10,000,000,000,000

10000000000000
CardinalTen trillion (short scale)
Ten billion (long scale)
Ten thousand billion
Ten million million
Ordinal10000000000000th (ten trillionth, short scale)
Factorization
  • 213
  • 513
Divisors196 total
Greek numeral
Roman numeralN/A, n/a
Binary100100011000010011100111001010100000000000002
Ternary10221012222020120200202111013
Senary331335341450241446
Octal2214116345200008
Duodecimal115609792505412
Hexadecimal9184E72A00016
Arabic١٠٠٠٠٠٠٠٠٠٠٠٠٠
Bengali১০০০০০০০০০০০০০
Devanagari१०००००००००००००
Khmer១០០០០០០០០០០០០០
Tamilக௦௦௦௦௦௦௦௦௦௦௦௦௦
Thai๑๐๐๐๐๐๐๐๐๐๐๐๐๐ (สิบล้านล้าน)

10,000,000,000,000 (ten trillion on the short scale; ten billion on the long scale; ten thousand billion; ten million million) is the natural number following 9,999,999,999,999 and preceding 10,000,000,000,001. It is known as 10000 arab, 100 kharab, 10 lakh crore, or 1 nil in the Indian numbering system.

Properties and usage

10,000,000,000,000 has the following properties and usage:

In mathematics

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, 20000, 20480, 25000, 25600, 31250, 32000, 40000, 40960, 50000, 51200, 62500, 64000, 78125, 80000, 100000, 102400, 125000, 128000, 156250, 160000, 200000, 204800, 250000, 256000, 312500, 320000, 390625, 400000, 500000, 512000, 625000, 640000, 781250, 800000, 1000000, 1024000, 1250000, 1280000, 1562500, 1600000, 1953125, 2000000, 2500000, 2560000, 3125000, 3200000, 3906250, 4000000, 5000000, 5120000, 6250000, 6400000, 7812500, 8000000, 9765625, 10000000, 12500000, 12800000, 15625000, 16000000, 19531250, 20000000, 25000000, 25600000, 31250000, 32000000, 39062500, 40000000, 48828125, 50000000, 62500000, 64000000, 78125000, 80000000, 97656250, 100000000, 125000000, 128000000, 156250000, 160000000, 195312500, 200000000, 244140625, 250000000, 312500000, 320000000, 390625000, 400000000, 488281250, 500000000, 625000000, 640000000, 781250000, 800000000, 976562500, 1000000000, 1220703125, 1250000000, 1562500000, 1600000000, 1953125000, 2000000000, 2441406250, 2500000000, 3125000000, 3200000000, 3906250000, 4000000000, 4882812500, 5000000000, 6250000000, 7812500000, 8000000000, 9765625000, 10000000000, 12500000000, 15625000000, 16000000000, 19531250000, 20000000000, 25000000000, 31250000000, 39062500000, 40000000000, 50000000000, 62500000000, 78125000000, 80000000000, 100000000000, 125000000000, 156250000000, 200000000000, 250000000000, 312500000000, 400000000000, 500000000000, 625000000000, 1000000000000, 1250000000000, 2000000000000, 2500000000000, 5000000000000, 10000000000000

  • The sum of all its divisors, including itself, is 24,998,474,116,998.
  • It has an Euler totient of 4,000,000,000,000, and an aliquot sum of 14,998,474,116,998.
  • There are a total of 346,065,536,839 positive primes less than it.[1]
  • Below is the list of basic calculations of 10,000,000,000,000:
Multiplication
Division
Exponentiation
nth root

2 20,000,000,000,000 5,000,000,000,000 1026 ≈3,162,277.6602
3 30,000,000,000,000 3,333,333,333,333.3 1039 ≈21,544.3469
4 40,000,000,000,000 2,500,000,000,000 1052 ≈1,778.2794
5 50,000,000,000,000 2,000,000,000,000 1065 ≈398.1072
6 60,000,000,000,000 1,666,666,666,666.6 1078 ≈146.7799
7 70,000,000,000,000 1,428,571,428,571.428571 1091 ≈71.9686
8 80,000,000,000,000 1,250,000,000,000 10104 ≈42.1697
9 90,000,000,000,000 1,111,111,111,111.1 10117 ≈27.8256
10 100,000,000,000,000 1,000,000,000,000 10130 ≈19.9526

In economy

10 trillion Zimbabwean Dollars (2008)

Selected 14-digit numbers (10,000,000,000,001–99,999,999,999,999)

10,000,000,000,001 to 19,999,999,999,999

  • 10,000,000,000,037 : smallest 14-digit prime number[2]
  • 10,000,002,437,316 : smallest 14-digit triangular number, 4,472,136th triangular number[3][4]
  • 10,153,507,819,457 : 177th Markov number[5]
  • 10,445,360,463,871 : 38th Woodall number[6]
  • 10,610,209,857,723 : 64th Fibonacci number
  • 11,038,251,159,312 : number of 51-bead necklaces (turning over is allowed) where complements are equivalent[7]
  • 11,111,111,111,111 : repunit
  • 11,258,999,739,560 : number of 50-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[8]
  • 13,046,940,568,625 : number of series-reduced planted trees with 48 nodes[9]
  • 13,432,403,613,621 : number of secondary structures of RNA molecules with 37 nucleotides[10]
  • 13,933,569,346,707 : 32nd Motzkin number[11]
  • 13,974,537,376,800 : 75th superabundant number[12]
  • 14,173,019,355,266 : 178th Markov number
  • 14,235,090,298,445 : 179th Markov number
  • 14,622,039,889,385 : 180th Markov number
  • 15,988,960,048,321 : 181st Markov number
  • 17,167,680,177,565 : 65th Fibonacci number, 182nd Markov number
  • 18,367,353,072,152 : 26th Catalan number[13]
  • 18,632,716,502,400 : 76th superabundant number
  • 18,696,424,380,481 : 183rd Markov number
  • 19,374,186,136,140 : 41st Wedderburn-Etherington number[14]
  • 19,696,509,177,019 : 16th alternating factorial[15]

20,000,000,000,000 to 29,999,999,999,999

  • 20,922,789,888,000 = 16!
  • 20,922,789,888,136 : 16th factoriangular number[16]
  • 21,246,581,423,810 : 184th Markov number
  • 21,300,003,689,580 : 36th Pell number[17]
  • 21,440,476,741,631 : 39th Woodall number
  • 21,651,955,485,304 : number of 52-bead necklaces (turning over is allowed) where complements are equivalent
  • 22,076,468,764,192 : number of 51-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
  • 22,222,222,222,222 : repdigit
  • 22,592,065,572,301 : 185th Markov number
  • 24,351,056,611,103 : number of (unordered, unlabeled) rooted trimmed trees with 39 nodes[18]
  • 26,500,373,448,281 : 186th Markov number
  • 27,673,060,569,305 : number of series-reduced planted trees with 49 nodes
  • 27,777,890,035,288 : 66th Fibonacci number
  • 27,949,074,753,600 : 77th superabundant number

30,000,000,000,000 to 39,999,999,999,999

  • 30,901,824,368,813 : 187th Markov number
  • 31,801,503,090,601 : 188th Markov number
  • 32,607,253,879,200 : 78th superabundant number
  • 33,333,333,333,333 : repdigit
  • 33,843,022,209,066 : number of secondary structures of RNA molecules with 38 nucleotides
  • 36,332,699,889,481 : 189th Markov number
  • 38,596,477,083,550 : number of square (0,1)-matrices without zero rows and with exactly 12 entries equal to 1[19]

40,000,000,000,000 to 49,999,999,999,999

  • 40,002,464,776,083 : 33rd Motzkin number
  • 40,081,787,109,376 : 25th automorphic number[20]
  • 42,486,822,491,890 : number of 53-bead necklaces (turning over is allowed) where complements are equivalent
  • 43,303,843,861,744 : number of 52-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
  • 43,520,999,798,747 : 50th repfigit[21]
  • 43,980,465,111,039 : 40th Woodall number
  • 44,444,444,444,444 : repdigit
  • 44,945,570,212,853 : 67th Fibonacci number, 190th Markov number
  • 46,127,828,641,049 : 191st Markov number
  • 46,384,328,517,112 : 42nd Wedderburn-Etherington number
  • 47,574,827,600,981 : 21st Schröder–Hipparchus number[22]
  • 48,795,987,025,021 : 192nd Markov number

50,000,000,000,000 to 59,999,999,999,999

  • 51,011,754,393,600 = 26!!
  • 51,422,757,785,981 : 37th Pell number, 193rd Markov number
  • 55,555,555,555,555 : repdigit
  • 55,898,149,507,200 : 79th superabundant number
  • 57,850,602,535,042 : 194th Markov number
  • 58,734,306,828,191 : number of series-reduced planted trees with 50 nodes
  • 59,918,212,890,625 : 26th automorphic number

60,000,000,000,000 to 69,999,999,999,999

  • 60,941,642,779,903 : number of (unordered, unlabeled) rooted trimmed trees with 40 nodes
  • 65,082,055,350,517 : 195th Markov number
  • 65,214,507,758,400 : 80th superabundant number, 19th superior highly composite number[23]
  • 66,666,666,666,666 : repdigit
  • 67,082,333,460,610 : 196th Markov number
  • 68,275,077,901,156 : number of posets with 15 unlabeled elements[24]
  • 69,533,550,916,004 : 27th Catalan number

70,000,000,000,000 to 79,999,999,999,999

  • 72,723,460,248,141 : 68th Fibonacci number
  • 73,224,462,646,361 : 197th Markov number
  • 74,596,893,730,427 : 51th repfigit
  • 77,777,777,777,777 : repdigit

80,000,000,000,000 to 89,999,999,999,999

  • 80,902,026,460,669 : 198th Markov number
  • 82,561,235,448,866 : 199th Markov number
  • 83,400,061,453,514 : number of 54-bead necklaces (turning over is allowed) where complements are equivalent
  • 84,973,577,874,916 : number of 53-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
  • 85,349,327,734,485 : number of secondary structures of RNA molecules with 39 nucleotides
  • 88,888,888,888,888 : repdigit

90,000,000,000,000 to 99,999,999,999,999

  • 90,159,953,477,631 : 41st Woodall number
  • 93,139,301,545,921 : 200th Markov number
  • 97,295,849,958,669 : 52nd repfigit
  • 97,568,760,404,309 : 201st Markov number
  • 97,821,761,637,600 : 81st superabundant number
  • 99,999,999,999,973 : largest 14-digit prime number[25]
  • 99,999,999,999,999 : largest 14-digit number, repdigit

See also

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A006880 (Number of primes less than 10^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A003617 (Smallest n-digit prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A068093 (Smallest n-digit triangular number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A068092 (Index of smallest triangular number with n digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall (or Riesel) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A000013 (Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A001678 (Number of series-reduced planted trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A004148 (Generalized Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. ^ Sloane, N. J. A. (ed.). "Sequence A004394 (Superabundant [or super-abundant] numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ^ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  15. ^ Sloane, N. J. A. (ed.). "Sequence A005165 (Alternating factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^ Sloane, N. J. A. (ed.). "Sequence A101292". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^ Sloane, N. J. A. (ed.). "Sequence A002955 (Number of (unordered, unlabeled) rooted trimmed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A122400 (Number of square (0,1)-matrices without zero rows and with exactly n entries equal to 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A003226 (Automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^ Sloane, N. J. A. (ed.). "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  22. ^ Sloane, N. J. A. (ed.). "Sequence A001003 (Schroeder's second problem (generalized parentheses))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  23. ^ Sloane, N. J. A. (ed.). "Sequence A002201 (Superior highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A000112 (Number of partially ordered sets ("posets") with n unlabeled elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  25. ^ Sloane, N. J. A. (ed.). "Sequence A003618 (Largest n-digit prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.