163 (number)

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163 is the natural number following one hundred sixty-two and preceding one hundred sixty-four.


List of numbers — Integers

<< 160 161 162 163 164 165 166 167 168 169 >>
Ordinal One hundred [and]
sixty-three
Cardinal 163rd
Factorization prime number
Roman numeral CLXIII
Binary 10100011
Hexadecimal A3

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.

Given 163, the Mertens function returns 0.

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

163 is a strictly non-palindromic number.

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.

[edit] \sqrt{163}

The square root of 163 occurs in several interesting pieces of mathematics.

The function f(n) = n2 + n + 41 gives prime values for all values of n between 0 and 39, and for n < 107 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, in which e^{\pi \sqrt{163}} almost equals the integer 262537412640768744 = 640320^3 + 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...

[edit] Other occurrences

One hundred sixty-three is also:

  • The first number that cannot be shot with three darts on a standard dart board.
  • The year AD 163 or 163 BC.

[edit] Reference

  • Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (pp. 141 - 142). London: Penguin Group.
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