167 (number)
167 (one hundred [and] sixty-seven) is the natural number following 166 and preceding 168.
| 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 |
In mathematics edit
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 .
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 edit
- 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 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
- 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 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
External links edit
- Prime curiosities: 167
References edit
- ^ Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.