167 (number)

← 166 167 168 →
← 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, chen, gaussian, safe
Divisors	1, 167
Greek numeral	ΡΞΖ´
Roman numeral	CLXVII
Binary	101001112
Ternary	200123
Senary	4356
Octal	2478
Duodecimal	11B12
Hexadecimal	A716

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, ^[1] a Gaussian prime, a safe prime, ^[2] and an Eisenstein prime with no imaginary part and a real part of the form ${\displaystyle 3n-1}$.

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, ^[3] 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. ^[4]

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, 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

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, N. J. A. (ed.). "SequenceA109611(Chen primes: primes p such that p + 2 is either a prime or a semiprime)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA005385(Safe primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA006892(Representation as a sum of squares requires n squares with greedy algorithm)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. "Tables of imaginary quadratic fields with small class number". numbertheory.org.