1,000,000,000,000

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

Etymology

The word trillion is borrowed from French trillion, which is from tri- ("three") + -illion. It can be abbreviated as tril, tln, tn, or simply t. Originally in British English, the word "trillion" referred to million million millions (while "billion" referred to million millions, which is equal to trillion in American English). However, to many people, the word refers to one thousand billion (1,000,000,000,000) in the present day.

Properties and usage

1,000,000,000,000 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 × 10¹² or 10¹² (1E+12 or simply 1E12 in E notation).
• It is the square of 1,000,000, the cube of 10,000, the fourth power of 1,000, and the sixth power of 100.
• It has a total of 169 divisors (156 even, 13 odd), whose geometric mean is 1,000,000. All divisors are displayed below:

<blockquote><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, 10000, 10240, 12500, 12800, 15625, 16000, 20000, 20480, 25000, 25600, 31250, 32000, 40000, 50000, 51200, 62500, 64000, 78125, 80000, 100000, 102400, 125000, 128000, 156250, 160000, 200000, 250000, 256000, 312500, 320000, 390625, 400000, 500000, 512000, 625000, 640000, 781250, 800000, 1000000, 1250000, 1280000, 1562500, 1600000, 1953125, 2000000, 2500000, 2560000, 3125000, 3200000, 3906250, 4000000, 5000000, 6250000, 6400000, 7812500, 8000000, 9765625, 10000000, 12500000, 12800000, 15625000, 16000000, 19531250, 20000000, 25000000, 31250000, 32000000, 39062500, 40000000, 48828125, 50000000, 62500000, 64000000, 78125000, 80000000, 97656250, 100000000, 125000000, 156250000, 160000000, 195312500, 200000000, 244140625, 250000000, 312500000, 320000000, 390625000, 400000000, 488281250, 500000000, 625000000, 781250000, 800000000, 976562500, 1000000000, 1250000000, 1562500000, 1600000000, 1953125000, 2000000000, 2500000000, 3125000000, 3906250000, 4000000000, 5000000000, 6250000000, 7812500000, 8000000000, 10000000000, 12500000000, 15625000000, 20000000000, 25000000000, 31250000000, 40000000000, 50000000000, 62500000000, 100000000000, 125000000000, 200000000000, 250000000000, 500000000000, 1000000000000</small></blockquote>

• The sum of all its divisors, including itself, is 2,499,694,822,171.
• It has an Euler totient of 400,000,000,000, and an aliquot sum of 1,499,694,822,171.
• There are a total of 37,607,912,018 positive primes less than it.
• Below is the list of basic calculations of 1,000,000,000,000:

In science

• For physical quantities, the metric prefix tera (symbol T) indicates 1,000,000,000,000 times the base unit. For example, 10¹² bits of data is called a terabit, 10¹² joules of energy is called a terajoule, and 10¹² watts of power is called a terawatt.
• The computing performance of 10¹² floating point operations per second is known as terascale computing. It is the performance of several supercomputers, such as NEC SX-4, Intel's ASCI Red, and iPhone 15 Pro September 2023 A17 Pro processor.

Sense of scale

Some comparisons below give a sense of how large 1,000,000,000,000 (10¹²) is, according to current evidence.

Time

• 10¹² seconds—a terasecond—is about 31 thousand years. Homo sapiens were living as 'hunter-gatherers' 10¹² seconds ago.
• 10¹² minutes (about 1.9 million years) ago, the human species Homo erectus was in existence.
• 10¹² hours (about 114 million years) ago, Late Cretaceous dinosaurs dominated the land, and giant squids thrived in the oceans.
• 10¹² days (about 2.74 billion years) ago, Earth was an alien world where only single-celled microorganisms existed.
• 10¹² months (about 83 billion years) ago, the universe itself did not exist, as it was created only 13.787 billion years ago. 10¹² months from now, the Moon may collide with the Earth or be torn apart to form an orbital ring, if both have not already been destroyed.
• 10¹² years—a teraannus—is 70 times the age of the universe.

Distance

• 10¹² inches is about 15 million miles (24 million kilometres), approximately 1/6th the distance from the Earth to the Sun.
• 10¹² metres (a terametre) is over six times the distance from the Earth to the Sun. It is the estimated diameter of Betelgeuse, a red supergiant star.
• 10¹² kilometres (a petametre) is about 1/10th a light-year.
• A light-year is approximately 5,878,600,000,000 miles.

Area

• 10¹² square inches is approximately the total area of Saint Lucia, an island country in the eastern Caribbean.
• 10¹² square feet is larger than the total area of Portugal.
• 10¹² square metres is approximately the total area of Ethiopia, the 26th largest country on Earth.
• 10¹² square kilometres is almost 2,000 times the Earth's total surface area.

Volume

• If 10¹² cubic metres of water were spread evenly over the Moon's surface, it would create a layer of water approximately 2.6 centimetres deep.
• 10¹² grains of sand would occupy a volume of about 0.5 cubic metres.

Economy

• Spain's GDP in 2024 is approximately $1.72 trillion.

Nature

• An average-sized mountain weighs about 10¹² kilograms.
• Andromeda Galaxy, Milky Way's neighbor, contains about 10¹² stars.
• It is estimated that there are around 2 trillion galaxies in the observable universe.
• There were around 3 trillion trees on Earth in 2015.
• Scientists have estimated that the number of fish in the ocean is around 3.5 trillion.
• The surface of the human body houses roughly 10¹² bacteria.

Selected 13-digit numbers (1,000,000,000,001–9,999,999,999,999)

1,000,000,000,001 to 1,999,999,999,999

• 1,000,000,000,039 : smallest 13-digit prime number
• 1,000,002,000,001 = 1000001², palindromic square
• 1,000,001,326,005 : smallest 13-digit triangular number, 1,414,214th triangular number
• 1,004,006,004,001 = 1002001² = 1001⁴, palindromic fourth power
• 1,061,520,150,601 = 1030301² = 10201³ = 101⁶
• 1,062,991,989,013 : number of square (0,1)-matrices without zero rows and with exactly 11 entries equal to 1
• 1,070,710,724,173 : 153rd Markov number
• 1,099,511,627,776 = 256⁵ = 16¹⁰ = 4²⁰ = 2⁴⁰, binary approximation of metric prefix tera
• 1,099,511,629,376 : Leyland number using 2 & 40 (2⁴⁰ + 40²)
• 1,099,511,787,776 : Leyland number using 4 & 20 (4²⁰ + 20⁴)
• 1,111,111,111,111 : repunit
• 1,124,388,064,800 : 67th superabundant number
• 1,125,000,750,000 : sum of first 1,500,000 natural numbers
• 1,141,246,682,444 = 2²ÃƒÂ—11¹¹
• 1,184,065,449,986 : 154th Markov number
• 1,202,590,842,879 : 35th Woodall number
• 1,226,280,710,981 : 15th alternating factorial
• 1,289,904,147,324 : 24th Catalan number
• 1,307,674,368,000 = 15!
• 1,307,674,368,120 : 15th factoriangular number
• 1,338,193,159,771 : number of posets with 14 unlabeled elements
• 1,373,119,300,369 : number of series-reduced planted trees with 45 nodes
• 1,419,855,914,607 : 38th Wedderburn-Etherington number
• 1,427,933,269,321 : 155th Markov number
• 1,466,024,067,850 : number of 48-bead necklaces (turning over is allowed) where complements are equivalent
• 1,489,877,926,680 : 5th 8-dimensional Catalan number
• 1,490,542,435,045 : 156th Markov number
• 1,497,207,322,930 : number of 47-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 1,499,694,822,171 : aliquot sum of 1,000,000,000,000
• 1,513,744,654,945 : 33rd Pell number, 157th Markov number
• 1,523,548,331,041 = 1234321² = 1111⁴
• 1,548,008,755,920 : 60th Fibonacci number
• 1,563,135,350,013 : number of (unordered, unlabeled) rooted trimmed trees with 36 nodes
• 1,618,362,158,587 : 19th Schröder–Hipparchus number
• 1,697,385,471,211 : 30th Motzkin number
• 1,706,111,387,068 : number of centered hydrocarbons with 37 carbon atoms
• 1,722,099,665,665 : 158th Markov number
• 1,915,868,454,737 : 159th Markov number
• 1,927,522,396,800 : 68th superabundant number
• 1,934,197,506,555 : 48th repfigit
• 1,961,990,553,600 = 24!!

2,000,000,000,000 to 2,999,999,999,999

• 2,000,001,000,000 : sum of first 2,000,000 natural numbers
• 2,076,871,684,802 : 160th Markov number
• 2,122,553,644,686 : number of secondary structures of RNA molecules with 35 nucleotides
• 2,135,248,790,338 : 161st Markov number
• 2,156,735,837,173 : 162nd Markov number
• 2,222,222,222,222 : repdigit
• 2,248,776,129,600 : 69th superabundant number, 18th superior highly composite number
• 2,262,366,343,746 : number of trees with 35 unlabeled nodes
• 2,473,901,162,495 : 36th Woodall number
• 2,499,694,822,171 : sum of all divisors of 1,000,000,000,000
• 2,504,730,781,961 : 61st Fibonacci number, 163rd Markov number
• 2,541,865,828,329 = 9¹³ = 3²⁶
• 2,541,865,845,905 : Leyland number using 3 & 26 (3²⁶ + 26³)
• 2,552,470,327,702 : Leyland number using 9 & 13 (9¹³ + 13⁹)
• 2,557,227,044,764 : number of free polyominoes with 25 cells
• 2,821,109,907,456 = 1679616² = 1296⁴ = 36⁸ = 6¹⁶
• 2,821,126,684,672 : Leyland number using 6 & 16 (6¹⁶ + 16⁶)
• 2,872,202,028,517 : number of 49-bead necklaces (turning over is allowed) where complements are equivalent
• 2,906,166,827,065 : number of series-reduced planted trees with 46 nodes
• 2,932,031,358,484 : number of 48-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 2,959,365,073,955 ~ 10^(3*π+3), rounded-up pi-illion

3,000,000,000,000 to 3,999,999,999,999

• 3,099,893,879,221 : 164th Markov number
• 3,125,001,250,000 : sum of first 2,500,000 natural numbers
• 3,204,941,750,802 : number of positive primes less than 10¹⁴
• 3,236,724,317,174 : 19th Schröder number
• 3,257,843,882,624 : 23rd telephone number
• 3,267,653,834,825 : 165th Markov number
• 3,333,333,333,333 : repdigit
• 3,373,164,194,400 : 70th superabundant number
• 3,389,524,479,050 : 39th Wedderburn-Etherington number
• 3,494,391,117,164 : number of signed trees with 22 nodes
• 3,512,479,453,921 = 1874161² = 1369⁴ = 37⁸
• 3,654,502,875,938 : 34th Pell number
• 3,809,950,977,008 : 16th logarithmic number
• 3,814,697,265,625 = 1953125² = 25⁹ = 5¹⁸
• 3,814,699,155,193 : Leyland number using 5 & 18 (5¹⁸ + 18⁵)
• 3,899,735,407,806 : number of (unordered, unlabeled) rooted trimmed trees with 37 nodes

4,000,000,000,000 to 4,999,999,999,999

• 4,052,739,537,881 : 62nd Fibonacci number
• 4,360,711,162,037 : 166th Markov number
• 4,444,444,444,444 : repdigit
• 4,492,268,106,137 : number of centered hydrocarbons with 38 carbon atoms
• 4,497,552,259,200 : 71st superabundant number
• 4,500,001,500,000 : sum of first 3,000,000 natural numbers
• 4,508,515,437,145 : 167th Markov number
• 4,643,961,467,965 : 168th Markov number
• 4,658,179,125,600 : 72nd superabundant number
• 4,747,561,509,943 = 16807³ = 343⁵ = 7¹⁵
• 4,747,732,369,318 : Leyland number using 7 & 15 (7¹⁵ + 15⁷)
• 4,859,761,676,391 : 31st Motzkin number
• 4,861,946,401,452 : 25th Catalan number

5,000,000,000,000 to 5,999,999,999,999

• 5,085,241,278,463 : 37th Woodall number
• 5,336,735,929,371 : number of secondary structures of RNA molecules with 36 nucleotides
• 5,528,778,008,357 : 169th Markov number
• 5,555,555,555,555 : repdigit
• 5,587,637,513,705 : 170th Markov number
• 5,629,516,646,996 : number of 50-bead necklaces (turning over is allowed) where complements are equivalent
• 5,744,387,279,818 : number of 49-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 5,832,742,205,057 : 19th Bell number

6,000,000,000,000 to 6,999,999,999,999

• 6,073,061,476,032 : self-descriptive number in base 12
• 6,125,001,750,000 : sum of first 3,500,000 natural numbers
• 6,155,434,522,614 : number of series-reduced planted trees with 47 nodes
• 6,226,306,037,178 : number of trees with 36 unlabeled nodes
• 6,557,470,319,842 : 63rd Fibonacci number, 171st Markov number
• 6,666,666,666,666 : repdigit
• 6,746,328,388,800 : 73rd superabundant number
• 6,963,472,309,248 : 4th taxicab number

7,000,000,000,000 to 7,999,999,999,999

• 7,163,627,708,162 : 172nd Markov number
• 7,420,738,134,810 : 12th primorial
• 7,625,597,484,987 = 19683³ = 27⁹ = 3²⁷ = 3^3³ = ³3, megafugathree
• 7,625,597,504,670 : Leyland number using 3 & 27 (3²⁷ + 27³)
• 7,777,777,777,777 : repdigit
• 7,905,853,580,625 = 25!!

8,000,000,000,000 to 8,999,999,999,999

• 8,000,002,000,000 : sum of first 4,000,000 natural numbers
• 8,099,766,813,570 : 40th Wedderburn-Etherington number
• 8,115,549,747,397 : 173rd Markov number
• 8,649,755,859,375 = 15¹¹
• 8,756,963,649,152 : 49th repfigit
• 8,759,309,660,445 : 20th Schröder–Hipparchus number
• 8,822,750,406,821 : 35th Pell number, 174th Markov number
• 8,888,888,888,888 : repdigit
• 8,916,100,448,256 = 2985984² = 20736³ = 144⁶ = 12¹²

9,000,000,000,000 to 9,999,999,999,999

• 9,210,000,001,000 : 10th autobiographical number
• 9,316,358,251,200 : 74th superabundant number
• 9,460,730,472,581 : rounded-up length of a light-year in kilometres
• 9,739,810,110,758 : number of (unordered, unlabeled) rooted trimmed trees with 38 nodes
• 9,787,184,545,081 : 175th Markov number
• 9,918,212,890,625 : 24th 1-automorphic number
• 9,925,594,216,162 : 176th Markov number
• 9,999,088,822,075 : number of free polyominoes with 26 cells
• 9,999,999,999,971 : largest 13-digit prime number
• 9,999,999,999,999 : largest 13-digit number, repdigit

See also

• Long and short scales
• Names of large numbers
• Orders of magnitude (numbers)
• Power of 10

References