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163 (number)

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Title: 163 (number)  
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Subject: List of prime numbers, 164 (number), 162 (number), 160 (number), 165 (number)
Collection: Integers
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163 (number)

162 163 164
Cardinal one hundred sixty-three
Ordinal 163rd
(one hundred and sixty-third)
Factorization prime
Prime 38th
Divisors 1, 163
Roman numeral CLXIII
Binary 101000112
Ternary 200013
Quaternary 22034
Quinary 11235
Senary 4316
Octal 2438
Duodecimal 11712
Hexadecimal A316
Vigesimal 8320
Base 36 4J36

163 (one hundred [and] sixty-three) is the natural number following 162 and preceding 164.


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

In mathematics

163 is a strong prime in the sense that it is greater than the arithmetic mean of its two neighboring primes.

163 is a lucky prime and a fortunate number.

163 is a strictly non-palindromic number, since it is not palindromic in any base between base 2 and base 161.

Given 163, the Mertens function returns 0, it is the third prime with this property, the first two such primes are 101 and 149.

163 figures in an approximation of π, in which \pi \approx {2^9 \over 163} \approx 3.1411.

163 figures in an approximation of e, in which e \approx {163 \over 3\cdot4\cdot5} \approx 2.7166\dots.

163 is a Heegner number. That is, the ring of integers of the field \mathbb{Q}(\sqrt{-a}) has unique factorization for a=163. The only other such integers are a = 1, 2, 3, 7, 11, 19, 43, 67. (sequence A003173 in OEIS)

163 is a permutable prime in base 12, which it is written as 117, the permutations of its digits are 171 and 711, the two numbers in base 12 is 229 and 1021 in base 10, both of them are primes.

The function f(n) = n^2 + n + 41 gives prime values for all values of n between 0 and 39, and for n < 10^7 approximately half of all values are prime. 163 appears as a result of solving f(n)=0, which gives n = (-1+ \sqrt{-163} ) / 2.

\sqrt{163} appears in the Ramanujan constant, since -163 in a quadratic nonresidue to modulo all the primes 3, 5, 7, ..., 37. In which e^{\pi \sqrt{163}} almost equals the integer 262537412640768744 = 6403203 + 744. Martin Gardner famously asserted that this identity was exact in a 1975 April Fools' hoax in Scientific American; in fact the value is 262537412640768743.99999999999925007259...

In astronomy

In the US military

In American sports

In transportation

In other fields

163 is also:

See also


  1. ^ Boise Weekly (July 2, 2008), "Generations of skateboarders keep rolling" by Katy Dang

External links

  • The Number 163
  • The Positive Integer 163
  • Prime curiosities: 163
  • website from NetEase
  • The coolest number is 163
  • 163, the Monster and Number Theory
  • VirtueScience: 163
  • International Brotherhood of Electrical Workers Local Union 163
  • US Highway 163
  • Planetmath.Org 163
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