64 (number)
Encyclopedia
64 is the natural number
following 63
and preceding 65
.
s. It is the lowest positive power of two
that is adjacent to neither a Mersenne prime
nor a Fermat prime. 64 is the sum of Euler's totient function
for the first fourteen integers. It is also a dodecagonal number and a centered triangular number
.
Since it is possible to find sequences of 64 consecutive integers such that each inner member shares a factor with either the first or the last member, 64 is an Erdős–Woods number
.
In base 10, no integer added up to its own digits yields 64, hence it is a self number
.
64 is a superperfect number
- a number such that σ
(σ(n))=2n.
64 is the index of Graham's number
in the rapidly growing sequence 3,27,7625597484987,....
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
following 63
63 (number)
63 is a natural number following 62 and preceding 64.-In mathematics:Although a number of the form 2n - 1, 63 is not a Mersenne prime since n is not prime and 63 is certainly not prime either. It is a Woodall number and a Harshad number. It is a highly cototient number. It is a repdigit in base 4...
and preceding 65
65 (number)
65 is the natural number following 64 and preceding 66.-In mathematics:Sixty-five is the 23rd semiprime and the 3rd of the form it is an octagonal number. It is also a Cullen number...
.
In mathematics
Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the smallest number with exactly seven divisorDivisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...
s. It is the lowest positive power of two
Power of two
In mathematics, a power of two means a number of the form 2n where n is an integer, i.e. the result of exponentiation with as base the number two and as exponent the integer n....
that is adjacent to neither a Mersenne prime
Mersenne prime
In mathematics, a Mersenne number, named after Marin Mersenne , is a positive integer that is one less than a power of two: M_p=2^p-1.\,...
nor a Fermat prime. 64 is the sum of Euler's totient function
Euler's totient function
In number theory, the totient \varphi of a positive integer n is defined to be the number of positive integers less than or equal to n that are coprime to n In number theory, the totient \varphi(n) of a positive integer n is defined to be the number of positive integers less than or equal to n that...
for the first fourteen integers. It is also a dodecagonal number and a centered triangular number
Centered triangular number
A centered triangular number is a centered figurate number that represents a triangle with a dot in the center and all other dots surrounding the center in successive triangular layers...
.
Since it is possible to find sequences of 64 consecutive integers such that each inner member shares a factor with either the first or the last member, 64 is an Erdős–Woods number
Erdos–Woods number
In number theory, an Erdős–Woods number is a positive integer that has the following property:Consider a sequence of consecutive positive integers [a, a+1, \dots, a+k]. The number k is an Erdős–Woods number if there exists such a sequence, beginning with some number a, in which each of the elements...
.
In base 10, no integer added up to its own digits yields 64, hence it is a self number
Self number
A self number, Colombian number or Devlali number is an integer which, in a given base, cannot be generated by any other integer added to the sum of that other integer's digits. For example, 21 is not a self number, since it can be generated by the sum of 15 and the digits comprising 15, that is,...
.
64 is a superperfect number
Superperfect number
In mathematics a superperfect number is a positive integer n that satisfies\sigma^2=\sigma=2n\, ,where σ is the divisor function...
- a number such that σ
Divisor function
In mathematics, and specifically in number theory, a divisor function is an arithmetical function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer. It appears in a number of remarkable identities, including relationships...
(σ(n))=2n.
64 is the index of Graham's number
Graham's number
Graham's number, named after Ronald Graham, is a large number that is an upper bound on the solution to a certain problem in Ramsey theory.The number gained a degree of popular attention when Martin Gardner described it in the "Mathematical Games" section of Scientific American in November 1977,...
in the rapidly growing sequence 3,27,7625597484987,....
Astronomy
- Messier objectMessier objectThe Messier objects are a set of astronomical objects first listed by French astronomer Charles Messier in 1771. The original motivation of the catalogue was that Messier was a comet hunter, and was frustrated by objects which resembled but were not comets...
M64, a magnitude 9.0 galaxyGalaxyA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
in the constellationConstellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
Coma BerenicesComa BerenicesComa Berenices is a traditional asterism that has since been defined as one of the 88 modern constellations. It is located near Leo, to which it formerly belonged, and accommodates the North Galactic Pole...
, also known as the Black Eye GalaxyBlack Eye GalaxyThe Black Eye Galaxy was discovered by Edward Pigott in March 1779, and independently by Johann Elert Bode in April of the same year, as well as by Charles Messier in 1780...
.
- The New General CatalogueNew General CatalogueThe New General Catalogue of Nebulae and Clusters of Stars is a well-known catalogue of deep sky objects in astronomy. It contains 7,840 objects, known as the NGC objects...
object NGC 64, a barred spiral galaxyBarred spiral galaxyA barred spiral galaxy is a spiral galaxy with a central bar-shaped structure composed of stars. Bars are found in approximately two-thirds of all spiral galaxies...
in the constellation CetusCetusCetus is a constellation. Its name refers to Cetus, a sea monster in Greek mythology, although it is often called 'the whale' today. Cetus is located in the region of the sky that contains other water-related constellations such as Aquarius, Pisces, and Eridanus.-Ecliptic:Although Cetus is not...
- The Saros number of the solar eclipseSolar eclipseAs seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...
series which began on -832 April 11 and ended on 430 May. The duration of Saros series 64 was 1262.1 years, and it contained 71 solar eclipses.
- The Saros number of the lunar eclipseLunar eclipseA lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...
series which began on -801 August 9 and ended on 714 February. The duration of Saros series 64 was 1514.5 years, and it contained 85 lunar eclipses.
In other fields
Sixty-four is:- In some computer programming languages, the size in bits of certain data types
- In chessChessChess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
or draughtsDraughtsDraughts is a group of abstract strategy board games between two players which involve diagonal moves of uniform pieces and mandatory captures by jumping over the enemy's pieces. Draughts developed from alquerque...
, the total number of black (dark) and white (light) squares on the game board - 6464 (chess magazine)The magazine 64 is a Russian chess and draughts publication, published in Moscow. Its name refers to the number of squares on a chessboard. The magazine awards the Chess Oscar annually.-History:...
is the name of the premier RussiaRussiaRussia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n chess magazineMagazineMagazines, periodicals, glossies or serials are publications, generally published on a regular schedule, containing a variety of articles. They are generally financed by advertising, by a purchase price, by pre-paid magazine subscriptions, or all three... - The code for international direct dial calls to New ZealandNew ZealandNew Zealand is an island country in the south-western Pacific Ocean comprising two main landmasses and numerous smaller islands. The country is situated some east of Australia across the Tasman Sea, and roughly south of the Pacific island nations of New Caledonia, Fiji, and Tonga...
- The designation of US Interstate 64Interstate 64Interstate 64 is an Interstate Highway in the Midwestern and Southeastern United States. Its western terminus is at I-70, U.S. 40, and U.S. 61 in Wentzville, Missouri. Its eastern terminus is at an interchange with I-264 and I-664 at Bowers Hill in Chesapeake, Virginia. As I-64 is concurrent with...
, a freeway from MissouriMissouriMissouri is a US state located in the Midwestern United States, bordered by Iowa, Illinois, Kentucky, Tennessee, Arkansas, Oklahoma, Kansas and Nebraska. With a 2010 population of 5,988,927, Missouri is the 18th most populous state in the nation and the fifth most populous in the Midwest. It...
to VirginiaVirginiaThe Commonwealth of Virginia , is a U.S. state on the Atlantic Coast of the Southern United States. Virginia is nicknamed the "Old Dominion" and sometimes the "Mother of Presidents" after the eight U.S. presidents born there... - The designation of U.S. Route 64U.S. Route 64U.S. Route 64 is an east–west United States highway that runs for 2,326 miles from eastern North Carolina to just southwest of the Four Corners in northeast Arizona. The western terminus is at U.S. Route 160 in Teec Nos Pos, Arizona. The highway's eastern terminus is at NC 12 and U.S. Route...
, a highway from ArizonaArizonaArizona ; is a state located in the southwestern region of the United States. It is also part of the western United States and the mountain west. The capital and largest city is Phoenix...
to North CarolinaNorth CarolinaNorth Carolina is a state located in the southeastern United States. The state borders South Carolina and Georgia to the south, Tennessee to the west and Virginia to the north. North Carolina contains 100 counties. Its capital is Raleigh, and its largest city is Charlotte... - The subject of the BeatlesThe BeatlesThe Beatles were an English rock band, active throughout the 1960s and one of the most commercially successful and critically acclaimed acts in the history of popular music. Formed in Liverpool, by 1962 the group consisted of John Lennon , Paul McCartney , George Harrison and Ringo Starr...
song "When I'm Sixty-FourWhen I'm Sixty-Four"When I'm Sixty-Four" is a song by The Beatles, written by Paul McCartney and released in 1967 on their album Sgt. Pepper's Lonely Hearts Club Band.-Composition:...
" - The registry of the U.S. Navy's aircraft carrier USS Constellation (CV-64)USS Constellation (CV-64)USS Constellation , a Kitty Hawk-class supercarrier, was the third ship of the United States Navy to be named in honor of the "new constellation of stars" on the flag of the United States and the only naval vessel ever authorized to display red, white, and blue designation numbers...
- The number of BrailleBrailleThe Braille system is a method that is widely used by blind people to read and write, and was the first digital form of writing.Braille was devised in 1825 by Louis Braille, a blind Frenchman. Each Braille character, or cell, is made up of six dot positions, arranged in a rectangle containing two...
characters in the old 6-dot system - In 8-bit8-bitThe first widely adopted 8-bit microprocessor was the Intel 8080, being used in many hobbyist computers of the late 1970s and early 1980s, often running the CP/M operating system. The Zilog Z80 and the Motorola 6800 were also used in similar computers...
home computerHome computerHome computers were a class of microcomputers entering the market in 1977, and becoming increasingly common during the 1980s. They were marketed to consumers as affordable and accessible computers that, for the first time, were intended for the use of a single nontechnical user...
s, a common shorthand for the Commodore 64Commodore 64The Commodore 64 is an 8-bit home computer introduced by Commodore International in January 1982.Volume production started in the spring of 1982, with machines being released on to the market in August at a price of US$595... - In video games, the Nintendo 64Nintendo 64The , often referred to as N64, was Nintendo′s third home video game console for the international market. Named for its 64-bit CPU, it was released in June 1996 in Japan, September 1996 in North America, March 1997 in Europe and Australia, September 1997 in France and December 1997 in Brazil...
video game consoleVideo game consoleA video game console is an interactive entertainment computer or customized computer system that produces a video display signal which can be used with a display device to display a video game...
and (historically) the Commodore 64Commodore 64The Commodore 64 is an 8-bit home computer introduced by Commodore International in January 1982.Volume production started in the spring of 1982, with machines being released on to the market in August at a price of US$595...
. Since 1996, the number 64 has been an abbreviation or slang for Nintendo 64 (though N64 is more common) - The maximum number of strokes in any Chinese characterChinese characterChinese characters are logograms used in the writing of Chinese and Japanese , less frequently Korean , formerly Vietnamese , or other languages...
- Number of hexagrams in the I ChingI ChingThe I Ching or "Yì Jīng" , also known as the Classic of Changes, Book of Changes and Zhouyi, is one of the oldest of the Chinese classic texts...
- Number of sexual positions in the Kama SutraKama SutraThe Kama Sutra is an ancient Indian Hindu text widely considered to be the standard work on human sexual behavior in Sanskrit literature written by Vātsyāyana. A portion of the work consists of practical advice on sexual intercourse. It is largely in prose, with many inserted anustubh poetry verses...
- Number of demons in the Dictionnaire InfernalDictionnaire InfernalThe Dictionnaire Infernal is a book on demonology, organised in hellish hierarchies. It was written by Jacques Auguste Simon Collin de Plancy and first published in 1818. There were several editions of the book, but perhaps the most famous is the edition of 1863, in which sixty-nine illustrations...
- Slang term referring to a 1964 Chevrolet ImpalaChevrolet ImpalaThe Chevrolet Impala is a full-size automobile built by the Chevrolet division of General Motors introduced for the 1958 model year. Deriving its name from the southern African antelope, Chevrolet's most expensive passenger model through 1965 had become the best-selling automobile in the United...
, often configured as a lowriderLowrider]A lowrider is a style of car originated by Chicano communities that sits lower to the ground than most other cars. Many lowriders have their suspension systems modified so that their ride can change height at the flip of a switch...
, a popular subject among early-90's gangsta rapGangsta rapGangsta Rap is a subgenre of hip hop music that evolved from hardcore hip hop and purports to reflect urban crime and the violent lifestyles of inner-city youths. Lyrics in gangsta rap have varied from accurate reflections to fictionalized accounts. Gangsta is a non-rhotic pronunciation of the word... - The number of classical arts listed in many Indian scriptures. They include: singing, dancing, painting, poetry, playing cards, making arguments, making flower garlands, etc.
- The number of the French department Pyrénées-AtlantiquesPyrénées-AtlantiquesPyrénées-Atlantiques is a department in the southwest of France which takes its name from the Pyrenees mountains and the Atlantic Ocean.- History :...
- The number of crayons in the popular Crayola 64 pack
- Base 64 is used for example with Base64Base64Base64 is a group of similar encoding schemes that represent binary data in an ASCII string format by translating it into a radix-64 representation...
encoding. - 64 (dog) is a character in the Donald DuckDonald DuckDonald Fauntleroy Duck is a cartoon character created in 1934 at Walt Disney Productions and licensed by The Walt Disney Company. Donald is an anthropomorphic white duck with a yellow-orange bill, legs, and feet. He typically wears a sailor suit with a cap and a black or red bow tie. Donald is most...
comicsComicsComics denotes a hybrid medium having verbal side of its vocabulary tightly tied to its visual side in order to convey narrative or information only, the latter in case of non-fiction comics, seeking synergy by using both visual and verbal side in...
universe. - Number of codons in the RNA codon table under genetic codeGenetic codeThe genetic code is the set of rules by which information encoded in genetic material is translated into proteins by living cells....
. - Number of golden disks in the myth of the Tower of HanoiTower of HanoiThe Tower of Hanoi or Towers of Hanoi, also called the Tower of Brahma or Towers of Brahma, is a mathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod...
. - A number referring to Tiananmen Square protests of 1989Tiananmen Square protests of 1989The Tiananmen Square protests of 1989, also known as the June Fourth Incident in Chinese , were a series of demonstrations in and near Tiananmen Square in Beijing in the People's Republic of China beginning on 15 April 1989...
in Chinese