167 (number)

167 (one hundred [and] sixty-seven) is the natural number following 166 and preceding 168.

In mathematics
167 is the 39th prime number, an emirp, an isolated prime, a Chen prime, a Gaussian prime, a safe prime, and an Eisenstein prime with no imaginary part and a real part of the form $$3n - 1$$.

167 is 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 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&times;6&times;7 = 3&times;(1+6+7)

167 is the smallest positive integer d such that the imaginary quadratic field Q(√–d) has class number = 11.

In astronomy

 * 167 Urda is a main belt asteroid
 * 167P/CINEOS is a periodic comet in the Solar System
 * IC 167 is interacting galaxies

In the military

 * Marine Light Attack Helicopter Squadron 167 is a United States Marine Corps helicopter squadron
 * Martin Model 167 was a U.S.-designed light bomber during World War II
 * USCGC Acushnet (WMEC-167) was a U.S. Navy Diver-class rescue and salvage ship during World War II
 * USS Acree (DE-167) was a U.S. Navy Cannon-class destroyer escort during World War II
 * USS Caledonia (AK-167) was a U.S. Navy Alamosa-class cargo ship during World War II
 * USS Cowell (DD-167) was a U.S. Navy Wickes-class destroyer during World War I
 * USS Freestone (APA-167) was a U.S. Navy Haskell-class attack transport during World War II
 * USS Leyden (IX-167) was a transport ship during World War II
 * USS Narwhal (SS-167) was a U.S. Navy Narwhal-class submarine 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
 * 167th Street is an elevated local station in the Bronx on the IRT Jerome Avenue Line,, of the New York City Subway.
 * 167th Street is an underground local station in the Bronx on the IND Concourse Line,, 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 (or ECMA-167) format of a file system for optical media storage
 * C167 family is a 16-bit microcontroller architecture from Infineon
 * Pips are dots on the face of a die, denoting its value. The pip count at the start of a backgammon game is 167