167 (number)

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

← 166 167 168 →
Cardinalone hundred sixty-seven
Ordinal167th
(one hundred sixty-seventh)
Factorizationprime
Prime39th
Divisors1, 167
Greek numeralΡΞΖ´
Roman numeralCLXVII
Binary101001112
Ternary200123
Octal2478
Duodecimal11B12
HexadecimalA716

In mathematicsEdit

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 smallest 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 + 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 astronomyEdit

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In transportationEdit

In other fieldsEdit

167 is also:

See alsoEdit

External linksEdit

ReferencesEdit

  1. ^ "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  2. ^ 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.
  3. ^ "Tables of imaginary quadratic fields with small class number". numbertheory.org.