Duodecimal
–
The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written by a rotated 2 and this notation was introduced by Sir Isaac Pitman. These digit forms are available as Unicode characters on computerized systems since June 2015 as ↊ and ↋, other notations use A, T, or X for ten and B or E for eleven. The number twelve is written as 10 in duodecimal, whereas the digit string 12 means 1 dozen and 2 units. Similarly, in duodecimal 100 means 1 gross,1000 means 1 great gross, the number twelve, a superior highly composite number, is the smallest number with four non-trivial factors, and the smallest to include as factors all four numbers within the subitizing range. As a result, duodecimal has been described as the number system. Of its factors,2 and 3 are prime, which means the reciprocals of all 3-smooth numbers have a representation in duodecimal. In particular, the five most elementary fractions all have a terminating

2.
A duodecimal multiplication table

Hexadecimal
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In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits, it allows a more human-friendly representation of binary-coded values, one hexadecimal digit represents a nibble, which is half of an octet or byte. For example, a byte can have values ranging from 00000000 to 11111111 in binary form. In a non-programming context, a subscript is typically used to give the radix, several notations are used to support hexadecimal representation of constants in programming languages, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, where this value might be denoted as 0x2AF3, in contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers express

2.
Bruce Alan Martin's hexadecimal notation proposal

3.
Hexadecimal finger-counting scheme.

Vigesimal
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The vigesimal or base 20 numeral system is based on twenty. In a vigesimal system, twenty individual numerals are used. One modern method of finding the extra needed symbols is to write ten as the letter A20, to write nineteen as J20, and this is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters A–F. Another method skips over the letter I, in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, the number twenty is written as 1020. According to this notation,2020 means forty in decimal = + D020 means two hundred and sixty in decimal = +10020 means four hundred in decimal = + +, in the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example,10 means ten,20 means twenty, in decimal, dividing by three twice only gives one digit periods because 9 is the number below ten. 21, however, the adjacent to 20 that is divisible by 3, is no

Base 36
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the

2.
34 senary = 22 decimal, in senary finger counting

Natural number
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In mathematics, the natural numbers are those used for counting and ordering. In common language, words used for counting are cardinal numbers, texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers. These chains of extensions make the natural numbers canonically embedded in the number systems. Properties of the numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics, the most primitive method of representing a natural number is to put down a mark for each object. Later, a set of objects could be tested for equality, excess or shortage, by striking out a mark, the first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording lar

2.
Natural numbers can be used for counting (one

apple, two apples, three apples, …)

Padovan sequence
–
The Padovan sequence is the sequence of integers P defined by the initial values P = P = P =1, and the recurrence relation P = P + P. The first few values of P are 1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200,265. The Padovan sequence is named after Richard Padovan who attributed its discovery to Dutch architect Hans van der Laan in his 1994 essay Dom, Hans van der Laan, Modern Primitive. The sequence was described by Ian Stewart in his Scientific American column Mathematical Recreations in June 1996 and he also writes about it in one of his books, Math Hysteria, Fun Games With Mathematics. The above definition is the one given by Ian Stewart and by MathWorld, other sources may start the sequence at a different place, in which case some of the identities in this article must be adjusted with appropriate offsets. This is a property of recurrence relations, the Perrin sequence can be obtained from the Padovan sequence by the following formula, P e r r i n = P + P. e. The Padov

1.
Spiral of equilateral triangles with side lengths which follow the Padovan sequence.

International Organization for Standardization
–
The International Organization for Standardization is an international standard-setting body composed of representatives from various national standards organizations. Founded on 23 February 1947, the organization promotes worldwide proprietary and it is headquartered in Geneva, Switzerland, and as of March 2017 works in 162 countries. It was one of the first organizations granted general consultative status with the United Nations Economic, ISO, the International Organization for Standardization, is an independent, non-governmental organization, the members of which are the standards organizations of the 162 member countries. It is the worlds largest developer of international standards and facilitates world trade by providing common standards between nations. Nearly twenty thousand standards have been set covering everything from manufactured products and technology to food safety, use of the standards aids in the creation of products and services that are safe, reliable and of good

1.
Plaque marking the building in

Prague where the ISO's predecessor, the ISA, was founded. (Click to enlarge / read.)

2.
ISO membership (see below)

Film speed
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Film speed is the measure of a photographic films sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system. A closely related ISO system is used to measure the sensitivity of digital imaging systems, highly sensitive films are correspondingly termed fast films. In both digital and film photography, the reduction of exposure corresponding to use of higher sensitivities generally leads to reduced image quality, in short, the higher the sensitivity, the grainier the image will be. Ultimately sensitivity is limited by the efficiency of the film or sensor. The speed of the emulsion was then expressed in degrees Warnerke corresponding with the last number visible on the plate after development. Each number represented an increase of 1/3 in speed, typical speeds were between 10° and 25° Warnerke at the time. The concept, however, was built upon in 1900 by Henry Chapman Jones in the development of his plate tester. In their

1.
This film container denotes its speed as ISO 100/21°, including both arithmetic (100 ASA) and logarithmic (21 DIN) components. The second is often dropped, making (e.g.) "ISO 100" effectively equivalent to the older ASA speed. (As is common, the "100" in the film name alludes to its ISO rating).

2.
Grainy high-speed B&W film negative

3.
A

CCD image sensor, 2/3 inch size

Euro
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Outside of Europe, a number of overseas territories of EU members also use the euro as their currency. Additionally,210 million people worldwide as of 2013 use currencies pegged to the euro, the euro is the second largest reserve currency as well as the second most traded currency in the world after the United States dollar. The name euro was adopted on 16 December 1995 in Madrid. The euro was introduced to world markets as an accounting currency on 1 January 1999. While the euro dropped subsequently to US$0.8252 within two years, it has traded above the U. S. dollar since the end of 2002, peaking at US$1.6038 on 18 July 2008. In July 2012, the euro fell below US$1.21 for the first time in two years, following concerns raised over Greek debt and Spains troubled banking sector, as of 26 March 2017, the euro–dollar exchange rate stands at ~ US$1.07. The euro is managed and administered by the Frankfurt-based European Central Bank, as an independent central bank, the ECB has sole authorit

2.
Euro banknotes as of 2015

3.
Euro coins and banknotes of various denominations.

Poland
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Poland, officially the Republic of Poland, is a country in Central Europe, situated between the Baltic Sea in the north and two mountain ranges in the south. Bordered by Germany to the west, the Czech Republic and Slovakia to the south, Ukraine and Belarus to the east, the total area of Poland is 312,679 square kilometres, making it the 69th largest country in the world and the 9th largest in Europe. With a population of over 38.5 million people, Poland is the 34th most populous country in the world, the 8th most populous country in Europe, Poland is a unitary state divided into 16 administrative subdivisions, and its capital and largest city is Warsaw. Other metropolises include Kraków, Wrocław, Poznań, Gdańsk and Szczecin, the establishment of a Polish state can be traced back to 966, when Mieszko I, ruler of a territory roughly coextensive with that of present-day Poland, converted to Christianity. The Kingdom of Poland was founded in 1025, and in 1569 it cemented a political associ

Electronvolt
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In physics, the electronvolt is a unit of energy equal to approximately 1. 6×10−19 joules. By definition, it is the amount of energy gained by the charge of an electron moving across an electric potential difference of one volt. Thus it is 1 volt multiplied by the elementary charge, therefore, one electronvolt is equal to 6981160217662079999♠1. 6021766208×10−19 J. The electronvolt is not a SI unit, and its definition is empirical, like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 J/C √2hα / μ0c0. It is a unit of energy within physics, widely used in solid state, atomic, nuclear. It is commonly used with the metric prefixes milli-, kilo-, in some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion electronvolts, it is equivalent to the GeV. By mass–energy equivalence, the electronvolt is also a unit of mass and it is common in particle physics, where units of mass and energy are often interchanged

HTTP
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The Hypertext Transfer Protocol is an application protocol for distributed, collaborative, and hypermedia information systems. HTTP is the foundation of data communication for the World Wide Web, Hypertext is structured text that uses logical links between nodes containing text. HTTP is the protocol to exchange or transfer hypertext, development of HTTP was initiated by Tim Berners-Lee at CERN in 1989. Standards development of HTTP was coordinated by the Internet Engineering Task Force and the World Wide Web Consortium, culminating in the publication of a series of Requests for Comments. The first definition of HTTP/1.1, the version of HTTP in common use, occurred in RFC2068 in 1997, although this was obsoleted by RFC2616 in 1999 and then again by RFC7230 and family in 2014. A later version, the successor HTTP/2, was standardized in 2015, HTTP functions as a request–response protocol in the client–server computing model. A web browser, for example, may be the client, the client submits

1.

URL beginning with the HTTP scheme and the

WWW domain name label.

List of HTTP status codes
–
This is a list of Hypertext Transfer Protocol response status codes. It includes codes from IETF Request for Comments, other specifications, the first digit of the status code specifies one of five standard classes of responses. The message phrases shown are typical, but any human-readable alternative may be provided, unless otherwise stated, the status code is part of the HTTP/1.1 standard. The Internet Assigned Numbers Authority maintains the registry of HTTP status codes. An informational response indicates that the request was received and understood and it is issued on a provisional basis while request processing continues. It alerts the client to wait for a final response, the message consists only of the status line and optional header fields, and is terminated by an empty line. As the HTTP/1.0 standard did not define any 1xx status codes,100 Continue The server has received the request headers and the client should proceed to send the request body. Sending a large request body

1.
404 error on German Wikipedia

Monopoly (game)
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The current version was first published by Parker Brothers in 1935. Subtitled The Fast-Dealing Property Trading Game, the game is named after the concept of monopoly—the domination of a market by a single entity. It is now owned and produced by the American game and toy company Hasbro and it was intended as an educational tool to illustrate the negative aspects of concentrating land in private monopolies. Magie took out a patent in 1904 and her game, The Landlords Game, was self-published, beginning in 1906. A series of variant board games based on her concept was developed from 1906 through the 1930s that involved the buying and selling of land, cardboard houses were added and rents were increased as they were added. Magie again patented the game in 1923, after the meal, the Darrows played The Landlords Game several times with them, a game that was entirely new to the Darrows, and before he left, Darrow asked for a written set of the rules. After Darrow brought his own Monopoly game o

1.
2014 US MONOPOLY Box

2.
The board cover of the standard British version, with the 2009–13 artwork

3.
During

World War II, the dice in the United Kingdom were replaced with a spinner because of a lack of materials.

4.
All twelve tokens from a pre-2008 copy of the US Deluxe Edition Monopoly

Go (Monopoly)
–
The current version was first published by Parker Brothers in 1935. Subtitled The Fast-Dealing Property Trading Game, the game is named after the concept of monopoly—the domination of a market by a single entity. It is now owned and produced by the American game and toy company Hasbro and it was intended as an educational tool to illustrate the negative aspects of concentrating land in private monopolies. Magie took out a patent in 1904 and her game, The Landlords Game, was self-published, beginning in 1906. A series of variant board games based on her concept was developed from 1906 through the 1930s that involved the buying and selling of land, cardboard houses were added and rents were increased as they were added. Magie again patented the game in 1923, after the meal, the Darrows played The Landlords Game several times with them, a game that was entirely new to the Darrows, and before he left, Darrow asked for a written set of the rules. After Darrow brought his own Monopoly game o

1.
2014 US MONOPOLY Box

2.
The Monopoly logo (2008–present)

3.
The board cover of the standard British version, with the 2009–13 artwork

4.
During

World War II, the dice in the United Kingdom were replaced with a spinner because of a lack of materials.

Cholesterol
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Cholesterol, from the Ancient Greek chole- and stereos followed by the chemical suffix -ol for an alcohol, is an organic molecule. Cholesterol enables animal cells to dispense with a wall, thereby allowing animal cells to change shape rapidly. In addition to its importance for cell structure, cholesterol also serves as a precursor for the biosynthesis of steroid hormones, bile acid. Cholesterol is the principal sterol synthesized by all animals, in vertebrates, hepatic cells typically produce the greatest amounts. It is absent among prokaryotes, although there are exceptions, such as Mycoplasma. François Poulletier de la Salle first identified cholesterol in solid form in gallstones in 1769, however, it was not until 1815 that chemist Michel Eugène Chevreul named the compound cholesterine. Furthermore, it can be absorbed directly from animal-based foods, a human male weighing 68 kg normally synthesizes about 1 gram per day, and his body contains about 35 g, mostly contained within the

2.
Cholesterol

3.
Microscopic appearance of cholesterol crystals in water. Photo taken under

polarized light.

NASCAR
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The National Association for Stock Car Auto Racing is an American family-owned and operated business venture that sanctions and governs multiple auto-racing sports events. Bill France Sr. founded the company in 1948 and his grandson Brian France became its CEO in 2003, NASCAR is motorsports preeminent stock-car racing organization. The three largest racing-series sanctioned by this company are the Monster Energy NASCAR Cup Series, the Xfinity Series, the company also oversees NASCAR Local Racing, the Whelen Modified Tour, the Whelen All-American Series, and the NASCAR iRacing. com Series. NASCAR sanctions over 1,500 races at over 100 tracks in 39 of the 50 US states as well as in Canada. NASCAR has presented exhibition races at the Suzuka and Motegi circuits in Japan, the Autódromo Hermanos Rodríguez in Mexico, NASCAR has its official headquarters in Daytona Beach, Florida, and also maintains offices in the North Carolina cities of Charlotte, Concord, and Conover. Regional offices are

1.
Nextel Cup Series (now Sprint Cup Series) race cars at Infineon Raceway (now Sonoma Raceway) in 2005

Sprint Cup Series
–
The Monster Energy NASCAR Cup Series is the top racing series of the National Association for Stock Car Auto Racing. It is named for the current sponsor, Monster Energy, but has been known by names in the past. The series began in 1949 as the Strictly Stock Series, in 1971, when the series began leasing its naming rights to the R. J. Reynolds Tobacco Company, it was referred to as the Winston Cup Series. A similar deal was made with Nextel in 2003, and it became the Nextel Cup Series, Sprint acquired Nextel in 2005, and in 2008 the series was renamed the Sprint Cup Series, which lasted until 2016. In December 2016, it was announced that Monster Energy would become the new sponsor starting in 2017. The championship is determined by a system, with points being awarded according to finish placement. The season is divided into two segments, after the first 26 races,16 drivers, selected primarily on the basis of wins during the first 26 races, are seeded based on their total number of wins.

Richard Petty
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Richard Lee Petty, nicknamed The King, is a former NASCAR driver who raced in the Strictly Stock/Grand National Era and the NASCAR Winston Cup Series. He won the NASCAR Championship seven times, winning a record 200 races during his career, winning the Daytona 500 a record seven times, and winning a record 27 races in the 1967 season alone. Statistically, he is the most accomplished driver in the history of the sport and is one of the most respected figures in motorsports as a whole. He also collected a number of poles and over 700 Top 10 finishes in his 1,184 starts. Petty was the driver to ever win in his 500th race start. He was inducted into the class of the NASCAR Hall of Fame in 2010. Petty is a second generation driver and his father, Lee Petty, won the first Daytona 500 in 1959 and was also a three-time NASCAR champion. His son Kyle is also a well-known NASCAR driver and his grandson, Adam, was killed in a practice crash at New Hampshire International Speedway on May 12,2000, f

1.
Richard Petty

4.
Petty's car used for his 1979 Daytona 500 win, on display at

Daytona USA
North West 200
–
The North West 200 is a motorcycle race meeting held each May in Northern Ireland. The course is a circuit, made up of public roads running between the towns of Portstewart, Coleraine and Portrush is one of the fastest in the world. In practice for the 2012 event Martin Jessopp was clocked at 208 mph and it is one of around fifteen events run on public roads between April and October throughout the island of Ireland. It is the largest annual sporting event in Ireland, with the race attracting over 150,000 visitors from all over the world. Since 1964 the event has been organised by the Coleraine and District Motor Club, in 2010 the meeting featured daytime practice on the Thursday for the first time. The 2011 event took place on Saturday 21 May, there were significant delays due to a hoax bomb alert and then an extensive oil spill on the track caused racing to be cancelled after the completion of only one race. The North West 200 was originally run over two hundred miles as a race, befo

1.
Riders approaching York from Juniper Hill during the 2009 event.

2.
North West 200

3.

Mick Grant passes the Railway Bank at Metropole Corner, Portrush, 1975

4.
A group of riders entering York Corner during the 2009 event

Northern Ireland
–
Northern Ireland is a constituent unit of the United Kingdom in the north-east of Ireland. It is variously described as a country, province, region, or part of the United Kingdom, Northern Ireland shares a border to the south and west with the Republic of Ireland. In 2011, its population was 1,810,863, constituting about 30% of the total population. Northern Ireland was created in 1921, when Ireland was partitioned between Northern Ireland and Southern Ireland by an act of the British parliament, Northern Ireland has historically been the most industrialised region of Ireland. After declining as a result of the political and social turmoil of the Troubles, its economy has grown significantly since the late 1990s. Unemployment in Northern Ireland peaked at 17. 2% in 1986, dropping to 6. 1% for June–August 2014,58. 2% of those unemployed had been unemployed for over a year. Prominent artists and sports persons from Northern Ireland include Van Morrison, Rory McIlroy, Joey Dunlop, Wayne M

2.
Location of Northern Ireland (dark green) – in

Europe (green & dark grey) – in the

United Kingdom (green)

12 (number)
–
12 is the natural number following 11 and preceding 13. The product of the first three factorials, twelve is a highly composite number, divisible by 2,3,4. It is central to systems of counting, including the Western calendar and units of time. The word twelve is the largest number with a name in English. Such uses gradually disappeared with the introduction of Arabic numerals during the 12th-century Renaissance and it derives from the Old English twelf and tuelf, first attested in the 10th-century Lindisfarne Gospels Book of John. It has cognates in every Germanic language, whose Proto-Germanic ancestor has been reconstructed as *twaliƀi, from *twa and suffix *-lif- or *-liƀ- of uncertain meaning. It is sometimes compared with the Lithuanian dvýlika, although -lika is used as the suffix for all numbers from 11 to 19, every other Indo-European language instead uses a form of two+ten, such as the Latin duōdecim. The usual ordinal form is twelfth but dozenth or duodecimal is also used in

15 (number)
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15 is the natural number following 14 and preceding 16. In English, it is the smallest natural number with seven letters in its spelled name, in spoken English, the numbers 15 and 50 are often confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed,15 /fɪfˈtiːn/ vs 50 /ˈfɪfti/, however, in dates such as 1500 or when contrasting numbers in the teens, the stress generally shifts to the first syllable,15 /ˈfɪftiːn/. In a 24-hour clock, the hour is in conventional language called three or three oclock. A composite number, its divisors being 1,3 and 5. A repdigit in binary and quaternary, in hexadecimal, as well as all higher bases,15 is represented as F. the 4th discrete semiprime and the first member of the discrete semiprime family. It is thus the first odd discrete semiprime, the number proceeding 15,14 is itself a discrete semiprime and this is the first such pair of discrete semiprimes. The next example is the pair commencing 21, the s

2.
The 15 perfect matchings of K 6

17 (number)
–
17 is the natural number following 16 and preceding 18. In spoken English, the numbers 17 and 70 are sometimes confused because they sound similar, when carefully enunciated, they differ in which syllable is stressed,17 /sɛvənˈtiːn/ vs 70 /ˈsɛvənti/. However, in such as 1789 or when contrasting numbers in the teens, such as 16,17,18. The number 17 has wide significance in pure mathematics, as well as in applied sciences, law, music, religion, sports,17 is the sum of the first 4 prime numbers. In a 24-hour clock, the hour is in conventional language called five or five oclock. Seventeen is the 7th prime number, the next prime is nineteen, with which it forms a twin prime. 17 is the sixth Mersenne prime exponent, yielding 131071,17 is an Eisenstein prime with no imaginary part and real part of the form 3n −1. 17 is the third Fermat prime, as it is of the form 22n +1, specifically with n =2, since 17 is a Fermat prime, regular heptadecagons can be constructed with compass and unmarked rul

19 (number)
–
19 is the natural number following 18 and preceding 20. In a 24-hour clock, the hour is in conventional language called seven or seven oclock. 19 is the 8th prime number, the sequence continues 23,29,31,37. 19 is the seventh Mersenne prime exponent,19 is the fifth happy number and the third happy prime. 19 is the sum of two odd discrete semiprimes,65 and 77 and is the base of the 19-aliquot tree. 19 is the number of fourth powers needed to sum up to any natural number. It is the value of g.19 is the lowest prime centered triangular number, a centered hexagonal number. The only non-trivial normal magic hexagon contains 19 hexagons,19 is the first number with more than one digit that can be written from base 2 to base 19 using only the digits 0 to 9, the other number is 20. 19 is The TCP/IP port used for chargen, astronomy, Every 19 years, the solar year and the lunar year align in whats known as the metonic cycle. Quran code, There have been claims that patterns of the number 19 are pre

20 (number)
–
20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score,20 is a tetrahedral number as 1,4,10,20. 20 is the basis for vigesimal number systems,20 is the third composite number comprising the product of a squared prime and a prime, and also the second member of the q family in this form. 20 has a sum of 22. Accordingly,20 is the abundant number and demonstrates an 8-member aliquot sequence. 20 is the smallest primitive abundant number,20 is the 4th composite number in the 7-aliquot tree. Two numbers have 20 as their sum, the discrete semiprime 34. Only 2 other square primes are abundant 12 and 18,20 can be written as the sum of three Fibonacci numbers uniquely, i. e.20 =13 +5 +2. The product of the number of divisors and the number of divisors of 20 is exactly 20. 20 is the number of required to optimally solve a Rubiks Cube in the worst case. 20 is the number with more than one digit that can be written from base 2 to base 20 us

21 (number)
–
21 is the natural number following 20 and preceding 22. In a 24-hour clock, the twenty-first hour is in conventional language called nine or nine oclock,21 is, the fifth discrete semiprime and the second in the family. With 22 it forms the second discrete semiprime pair, a Blum integer, since it is a semiprime with both its prime factors being Gaussian primes. A composite number, its divisors being 1,3 and 7. The sum of the first six numbers, making it a triangular number. The sum of the sum of the divisors of the first 5 positive integers, the smallest non-trivial example of a Fibonacci number whose digits are Fibonacci numbers and whose digit sum is also a Fibonacci number. The smallest natural number that is not close to a power of 2, 2n,21 has an aliquot sum of 11 though it is the second composite number found in the 11-aliquot tree with the abundant square prime 18 being the first such member. Twenty-one is the first number to be the sum of three numbers 18,51,91. 21 appears in th

3.
Detail of the building entrance

24 (number)
–
24 is the natural number following 23 and preceding 25. The SI prefix for 1024 is yotta, and for 10−24 yocto and these numbers are the largest and smallest number to receive an SI prefix to date. In a 24-hour clock, the hour is in conventional language called twelve or twelve oclock. 24 is the factorial of 4 and a number, being the first number of the form 23q. It follows that 24 is the number of ways to order 4 distinct items and it is the smallest number with exactly eight divisors,1,2,3,4,6,8,12, and 24. It is a composite number, having more divisors than any smaller number. 24 is a number, since adding up all the proper divisors of 24 except 4 and 8 gives 24. Subtracting 1 from any of its divisors yields a number,24 is the largest number with this property. 24 has a sum of 36 and the aliquot sequence. It is therefore the lowest abundant number whose aliquot sum is itself abundant, the aliquot sum of only one number,529 =232, is 24. There are 10 solutions to the equation φ =24, name

1.
Astronomical clock in Prague

25 (number)
–
25 is the natural number following 24 and preceding 26. It is a number, being 52 =5 ×5. It is one of two numbers whose square and higher powers of the number also ends in the same last two digits, e. g.252 =625, the other is 76. It is the smallest square that is also a sum of two squares,25 =32 +42, hence it often appears in illustrations of the Pythagorean theorem. 25 is the sum of the odd natural numbers 1,3,5,7 and 9. 25 is an octagonal number, a centered square number. 25 percent is equal to 1/4,25 has an aliquot sum of 6 and number 6 is the first number to have an aliquot sequence that does not culminate in 0 through a prime. 25 is the sum of three integers,95,119, and 143. Twenty-five is the second member of the 6-aliquot tree. It is the smallest base 10 Friedman number as it can be expressed by its own digits,52 and it is also a Cullen number. 25 is the smallest pseudoprime satisfying the congruence 7n =7 mod n.25 is the smallest aspiring number — a composite non-sociable number

30 (number)
–
30 is the natural number following 29 and preceding 31. Thirty is the sum of the first four squares, which makes it a square pyramidal number and it is a primorial and is the smallest Giuga number. 30 is the smallest sphenic number, and the smallest of the form 2 ×3 × r,30 has an aliquot sum of 42, the second sphenic number and all sphenic numbers of this form have an aliquot sum 12 greater than themselves. The aliquot sequence of 30 is 16 members long, it comprises Thirty has but one number for which it is the aliquot sum, adding up some subsets of its divisors gives 30, hence 30 is a semiperfect number. 30 is the largest number such that all smaller than itself. A polygon with thirty sides is called a triacontagon, the icosahedron and the dodecahedron are Platonic solids with 30 edges. The icosidodecahedron is an Archimedean solid with 30 vertices, and the Tutte–Coxeter graph is a graph with 30 vertices. The atomic number of zinc is 30 Messier object M30, a magnitude 8, the duration

31 (number)
–
31 is the natural number following 30 and preceding 32. As a Mersenne prime,31 is related to the perfect number 496,31 is also the 4th lucky prime and the 11th supersingular prime. 31 is a triangular number, the lowest prime centered pentagonal number. For the Steiner tree problem,31 is the number of possible Steiner topologies for Steiner trees with 4 terminals, at 31, the Mertens function sets a new low of −4, a value which is not subceded until 110. No integer added up to its base 10 digits results in 31,31 is a repdigit in base 5, and base 2. The numbers 31,331,3331,33331,333331,3333331, for a time it was thought that every number of the form 3w1 would be prime. Here,31 divides every fifteenth number in 3w1, the atomic number of gallium Messier object M31, a magnitude 4.5 galaxy in the constellation Andromeda. It is also known as the Andromeda Galaxy, and is visible to the naked eye in a modestly dark sky. The New General Catalogue object NGC31, a galaxy in the constellation Phoeni

34 (number)
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34 is the natural number following 33 and preceding 35. 34 is the ninth distinct semiprime and has four divisors including one and its neighbors,33 and 35, also are distinct semiprimes, having four divisors each, and 34 is the smallest number to be surrounded by numbers with the same number of divisors as it has. It is also in the first cluster of three distinct semiprimes, being within 33,34,35, the next cluster of semiprimes is 85,86,87. It is the ninth Fibonacci number and a companion Pell number, since it is an odd-indexed Fibonacci number,34 is a Markov number, appearing in solutions with other Fibonacci numbers, such as, etc. This number is the constant of a 4 by 4 normal magic square. It has the sum,20, in the following descending sequence 34,20,22,14,10,8,7,1. There is no solution to the equation φ =34, making 34 a nontotient, nor is there a solution to the equation x − φ =34, making 34 a noncototient. The atomic number of selenium One of the numbers in physics. Messier object

35 (number)
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35 is the natural number following 34 and preceding 36. 35 is the sum of the first five numbers, making it a tetrahedral number. 35 is the number of ways that three things can be selected from a set of seven unique things also known as the combination of seven things taken three at a time,35 is a centered cube number, a pentagonal number and a pentatope number. 35 is a highly cototient number, since there are solutions to the equation x − φ =35 than there are for any other integers below it except 1. There are 35 free hexominoes, the polyominoes made from six squares, since the greatest prime factor of 352 +1 =1226 is 613, which is obviously more than 35 twice,35 is a Størmer number. 35 is a semiprime, the tenth, and the first with 5 as the lowest non-unitary factor. The aliquot sum of 35 is 13 this being the composite number with such an aliquot sum. 35 is the last member of the first triple cluster of semiprimes 33,34,35, the second such triple discrete semiprime cluster is 85,86,87.

1.
The 35 free hexominoes

37 (number)
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37 is the natural number following 36 and preceding 38. Thirty-seven is the 12th prime number, a prime with 73. It is a hexagonal number and a star number. Every positive integer is the sum of at most 37 fifth powers,37 appears in the Padovan sequence, preceded by the terms 16,21, and 28. Since the greatest prime factor of 372 +1 =1370 is 137, the atomic number of rubidium The normal human body temperature in degrees Celsius Messier object M37, a magnitude 6. The duration of Saros series 37 was 1298.1 years, the Saros number of the lunar eclipse series which began on -1492 April 3 and ended on -194 May 22. The duration of Saros series 37 was 1298.1 years, kepler-37b is the smallest known planet. The New York Yankees, also for Stengel and this honor made him the first manager to have had his number retired by two different teams. In the NFL, The Detroit Lions, for Doak Walker, the San Francisco 49ers, for Jimmy Johnson. Thirty-seven is, The number of plays William Shakespeare is thought

1.
House number in

Baarle (in its Belgian part)

38 (number)
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38 is the natural number following 37 and preceding 39. 38 is the 11th distinct semiprime and the 7th in the family and it is the initial member of the third distinct semiprime pair. 38 has a sum of 22 which is itself a distinct semiprime In fact 38 is the first number to be at the head of a chain of four distinct semiprimes in its 8-member aliquot sequence. 38 is the 8th member of the 7-aliquot tree, −1 yields 523022617466601111760007224100074291199999999, which is the 16th factorial prime. There is no answer to the equation φ =38, making 38 a nontotient,38 is the sum of the squares of the first three primes. 37 and 38 are the first pair of positive integers not divisible by any of their digits. 38 is the largest even number which cannot be written as the sum of two odd composite numbers, there are only two normal magic hexagons, order 1 and order 3. The sum of row of an order 3 magic hexagon is 38. The duration of Saros series 38 was 1298.1 years, the lunar eclipse series which began

1.
Most people will see the number 38, but people with red-green color blindness might see

88 instead.

39 (number)
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39 is the natural number following 38 and preceding 40. Thirty-nine is the sum of consecutive primes and also is the product of the first, among small semiprimes only three other integers share this attribute. 39 also is the sum of the first three powers of 3, given 39, the Mertens function returns 0. 39 is the smallest natural number which has three partitions into three parts which all give the product when multiplied. 39 is the 12th distinct semiprime and the 4th in the family and it is the last member of the third distinct biprime pair. 39 has a sum of 17 which is itself a prime. 39 is the 4th member of the 17-aliquot tree and it is a perfect totient number. The thirteenth Perrin number is 39, which comes after 17,22,29, since the greatest prime factor of 392 +1 =1522 is 761, which is obviously more than 39 twice,39 is a Størmer number. The F26A graph is a graph with 39 edges. The atomic number of yttrium Astronomy Messier object Open Cluster M39, the duration of Saros series 39 wa

40 (number)
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Despite being related to the word four, the modern spelling of 40 is forty. The archaic form fourty is now considered a misspelling, the modern spelling possibly reflects a pronunciation change due to the horse–hoarse merger. Forty is a number, an octagonal number, and as the sum of the first four pentagonal numbers. Adding up some subsets of its divisors gives 40, hence 40 is a semiperfect number, given 40, the Mertens function returns 0. 40 is the smallest number n with exactly 9 solutions to the equation φ = n, Forty is the number of n-queens problem solutions for n =7. Since 402 +1 =1601 is prime,40 is a Størmer number,40 is a repdigit in base 3 and a Harshad number in base 10. Negative forty is the temperature at which the Fahrenheit and Celsius scales correspond. It is referred to as either minus forty or forty below, the planet Venus forms a pentagram in the night sky every eight years with it returning to its original point every 40 years with a 40-day regression. The duration

1.
The number on the logo for the American-Japanese hard rock band Crush 40.

42 (number)
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42 is the natural number that succeeds 41 and precedes 43. Forty-two is a number and an abundant number, its prime factorization 2 ·3 ·7 makes it the second sphenic number. As with all numbers of this form, the aliquot sum is abundant by 12. 42 is also the second number to be bracketed by twin primes,30 is also a pronic number. 42 has a 14-member aliquot sequence 42,54,66,78,90,144,259,45,33,15,9,4,3,1,0 and is part of the aliquot sequence commencing with the first sphenic number 30. Further,42 is the 10th member of the 3-aliquot tree, additional properties of the number 42 include, It is the third primary pseudoperfect number. It is an alternating sign matrix number, that is, the number of 4-by-4 alternating sign matrices and it is the number of partitions of 10—the number of ways of expressing 10 as a sum of positive integers. It is the third pentadecagonal number and it is a meandric number and an open meandric number. It is conjectured to be the factor in the leading order term of

2.
The 3 × 3 × 3

magic cube with rows summing to 42.

45 (number)
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45 is the natural number following 44 and followed by 46. Forty-five is a number, and in particular the sum of all the decimal digits. It is the smallest triangle number which can be written as the sum of two squares and it is also a hexagonal and 16-gonal number. 45 is the positive integer with a prime factorization of the form p2q. 33 is the sum of 45 and the aliquot sequence of 45 is. Since the greatest prime factor of 452 +1 =2026 is 1013, in base 10, it is a Kaprekar number and a Harshad number. The duration of Saros series 45 was 1280.1 years, the Saros number of the lunar eclipse series which began on −1369 August 19 and ended on 182 March. The duration of Saros series 45 was 1550.6 years, a card game, Forty-five.45, a 2006 motion picture. In the United States,45 is often a reference to one of two specific.45 caliber cartridges— the.45 Colt or the.45 ACP, in years of marriage, the sapphire wedding anniversary. Forty Five a Big Finish 2008 audio play made for the forty fifth anni

46 (number)
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46 is the natural number following 45 and preceding 47. Forty-six is a Wedderburn-Etherington number, a number and a centered triangular number. It is the sum of the totient function for the first twelve integers,46 is the largest even integer that can not be expressed as a sum of two abundant numbers. 46 is the third semiprime with an aliquot sum. The aliquot sequence of 46 is, since it is possible to find sequences of 46 consecutive integers such that each inner member shares a factor with either the first or the last member,46 is an Erdős–Woods number. The approximate molar mass of ethanol Messier object M46, a magnitude 6.5 open cluster in the constellation Puppis, the New General Catalogue object NGC46, a star in the constellation Pisces. The Saros number of the solar eclipse series began on April 1,1371 BC. The duration of Saros series 46 was 1280.1 years, the Saros number of the lunar eclipse series which began on July 19,1358 BC and ended on October 8,12. The duration of Saros