# 167 (number)

This article may contain indiscriminate, excessive, or irrelevant examples. (April 2018) |

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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 |
10100111_{2} | |||

Ternary |
20012_{3} | |||

Quaternary |
2213_{4} | |||

Quinary |
1132_{5} | |||

Senary |
435_{6} | |||

Octal |
247_{8} | |||

Duodecimal |
11B_{12} | |||

Hexadecimal |
A7_{16} | |||

Vigesimal |
87_{20} | |||

Base 36 |
4N_{36} |

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

## Contents

## In mathematics[edit]

167 is 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 .

167 is the only prime which can not be expressed as a sum of seven or fewer cubes.
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,^{[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 + 1 + 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[edit]

- 167 Urda is a main belt asteroid
- 167P/CINEOS is a periodic comet in our solar system
- IC 167 is interacting galaxies

## In the military[edit]

- 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[edit]

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

## In transportation[edit]

- London Buses route 167
- SMRT Bus Service 167 in Singapore
- 167th Street is an elevated local station in the Bronx on the IRT Jerome Avenue Line, 4 train, of the New York City Subway.
- 167th Street is an underground local station in the Bronx on the IND Concourse Line, B and D trains, of the New York City Subway.
- List of highways numbered 167

## In other fields[edit]

**167** is also:

- The year AD 167 or 167 BC
- The atomic number of an element temporarily called Unhexseptium
- 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[edit]

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

## External links[edit]

Wikimedia Commons has media related to .167 (number) |

## References[edit]

**^**"Sloane's A005385 : Safe primes".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-28.**^**Sloane, N.J.A. (ed.). "Sequence A006892 (Representation as a sum of squares requires n squares with greedy algorithm)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.**^**"Tables of imaginary quadratic fields with small class number".*numbertheory.org*.