This article is about the natural number (and other integers between 10,000 and 19,999). For other uses, see
10,000 (disambiguation) .
Natural number
10,000 (ten thousand ) is the natural number following 9,999 and preceding 10,001.
Many languages have a specific word for this number: in Ancient Greek it is μύριοι (the etymological root of the word myriad in English ), in Aramaic ܪܒܘܬܐ , in Hebrew רבבה [revava ], in Chinese 萬/万 (Mandarin wàn , Cantonese maan6 , Hokkien bān ), in Japanese 万/萬 [man ], in Khmer ម៉ឺន [meun ], in Korean 만/萬 [man ], in Russian тьма [t'ma ], in Vietnamese vạn , in Sanskrit अयुत [ayuta ], in Thai หมื่น [meun ], in Malayalam പതിനായിരം [patinayiram ], and in Malagasy alina .[ 1] In many of these languages, it often denotes a very large but indefinite number .[ 2]
The classical Greeks used letters of the Greek alphabet to represent Greek numerals : they used a capital letter mu (Μ) to represent ten thousand.[citation needed ] This Greek root was used in early versions of the metric system in the form of the decimal prefix myria- .[ 3]
Depending on the country, the number ten thousand is usually written as 10,000 (including in the UK and US), 10.000, or 10 000.[ 4]
In scientific notation it is written as 104 or 1 E+4 (equivalently 1 E4 ) in E notation .
It is the square of 100 and the square root of 100,000,000 .
The value of a myriad to the power of itself, 1000010000 = 1040000 .
It has a total of 25 divisors , whose geometric mean is a whole number , 100 (the number of primes below this value is 25).[ 5]
It has a reduced totient of 500 , and a totient of 4,000 , with a total of 16 integers having a totient value of 10,000.[ 6] [ 7]
There are a total of 1,229 prime numbers less than ten thousand, a count that is itself prime.[ 5] [ 8]
A myriagon is a polygon with ten thousand edges and a total of 25 dihedral symmetry groups when including the myriagon itself, alongside 25 cyclic groups as subgroups .[ 9]
In astronomy ,
In climate , Summary of 10000 Years is one of several pages of the Climate Timeline Tool: Exploring Weather & Climate Change Through the Powers of 10 sponsored by the National Climatic Data Center of the National Oceanic & Atmospheric Administration .[ 10]
In computing ,
In geography ,
In physics ,
Myria- (and myrio- )[ 15] [ 16] [ 17] is an obsolete metric prefix that denoted a factor of 10+4 , ten thousand , or 10,000 .
10,000 hertz , 10 kilohertz , or 10 kHz of the radio frequency spectrum falls in the very low frequency or VLF band and has a wavelength of 30 kilometres.
In orders of magnitude (speed) , the speed of a fast neutron is 10000 km/s .
In acoustics , 10,000 hertz , 10 kilohertz , or 10 kHz of a sound signal at sea level has a wavelength of about 34 mm.
In music , a 10 kilohertz sound is a E♭9 in the A440 pitch standard , a bit more than an octave higher in pitch than the highest note on a standard piano.
In currency,
In distances,
10 km, 10,000 m, or 1 E+4 m is equal to:
In finance, on March 29, 1999, the Dow Jones Industrial Average closed at 10006.78, which was the first time the index closed above the 10,000 mark.
In futurology , Stewart Brand in Visions of the Future: The 10,000-Year Library proposes a museum built around a 10,000-year clock as an idea for assuring that vital information survives future crashes of civilizations.[ 20]
In games,
Ten Thousand is one name of a dice game called farkle .
In game shows, The $10,000 Pyramid ran on television from 1973 to 1974.
In history,
Army of 10,000 Mississippi American Civil War military unit, 1861–1862.[ 21]
The Army of the Ten Thousand were a group of Ancient Greek mercenaries who marched against Artaxerxes II of Persia .
The Persian Immortals were also called the Ten Thousand or 10,000 Immortals , so named because their Number of 10,000 was immediately re-established after every loss.
The 10,000 Day War: Vietnam by Michael Maclear ISBN 0-312-79094-5 also alternate titles The ten thousand day war: Vietnam, 1945–1975 (10,000 days is 27.4 years).
Tomb of Ten Thousand Soldiers – defeat of the Tang dynasty army of China in the Nanzhao kingdom in 751.
In Islamic history, 10,000 is the Number of besieging forces led by Muhammad's adversary, Abu Sufyan , during the Battle of the Trench .
10,000 is the number of Muhammad 's soldiers during the conquest of Mecca .
In language ,
the Chinese, Japanese, Korean, and Vietnamese phrase live for ten thousand years was used to bless emperors in East Asia.
Μύριοι is an Ancient Greek name for 10.000 taken into the modern European languages as 'myriad' (see above). Hebrew, Chinese, Japanese, and Korean have words with the same meaning.
In literature,
Man'yōshū (万葉集 Man'yōshū , Collection of Ten Thousand Leaves ) is the oldest existing, and most highly revered, collection of Japanese poetry .
Ten Thousand a Year 1839 by Samuel Warren .
Ten Thousand a Year 1883?. A drama in three acts. Adapted from the celebrated novel of the same name, by the author of the Diary of a Physician , and arranged for the stage by Richard Brinsley Peake .[ 22]
Anabasis , by the Greek writer Xenophon (431–360 B.C.), about the Army of the Ten Thousand – Greek mercenaries taking part in the expedition of Cyrus the Younger, a Persian prince, against his brother, King Artaxerxes II.
The Ten Thousand: A Novel of Ancient Greece by Michael Curtis Ford . 2001. ISBN 0-312-26946-3 Historic fiction about the Army of the Ten Thousand .
The World of the Ten Thousand Things: Poems 1980–1990 by Charles Wright ISBN 0-374-29293-0 ISBN 0-374-52326-6 .
Ten Thousand Lovers by Edeet Ravel ISBN 0-06-056562-4 .
In philosophy, Lao Zi writes about ten thousand things in the Tao Te Ching . In Taoism , the "10,000 Things" is a term meaning all of phenomenal reality .[ 23]
In piphilology , ten thousand is the current world record for the Number of digits of pi memorized by a human being.
In psychology, Ten Thousand Dreams Interpreted , or what's in a dream : a scientific and practical, by Miller, Gustavus Hindman (1857–1929). Project Gutenberg .[ 24]
In religion,
In software,
The Year 10,000 problem is the collective name for all potential software bugs that will emerge as the need to express years with five digits arises.
In sports,
In athletics, 10,000 meters , 10 kilometers , 10 km , or 10K (6.2 miles) is the final standard track event in a long-distance track event and a distance in other racing events such as running , cycling , and skiing .
In bicycle racing, annual Tour of 10,000 Lakes Stage Race in Minneapolis .[ 29]
In baseball, on July 15, 2007, the Philadelphia Phillies became the first team in American professional sports history to lose 10,000 games.
Selected numbers in the range 10001-19999 [ edit ]
10007 = smallest five-digit prime number, twin prime with 10009
10008 = palindromic in bases 5 (3100135 ), 22 (KEK22 ), 28 (CLC28 ) and 33 (96933 ) and a Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 10, 13, 14 and 16
10009 = twin prime with 10007
10080 = highly composite number ;[ 30] number of minutes in a week
10111 = palindromic prime in bases 3 (1112121113 ) and 27 (DND27 )
10143 = number of partitions of 33[ 31]
10176 = smallest (provable) generalized Riesel number in base 10 : 10176*10n -1 is always divisible by one of the prime numbers {7, 11, 13, 37 [ 32]
10201 = 1012 , palindromic square (in the decimal system)
10206 = pentagonal pyramidal number [ 33]
10223 = sixth last number to be eliminated (in 2016) by Seventeen or Bust (now a sub-project of PrimeGrid ) in the Sierpiński problem
10239 = Woodall number [ 34]
10252 = Padovan number [ 35]
10267 = cuban prime [ 36]
10301 = palindromic prime in bases 10 (1030110 ), 27 (E3E27 ), 30 (BDB30 ) and 44 (5E544 )
10333 = star prime ,[ 37] palindromic in bases 9 (151519 ), 31 (ANA31 ) and 35 (8F835 )
10368 = 3-smooth number (27 ×34 )
10395 = double factorial of 11
10416 = square pyramidal number [ 38]
10425 = octahedral number [ 39]
10430 = weird number [ 40]
10433 = palindromic prime in base 44 (5H544 )
10440 = 144th triangular number
10499 = twin prime with 10501
10500 = Harshad number in bases 2, 3, 4, 6, 7, 8, 9, 10, 11, 15 and 16
10501 = palindromic prime in bases 10 (1050110 )[ 41] and 58 (37358 )
10512 = Harshad number in bases 2, 3, 4, 5, 7, 8, 9, 10, 13 and 16
10538 = 10538 Overture is a hit single by Electric Light Orchestra
10560 = Harshad number in bases 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14 and 16
10570 = weird number[ 40]
10585 = Carmichael number [ 42]
10601 = palindromic prime in bases 10 (1060110 )[ 41] and 30 (BNB30 )
10609 = 1032 , tribonacci number [ 43]
10631 = palindromic prime in base 30 (BOB30 )
10646 = ISO 10646 is the standard for Unicode
10648 = 223 , the smallest 5-digit cube
10660 = tetrahedral number [ 44]
10671 = tetranacci number [ 45]
10700 = 10700 kHz or 10.7 MHz is a standard intermediate frequency for analog superheterodyne FM broadcast band receivers
10744 = amicable number with 10856
10752 = the second 16-bit word of a TIFF file if the byte order marker is misunderstood
10792 = weird number[ 40]
10800 = number of bricks used for the uttaravedi in the Agnicayana ritual
10837 = star prime[ 37]
10856 = amicable number with 10744
10905 = Wedderburn–Etherington number [ 46]
10922 = repdigit in base 4 (22222224 ), and palindromic in base 8 (252528 )
10946 = Fibonacci number ,[ 47] Markov number [ 48]
10958 = the smallest positive integer that cannot be represented by an equation using increasing order of integers from 1 to 9 and basic arithmetic operations[ 49]
10981 = number of reduced trees with 22 nodes[ 50]
10989 = reverses when multiplied by 9
10990 = weird number[ 40]
11025 = 1052 , the sum of the first 14 positive integer cubes
11083 = palindromic prime in 2 consecutive bases: 23 (KLK23 ) and 24 (J5J24 )
11111 = Repunit [ 51]
11297 = Number of planar partitions of 16[ 52]
11298 = Riordan number
11311 = palindromic prime in decimal[ 41]
11340 = Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
11353 = star prime [ 37]
11368 = pentagonal pyramidal number[ 33]
11410 = weird number [ 40]
11411 = palindromic prime in decimal[ 41]
11424 = Harshad number in bases 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
11440 = square pyramidal number[ 38]
11480 = tetrahedral number[ 44]
11574 = approximate number of days in a billion seconds
11593 = smallest prime to start a run of nine consecutive primes of the form 4k + 1
11605 = smallest integer to start a run of five consecutive integers with the same number of divisors
11664 = 3-smooth number (24 ×36 ).
11690 = weird number[ 40]
11717 = twin prime with 11719
11719 = cuban prime,[ 36] twin prime with 11717
11726 = octahedral number[ 39]
11781 = triangular number , hexagonal number , octagonal number , and also 58-gonal, 216-gonal, 329-gonal, 787-gonal and 3928-gonal number[ 53] [ 54] [ 55]
11826 = smallest number whose square is pandigital without zeros
11953 = palindromic prime in bases 7 (465647 ) and 30 (D8D30 )
12000 = 12,000 of each of the twelve tribes of Israel made up the 144,000 servants of God who were 'sealed' according to the Book of Revelation in the New Testament [ 56]
12048 = number of non-isomorphic set-systems of weight 12
12097 = cuban prime[ 36]
12101 = Friedman prime
12107 = Friedman prime
12109 = Friedman prime
12110 = weird number[ 40]
12167 = 233
12172 = number of triangle-free graphs on 10 vertices[ 57]
12198 = semi-meandric number [ 58]
12251 = number of primes
≤
2
17
{\displaystyle \leq 2^{17}}
[ 59]
12285 = amicable number with 14595
12287 = Thabit number
12288 = 3-smooth number (212 ×3).
12289 = Proth prime , Pierpont prime
12310 = number of partitions of 34[ 31]
12321 = 1112 , Demlo number , palindromic square
12341 = tetrahedral number[ 44]
12345 = smallest whole number containing all numbers from 1 to 5
12407 = cited on Q.I. as the smallest uninteresting positive integer regarding arithmetical mathematics[ notes 1] [ 60]
12421 = palindromic prime[ 41]
12496 = smallest sociable number
12500 = 22 ×55 [ 61]
12529 = square pyramidal number[ 38]
12530 = weird number[ 40]
12542 = there is a match puzzle called MOST + MOST = TOKYO, where each letter represents a digit. When one solves the puzzle, TOKYO = 12542, as 6271 + 6271 = 12542 [ 62]
12670 = weird number[ 40]
12721 = palindromic prime[ 41]
12726 = Ruth–Aaron pair
12758 = most significant Number that cannot be expressed as the sum of distinct cubes
12765 = Finnish internet meme ; the code accompanying no-prize caps in a Coca-Cola bottle top prize contest. Often spelled out yksi – kaksi – seitsemän – kuusi – viisi , ei voittoa , "one – two – seven – six – five, no prize".
12769 = 1132 , palindromic in base 3
12821 = palindromic prime[ 41]
13122 = 3-smooth number (2×38 ).
13131 = octahedral number[ 39]
13244 = tetrahedral number[ 44]
13267 = cuban prime[ 36]
13331 = palindromic prime[ 41]
13370 = weird number [ 40]
13510 = weird number[ 40]
13581 = Padovan number[ 35]
13648 = number of 20-bead necklaces (turning over is allowed) where complements are equivalent[ 63]
13669 = cuban prime[ 36]
13685 = square pyramidal number[ 38]
13790 = weird number[ 40]
13792 = largest number that is not a sum of 16 fourth powers
13798 = number of 19-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[ 64]
13820 = meandric number , open meandric number
13824 = 243
13831 = palindromic prime[ 41]
13860 = Pell number [ 65]
13930 = weird number[ 40]
13931 = palindromic prime
13950 = pentagonal pyramidal number[ 33]
14190 = tetrahedral number[ 44]
14200 = number of n-Queens Problem solutions for n – 12
14341 = palindromic prime[ 41]
14400 = 1202 , the sum of the first 15 positive integers cubes
14595 = amicable number with 12285
14641 = 1212 = 114 , palindromic square (base 10)
14644 = octahedral number[ 39]
14701 = Markov number [ 48]
14741 = palindromic prime[ 41]
14770 = weird number [ 40]
14883 = number of partitions of 35[ 31]
14884 = 1222 , palindromic square in base 11
14910 = square pyramidal number[ 38]
15015 = smallest odd and square-free abundant number [ 66]
15120 = highly composite number; smallest number with exactly 80 factors[ 30]
15180 = tetrahedral number[ 44]
15376 = 1242 , pentagonal pyramidal number[ 33]
15387 = Zeisel number[ 67]
15451 = palindromic prime[ 41]
15511 = Motzkin prime [ 68]
15551 = palindromic prime[ 41]
15552 = 3-smooth number (26 ×35 )
15610 = weird number [ 40]
15625 = 1252 = 253 = 56
15629 = Friedman prime
15640 = initial number of only four-, five-, or six-digit century to contain two prime quadruples [ 69] (in between which lies a record prime gap of 43[ 70] )
15661 = Friedman prime
15667 = second nice Friedman prime
15679 = Friedman prime
15793 – Number of parallelogram polyominoes with 13 cells[ 71]
15841 = Carmichael number[ 42]
15876 = 1262 , palindromic square in base 5
15890 = weird number[ 40]
17073 = number of free 11-ominoes
17163 = the most significant number that is not the sum of the squares of distinct primes
17272 = weird number[ 40]
17296 = amicable number with 18416[ 78]
17344 = Kaprekar number [ 79]
17389 = 2000th prime number
17471 = palindromic prime[ 41]
17496 = 3-smooth number (23 ×37 )
17570 = weird number[ 40]
17575 = square pyramidal number[ 38]
17576 = 263 , palindromic in base 5
17689 = 1332 , palindromic in base 11
17711 = Fibonacci number [ 47]
17971 = palindromic prime[ 41]
17977 = number of partitions of 36[ 31]
17990 = weird number [ 40]
17991 = Padovan number[ 35]
18010 = octahedral number[ 39]
18181 = palindromic prime,[ 41] strobogrammatic prime[ 73]
18334 = number of planar partitions of 17[ 52]
18410 = weird number[ 40]
18416 = amicable number with 17296[ 80]
18432 = 3-smooth number (211 ×32 ).
18481 = palindromic prime[ 41]
18496 = 1362 , the sum of the first 16 positive integers cubes
18600 = harmonic divisor number [ 81]
18620 = harmonic divisor number[ 81]
18785 = Leyland number [ 74] using 4 & 7 (47 + 47 )
18830 = weird number[ 40]
18970 = weird number[ 40]
19019 = square pyramidal number[ 38]
19141 = unique prime in base 12
19302 = Number of ways to partition {1,2,3,4,5,6,7} and then partition each cell (block) into subcells[ 82]
19320 = number of trees with 16 unlabeled nodes[ 83]
19390 = weird number[ 40]
19391 = palindromic prime[ 41]
19417 = prime sextuplet , along with 19421, 19423, 19427, 19429, and 19433
19441 = cuban prime[ 36]
19455 = smallest integer that cannot be expressed as a sum of fewer than 548 ninth powers
19513 = tribonacci number[ 43]
19531 = repunit prime in base 5
19600 = 1402 , tetrahedral number
19601 /13860 ≈ √2
19609 = first prime followed by a prime gap of over fifty[ 70]
19670 = weird number [ 40]
19683 = 273 , 39 . Furthermore, there is a math puzzle regarding the word logic, such that LOGIC = (L+O+G+I+C)3 . The solution to this is (1+9+6+8+3) (1+9+6+8+3) (1+9+6+8+3), which is (27)(27)(27), which equals to 19683. This is one of two digits for which this works, although the other solution has O and I are the same digit: 17576, as (1+7+5+7+6) (1+7+5+7+6) (1+7+5+7+6) = (26)(26)(26) = 17576.[ 84]
19729 is the number of digits in
2
↑↑
5
{\displaystyle 2\uparrow \uparrow 5}
(Tetration )
19739 = fourth nice Friedman prime
19871 = octahedral number[ 39]
19891 = palindromic prime[ 41]
19927 = cuban prime[ 36]
19991 = palindromic prime[ 41]
There are 1033 prime numbers between 10000 and 20000, a count that is itself prime. It is 196 prime numbers less than the number of primes between 0 and 10000 (1229 , also prime).
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^ a b c d Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A273987 (Smallest Riesel number to base n )" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
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^ Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall (or Riesel) numbers: n*2^n - 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
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^ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
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^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
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^ Revelation 7:4–8
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^ Sloane, N. J. A. (ed.). "Sequence A048102 (Numbers k such that if k equals Product p_i^e_i then p_i equals e_i for all i)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "MOST+MOST Puzzle - Solution" .
^ 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.
^ Sloane, N. J. A. (ed.). "Sequence A000013 (Definition (1): 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.
^ Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A112643 (Odd and square-free abundant numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A051015 (Zeisel numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007530 (Prime quadruples: numbers k such that k , k +2, k +6, k +8 are all prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b "Table of Known Maximal Gaps" . Prime Pages.
^ Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002104 (Logarithmic numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A007597 (Strobogrammatic primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A088164 (Wolstenholme primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ 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.
^ Higgins, Peter (2008). Number Story: From Counting to Cryptography . New York: Copernicus. p. 61 . ISBN 978-1-84800-000-1 .
^ Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Higgins, ibid.
^ a b Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Algebra LOGIC 2 Puzzle - Solution" .
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000