167 (number)

Short description: Natural number

| <- 166  | 167 |  168 ->

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← 160 161 162 163 164 165 166 167 168 169 →

List of numbers — Integers

← 0 100 200 300 400 500 600 700 800 900 →

Cardinal| one hundred sixty-seven
Ordinal| 167th
(one hundred sixty-seventh)
Factorization| prime
Prime| 39th
Divisors| 1, 167
Greek numeral| ΡΞΖ´
Roman numeral| CLXVII
Binary| 101001112
Ternary| 200123
Quaternary| 22134
Quinary| 11325
Senary| 4356
Octal| 2478
Duodecimal| 11B12
Hexadecimal| A716
Vigesimal| 8720
Base 36| 4N36

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

## Contents

* 1 In mathematics
* 2 In astronomy
* 3 In the military
* 4 In sports
* 5 In transportation
* 6 In other fields
* 7 See also
* 8 External links
* 9 References

## In mathematics

167 is an emirp, an isolated prime, a Chen prime, a Gaussian prime, a safe prime,[1] 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,[2] 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., 1×6×7 = 3×(1+6+7)

167 is the smallest positive integer d such that the imaginary quadratic field Q(√–d) has class number = 11.[3]

## 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 United States -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
* Engineering:USS Acree (DE-167) was a U.S. Navy Cannon-class destroyer escort during World War II
* Engineering:USS Caledonia (AK-167) was a U.S. Navy Alamosa-class cargo ship during World War II
* Engineering:USS Cowell (DD-167) was a U.S. Navy Wickes-class destroyer during World War I
* Engineering:USS Freestone (APA-167) was a U.S. Navy Haskell-class attack transport during World War II
* Engineering:USS Leyden (IX-167) was a transport ship during World War II
* Engineering: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, Template:NYCS Jerome train, of the New York City Subway.
* 167th Street is an underground local station in the Bronx on the IND Concourse Line, Template:NYCS Concourse local train, 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[importance?]

## See also

* M167 (disambiguation)
* List of highways numbered 167
* United States Supreme Court cases, Volume 167
* United Nations Security Council Resolution 167

## External links

* Prime curiosities: 167

## References

1. ↑ "Sloane's A005385 : Safe primes". OEIS Foundation. https://oeis.org/A005385.
2. ↑ Sloane, N. J. A., ed. "Sequence A006892 (Representation as a sum of squares requires n squares with greedy algorithm)". OEIS Foundation. https://oeis.org/A006892.
3. ↑ "Tables of imaginary quadratic fields with small class number". http://www.numbertheory.org/classnos/.

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