000,000,000 to 499,999,999,999,999 ===
=== 400,000,000,000,000 to 499,999,999,999,999 ===
*'''426,776,599,819,081''' : 220th Markov number
*'''426,776,599,819,081''' : 220th Markov number
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*'''971,341,527,703,714''' : 230th Markov number
*'''971,341,527,703,714''' : 230th Markov number
*'''998,123,312,425,769''' : 231st 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>
*'''999,999,999,999,989''' : largest 15-digit prime number<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Previous Prime |url=https://mathworld.wolfram.com/PreviousPrime.html |access-date=2026-09-27 |website=mathworld.wolfram.com |publisher=Wolfram Research, Inc. |language=en}}</ref><ref name="A003618">{{Cite OEIS|A003618|Largest n-digit prime}}</ref>
*'''999,999,999,999,999''' : largest 15-digit number, repdigit
*'''999,999,999,999,999''' : largest 15-digit number, repdigit


Revision as of 21:59, 1 October 2026

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Portal Mathematics portal


100,000,000,000,000 (hundred trillion on the short scale;[1] 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.

In mathematics

Divisors

100,000,000,000,000 has a total of 225 divisors (210 even, 15 odd). All divisors are displayed below:[1]

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

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][3]
  • 100,000,012,392,316 : smallest 15-digit triangular number, 14,142,136th triangular number[4][5]
  • 100,169,256,075,517 : 202nd Markov number[6]
  • 106,974,698,806,081 : 203rd Markov number
  • 111,111,111,111,111 : repunit
  • 111,146,809,165,122 : 43rd Wedderburn-Etherington number[7]
  • 114,988,706,524,270 : 34th Motzkin number[8]
  • 117,669,030,460,994 : 204th Markov number, 69th Fibonacci number
  • 120,984,833,091,531 : 53rd repfigit[9]
  • 124,145,519,261,542 : 38th Pell number[10]
  • 124,738,635,483,875 : number of series-reduced planted trees with 51 nodes[11]
  • 127,353,146,734,466 : 205th Markov number
  • 130,429,015,516,800 : 82nd superabundant number[12]
  • 144,403,552,893,600 : 83rd superabundant 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
  • 152,657,555,033,144 : number of (unordered, unlabeled) rooted trimmed trees with 41 nodes[13]
  • 163,767,326,286,012 : number of 55-bead necklaces (turning over is allowed) where complements are equivalent[14]
  • 166,799,988,689,300 : number of 54-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[15]
  • 180,995,342,924,521 : 209th Markov number
  • 184,717,953,466,367 : 42nd Woodall number[16]
  • 187,611,224,490,881 : 210th Markov number
  • 190,392,490,709,135 : 70th Fibonacci number
  • 195,643,523,275,200 : 84th superabundant number, 20th superior highly composite number[17]

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

  • 213,458,046,676,875 = 27!!. There are 213,458,046,676,875 total unrooted trees for 16 taxa[18][19]
  • 215,440,028,338,359 : number of secondary structures of RNA molecules with 40 nucleotides[20]
  • 217,774,440,785,026 : 211th Markov number
  • 222,222,222,222,222 : repdigit
  • 238,763,690,000,642 : 212th Markov number
  • 259,215,937,709,463 : 22nd Schröder–Hipparchus number[21]
  • 259,918,212,890,625 : 27th automorphic number[22]
  • 262,229,286,072,101 : 213th Markov number
  • 263,747,951,750,360 : 28th Catalan number[23]
  • 265,077,991,831,995 : number of series-reduced planted trees with 52 nodes
  • 266,552,682,265,118 : 44th Wedderburn-Etherington number
  • 270,585,509,032,586 : 54th repfigit
  • 288,807,105,787,200 : 85th superabundant number
  • 299,713,796,309,065 : 214th Markov number, 39th Pell number

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

  • 308,061,521,170,129 : 215th Markov number, 71st Fibonacci number
  • 314,159,265,358,979 : the first 15 decimal digits of pi[24][25]
  • 316,141,040,381,993 : 216th Markov number
  • 321,685,824,284,100 : number of 56-bead necklaces (turning over is allowed) where complements are equivalent
  • 327,534,518,354,296 : number of 55-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
  • 330,931,069,469,828 : 35th Motzkin number
  • 332,380,318,337,465 : 217th Markov number
  • 333,333,333,333,333 : repdigit
  • 335,990,918,918,981 : 17th alternating factorial[26]
  • 355,687,428,096,000 = 17!
  • 355,687,428,096,153 : 17th factoriangular number[27]
  • 378,231,999,954,943 : 43rd Woodall number
  • 379,325,837,704,445 : 218th Markov number
  • 381,249,713,544,034 : 219th Markov number
  • 382,745,902,953,654 : number of (unordered, unlabeled) rooted trimmed trees with 42 nodes

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

  • 426,776,599,819,081 : 220th Markov number
  • 433,210,658,680,800 : 86th superabundant number
  • 444,444,444,444,444 : repdigit
  • 459,789,046,174,429 : 221st Markov number
  • 473,638,416,248,177 : 222nd Markov number
  • 498,454,011,879,264 : 72nd Fibonacci number

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

  • 542,557,456,311,485 : 223rd Markov number
  • 544,288,586,926,914 : number of secondary structures of RNA molecules with 41 nucleotides
  • 554,510,738,235,029 : 224th Markov number
  • 555,555,555,555,555 : repdigit
  • 563,637,117,190,957 : number of series-reduced planted trees with 53 nodes
  • 577,614,211,574,400 : 87th superabundant number

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

  • 632,084,292,449,766 : number of 57-bead necklaces (turning over is allowed) where complements are equivalent
  • 639,754,054,803,187 : 45th Wedderburn-Etherington number
  • 643,371,380,132,744 : number of 56-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
  • 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

  • 723,573,111,879,672 : 40th Pell number
  • 740,081,787,109,376 : 28th automorphic number
  • 754,788,753,590,897 : 55th repfigit
  • 767,465,181,141,553 : 227th Markov number
  • 774,056,185,954,303 : 44th Woodall 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, 73rd Fibonacci number
  • 866,421,317,361,600 : 88th superabundant 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

  • 953,467,954,114,363 : 36th Motzkin number, largest known Motzkin prime
  • 960,445,232,762,244 : number of (unordered, unlabeled) rooted trimmed trees with 43 nodes
  • 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[28][29]
  • 999,999,999,999,999 : largest 15-digit number, repdigit

See also

References

  1. ↑ 1.0 1.1 "100000000000000 (Number)" (in en). https://metanumbers.com/100000000000000. 
  2. ↑ Template:Cite OEIS
  3. ↑ Weisstein, Eric W.. "Next Prime" (in en). Wolfram Research, Inc.. https://mathworld.wolfram.com/NextPrime.html. 
  4. ↑ Gupta, Shyam Sunder (2002-10-26). "Fascinating Triangular Numbers". https://www.shyamsundergupta.com/triangle.htm. 
  5. ↑ Samojluk, Artur; Siemaszko, Artur (2026-06-30). "An Efficient Algorithm for Estimating Prime Counts" (in en). https://arxiv.org/abs/2606.31761v2. 
  6. ↑ Template:Cite OEIS
  7. ↑ Template:Cite OEIS
  8. ↑ Template:Cite OEIS
  9. ↑ Template:Cite OEIS
  10. ↑ Template:Cite OEIS
  11. ↑ Template:Cite OEIS
  12. ↑ Template:Cite OEIS
  13. ↑ Template:Cite OEIS
  14. ↑ Template:Cite OEIS
  15. ↑ Template:Cite OEIS
  16. ↑ Template:Cite OEIS
  17. ↑ Template:Cite OEIS
  18. ↑ Kong, Yibo; Tiley, George P.; Solis-Lemus, Claudia (2023-12-26). "Unsupervised Learning of Phylogenetic Trees via Split-Weight Embedding" (in en). https://arxiv.org/abs/2312.16074v2. 
  19. ↑ Perretto, Mauricio; Lopes, Heitor Silvério (2005-09-30). "Reconstruction of phylogenetic trees using the ant colony optimization paradigm". Genetics and Molecular Research 4 (3): 581–589. ISSN 1676-5680. http://silverio.net.br/heitor/publicacoes/2005/gmr43.pdf. 
  20. ↑ Template:Cite OEIS
  21. ↑ Template:Cite OEIS
  22. ↑ Template:Cite OEIS
  23. ↑ Template:Cite OEIS
  24. ↑ Galperin, G. (2003). "Playing Pool With π (The number π from a billard point of view)" (in en). Regular and Chaotic Dynamics 8 (4): 375. doi:10.1070/RD2003v008n04ABEH000252. ISSN 1560-3547. http://rcd.ics.org.ru/RD2003v008n04ABEH000252. 
  25. ↑ Template:Cite OEIS
  26. ↑ Template:Cite OEIS
  27. ↑ Template:Cite OEIS
  28. ↑ Weisstein, Eric W.. "Previous Prime" (in en). Wolfram Research, Inc.. https://mathworld.wolfram.com/PreviousPrime.html. 
  29. ↑ Template:Cite OEIS

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