10,000
| ||||
---|---|---|---|---|
Cardinal | ten thousand | |||
Ordinal | 10000th (ten thousandth) | |||
Numeral system | decamillesimal | |||
Factorization | 24 × 54 | |||
Divisors | 25 total | |||
Greek numeral | ||||
Roman numeral | X | |||
Unicode symbol(s) | X, ↂ | |||
Greek prefix | myria- | |||
Latin prefix | decamilli- | |||
Binary | 100111000100002 | |||
Ternary | 1112011013 | |||
Senary | 1141446 | |||
Octal | 234208 | |||
Duodecimal | 595412 | |||
Hexadecimal | 271016 | |||
Chinese numeral | 万, 萬 | |||
Armenian | Օ | |||
Egyptian hieroglyph | 𓂭 |
10,000 (ten thousand) is the natural number following 9,999 and preceding 10,001.
Name
[edit]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 mathematics
[edit]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 science
[edit]- In astronomy,
- asteroid Number: 10000 Myriostos, Provisional Designation: 1951 SY, Discovery Date: September 30, 1951, by A. G. Wilson:List of asteroids (9001-10000).
- 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,
- Land of 10000 Lakes is the nickname for the state of Minnesota.
- Land of 10000 Trails or 10000trails.com is an organization created in 1999 by the TN/KY Lakes Area Coalition and based in West Tennessee and West Kentucky to promote tourism by developing trails in the region.[13]
- Ten Thousand Islands National Wildlife Refuge is situated in the lower end of the Fakahatchee and Picayune Strands of Big Cypress Swamp and west of Everglades National Park in Florida.[14]
- Valley of Ten Thousand Smokes in Alaska.
- 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 time
[edit]- 10000 BC, 10000 BCE, or 10th millennium BC.
- 10000-year clock or the Clock of the Long Now is a mechanical clock designed to keep time for 10000 years.
In Arts
[edit]- In films,
- 10,000 Black Men Named George (2002, TV).
- The Phantom from 10,000 Leagues (1956).
- Vietnam: The Ten Thousand Day War (1980, mini).
- In music,
- 10,000 Days is the title of the fourth studio album by Tool.
- Ten Thousand Fists is an album by Disturbed.
- 10,000 Hz Legend album by Air 2001.
- 10,000 Maniacs is a US rock band.
- Ten Thousand Men of Harvard is a fight song of Harvard University.
- 10,000 Reasons (album) is a 2013 Christian album by Matt Redman.
- "10,000 Reasons (Bless the Lord)" is a 2013 single by Matt Redman.
- 10,000 Promises. is a Japanese pop group.
- "Ten Thousand Strong" is a song by American power metal band Iced Earth.
- 10,000 Gecs is the title of the second studio album by American experimental duo 100 gecs.
In other fields
[edit]- In currency,
- A version of Iraq's 10,000 dinar banknote has Abu Ali Hasan Ibn al-Haitham (also known as Alhazen) on the front, and a later issue has sculptor Jawad Saleem's Freedom Monument in Baghdad on the front. Both notes have an image of Mosul's al-Hadba' Minaret on the back.[18] The first issue had an image of former Iraqi president Saddam Hussein and the Spiral Minaret - Al-Minārat Al-Malwiyyah in Samarra.[19]
- the Japanese ¥10,000 banknote depicts Fukuzawa Yukichi.
- Kazakhstan's 10,000₸ banknote.
- the Lebanese £L10,000 banknote depicts Beirut's Martyrs' Square.
- Myanmar's (Burma's) Ks.10,000/- banknote.
- the U.S. $10,000 note depicts a picture of Salmon P. Chase.
- In distances,
- 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,
- The Bible,
- has 52 references to ten thousand in the King James Version.[25]
- Revelation 5:11 And I beheld, and I heard the voice of many angels round about the throne and the beasts and the elders: and the number of them was ten thousand times ten thousand, and thousands of thousands.[26]
- hymn, Ten thousand times ten thousand.[27]
- The Ten thousand martyrs.[28]
- The Bible,
- 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 professional sports history to lose 10,000 games.
Selected numbers in the range 10001-19999
[edit]10001 to 10999
[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).
- 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]
11000 to 11999
[edit]- 11025 = 1052, the sum of the first 14 positive integers 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.
- 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 to 12999
[edit]- 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 .[59]
- 12285 = amicable number with 14595.
- 12287 = Thabit number.
- 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]
13000 to 13999
[edit]- 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]
14000 to 14999
[edit]- 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]
15000 to 15999
[edit]- 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]
- 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]
16000 to 16999
[edit]- 16030 = weird number.[40]
- 16057 = the following prime sextuplet after 97, 16061, 16063, 16067, 16069, and 16073.
- 16061 = palindromic prime.[41]
- 16072 = logarithmic number.[72]
- 16091 = strobogrammatic prime.[73]
- 16206 = square pyramidal number.[38]
- 16269 = octahedral number.[39]
- 16310 = weird number.[40]
- 16361 = palindromic prime.[41]
- 16381 = Friedman prime.
- 16384 = 1282 = 214, palindromic in base 15.
- 16447 = third nice Friedman prime.
- 16561 = palindromic prime.[41]
- 16580 = Leyland number.[74]
- 16651 = cuban prime.[36]
- 16661 = palindromic prime.[41]
- 16730 = weird number.[40]
- 16759 = Friedman prime.
- 16796 = Catalan number.[75]
- 16807 = 75
- 16843 = smallest Wolstenholme prime.[76]
- 16870 = weird number.[40]
- 16879 = Friedman prime.
- 16896 = pentagonal pyramidal number.[33]
- 16999 = number of partially ordered set with 8 unlabeled elements.[77]
17000 to 17999
[edit]- 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]
18000 to 18999
[edit]- 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]
- 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]
- 18830 = weird number.[40]
- 18970 = weird number.[40]
19000 to 19999
[edit]- 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 (Tetration)
- 19739 = fourth nice Friedman prime.
- 19871 = octahedral number.[39]
- 19891 = palindromic prime.[41]
- 19927 = cuban prime.[36]
- 19991 = palindromic prime.[41]
Primes
[edit]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).
See also
[edit]Notes
[edit]- ^ On the basis that it did not then (November 2011) appear in Sloane's On-Line Encyclopedia of Integer Sequences.
References
[edit]- ^ "Malagasy Dictionary and Madagascar Encyclopedia : Alina".
- ^ "Myriad Definition & Meaning - Merriam-Webster". Merriam-Webster's Online Dictionary. 13 March 2024.
- ^ Baldwin, James (1885). "Notes on Teaching History". Educational Weekly. 5 (2): 4–5. ISSN 2475-3262. JSTOR 44009109.
- ^ "Decimal and Thousands Separators (International Language Environments Guide)". oracle.com.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A006880 (Number of primes less than 10^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002322 (Reduced totient function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. See "Table of n, prime(n) for n = 1..10000" under "Links".
- ^ John Horton Conway; Heidi Burgiel; Chaim Goodman-Strauss (2008). The Symmetries of Things. A K Peters/CRC Press. ISBN 978-1-56881-220-5. Chapter 20.
- ^ Climate Timeline Information Tool
- ^ news
- ^ "NASA Project: Columbia". Archived from the original on 2005-04-08. Retrieved 2005-02-15.
- ^ 10000 trails web site
- ^ "Ten Thousand Islands NWR". U.S. Fish & Wildlife Service. Archived from the original on 2005-03-01. Retrieved 2005-02-14.
- ^ Brewster, David (1830). The Edinburgh Encyclopædia. Vol. 12. Edinburgh, UK: William Blackwood, John Waugh, John Murray, Baldwin & Cradock, J. M. Richardson. p. 494. Retrieved 2015-10-09.
- ^ Brewster, David (1832). The Edinburgh Encyclopaedia. Vol. 12 (1st American ed.). Joseph and Edward Parker. Retrieved 2015-10-09.
- ^ Dingler, Johann Gottfried (1823). Polytechnisches Journal (in German). Vol. 11. Stuttgart, Germany: J.W. Gotta'schen Buchhandlung. Retrieved 2015-10-09.
- ^ "Iraq Dinar Currency Photos| Banknote Series | 25000, 10000, 5000, 1000, 250, 50 Dinars". iraqi-dinar.com. Archived from the original on 2005-02-07. Retrieved 2022-08-04.
- ^ http://www.iraqsales.com/10%2C000.htm Archived 2005-02-06 at the Wayback Machine
- ^ Brand, Stewart. "The 10,000-Year Library". kurzweilai.net. Archived from the original on 2005-02-05. Retrieved 2022-08-04.
- ^ "Army of 10,000". mississippiscv.org. Archived from the original on 2002-04-01. Retrieved 2022-08-04.
- ^ "University of Michigan Digital Library - Login Options".
- ^ "Tao Te Ching, Verse 34". thebigview.com. Archived from the original on 2007-08-17. Retrieved 2022-08-04.
- ^ https://www.gutenberg.org/ebooks/926 : Ten Thousand Dreams Interpreted
- ^ http://bible.gospelcom.net/keyword/?search=ten%20thousand&version1=9&searchtype=phrase&wholewordsonly=yes , [1]
- ^ (KJV) The Apocalypse of John
- ^ [2][dead link]
- ^ The Catholic Encyclopedia
- ^ Ulmer, Jeanne. "Minnesota Cycling Team –Tour of 10,000 Lakes". tourof10000lakes.net. Archived from the original on 2005-02-21. Retrieved 2022-08-04.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A083577 (Prime star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab Sloane, N. J. A. (ed.). "Sequence A006037 (Weird numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j k l m n o p q r s t u v w x Sloane, N. J. A. (ed.). "Sequence A002385 (Palindromic primes: prime numbers whose decimal expansion is a palindrome)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A002997 (Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000073 (Tribonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000078 (Tetranacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Taneja, Inder (2013). "Crazy Sequential Representation: Numbers from 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9". arXiv:1302.1479 [math.HO].
- ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002275 (Repunits: (10^n - 1)/9. Often denoted by R_n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Revelation 7:4–8
- ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000682 (Semimeanders)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007053 (Number of primes <= 2^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Host: Stephen Fry; Panellists: Alan Davies, Al Murray, Dara Ó Briain and Sandi Toksvig (11 November 2011). "Inland Revenue". QI. Series I. Episode 10. London, England. 19:55 minutes in. BBC. BBC Two.
- ^ 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".
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