167 (one hundred ndsixty-seven) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal ...

following 166 and preceding

168 Year 168 ( CLXVIII) was a leap year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Apronianus and Paullus (or, less frequently, year 921 '' Ab urbe c ...

In mathematics

167 is an

emirp An emirp (''prime'' spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed. This definition excludes the related palindromic primes. The term ''reversible prime'' is used to mean the same as e ...

, an isolated prime, a

Chen prime A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingru ...

, a

Gaussian prime In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as \mathbf /ma ...

, a

safe prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + ...

, and an

Eisenstein prime In mathematics, an Eisenstein prime is an Eisenstein integer : z = a + b\,\omega, \quad \text \quad \omega = e^, that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units , itself ...

with no imaginary part and a real part of the form

3n - 1

. 167 is the smallest prime which can not be expressed as a sum of seven or fewer

cubes In geometry, a cube is a three-dimensional space, three-dimensional solid object bounded by six square (geometry), square faces, Facet (geometry), facets or sides, with three meeting at each vertex (geometry), vertex. Viewed from a corner it i ...

. It is also the smallest number which requires six terms when expressed using the greedy algorithm as a sum of squares, 167 = 144 + 16 + 4 + 1 + 1 + 1, although by

Lagrange's four-square theorem Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares. That is, the squares form an additive basis of order four. p = a_0^2 + a_1^2 + a_2^2 + a_ ...

its non-greedy expression as a sum of squares can be shorter, e.g. 167 = 121 + 36 + 9 + 1. 167 is a full reptend prime in base 10, since the decimal expansion of 1/167 repeats the following 166 digits: 0.00598802395209580838323353293413173652694610778443113772455089820359281437125748502994 0119760479041916167664670658682634730538922155688622754491017964071856287425149700... 167 is a highly cototient number, as it is the smallest number ''k'' with exactly 15 solutions to the equation ''x'' - φ(''x'') = ''k''. It is also a strictly non-palindromic number. 167 is the smallest multi-digit prime such that the product of digits is equal to the number of digits times the sum of the digits, i. e., 1×6×7 = 3×(1+6+7) 167 is the smallest positive integer ''d'' such that the imaginary

quadratic field In algebraic number theory, a quadratic field is an algebraic number field of degree two over \mathbf, the rational numbers. Every such quadratic field is some \mathbf(\sqrt) where d is a (uniquely defined) square-free integer different from 0 a ...

Q() has class number = 11.

In astronomy

* 167 Urda is a

main belt The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, called ...

asteroid * 167P/CINEOS is a periodic

comet A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena ...

in the

Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...

* IC 167 is interacting galaxies

In the military

* Marine Light Attack Helicopter Squadron 167 is a

United States Marine Corps The United States Marine Corps (USMC), also referred to as the United States Marines, is the maritime land force service branch of the United States Armed Forces responsible for conducting expeditionary and amphibious operations through combi ...

helicopter A helicopter is a type of rotorcraft in which lift and thrust are supplied by horizontally spinning rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forward, backward and laterally. These attributes ...

squadron * Martin Model 167 was a

U.S. The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territori ...

-designed light bomber during World War II * was a

U.S. Navy The United States Navy (USN) is the maritime service branch of the United States Armed Forces and one of the eight uniformed services of the United States. It is the largest and most powerful navy in the world, with the estimated tonnage o ...

Diver-class

rescue and salvage ship Rescue and salvage ships (hull classification symbol ARS) are a type of military salvage tug. They are tasked with coming to the aid of stricken vessels. Their general mission capabilities include combat salvage, lifting, towing, retraction of grou ...

during World War II * was a U.S. Navy during World War II * was a U.S. Navy during World War II * was a U.S. Navy during World War I * was a U.S. Navy during World War II * was a transport ship during World War II * was a U.S. Navy during World War II

In sports

* Martina Navratilova has 167 tennis titles, an all-time record for men or women

In transportation

London Buses route 167 London Buses route 167 is a Transport for London contracted bus route in London, England. Running between Ilford and Loughton station, it is operated by Stagecoach London. History In 1986, the operation of the route was put out to tender, an ...

* 167th Street is an elevated local station in

the Bronx The Bronx () is a borough of New York City, coextensive with Bronx County, in the state of New York. It is south of Westchester County; north and east of the New York City borough of Manhattan, across the Harlem River; and north of the New Y ...

on the

IRT Jerome Avenue Line The IRT Jerome Avenue Line, also unofficially known as IRT Woodlawn Line and IRT Burnside Avenue Line is an A Division New York City Subway line mostly along Jerome Avenue in the Bronx. Originally an Interborough Rapid Transit Company-operated r ...

, , of the New York City Subway. * 167th Street is an underground local station in

on the

IND Concourse Line The Concourse Line is an IND rapid transit line of the New York City Subway system. It runs from 205th Street in Norwood, Bronx, primarily under the Grand Concourse, to 145th Street in Harlem, Manhattan. It is the only B Division line, and a ...

, , of the New York City Subway. * List of highways numbered 167

In other fields

167 is also: * The year AD 167 or 167 BC * The

Universal Disk Format Universal Disk Format (UDF) is an open, vendor-neutral file system for computer data storage for a broad range of media. In practice, it has been most widely used for DVDs and newer optical disc formats, supplanting ISO 9660. Due to its design ...

(or ECMA-167) format of a file system for optical media storage * C167 family is a 16-bit microcontroller architecture from

Infineon Infineon Technologies AG is a German semiconductor manufacturer founded in 1999, when the semiconductor operations of the former parent company Siemens AG were spun off. Infineon has about 50,280 employees and is one of the ten largest semicond ...

* Pips are dots on the face of a die, denoting its value. The pip count at the start of a

backgammon Backgammon is a two-player board game played with counters and dice on tables boards. It is the most widespread Western member of the large family of tables games, whose ancestors date back nearly 5,000 years to the regions of Mesopotamia and Pe ...

game is 167

External links

Prime curiosities: 167

References

{{DEFAULTSORT:167 (Number) Integers