163 (number)

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162163164
Cardinalone hundred and sixty-three
Ordinal163rd
(one hundred and sixty-third)
Factorizationprime
Prime38th
Divisors1, 163
Roman numeralCLXIII
Binary101000112
Ternary200013
Quaternary22034
Quinary11235
Senary4316
Octal2438
Duodecimal11712
HexadecimalA316
Vigesimal8320
Base 364J36
 
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162163164
Cardinalone hundred and sixty-three
Ordinal163rd
(one hundred and sixty-third)
Factorizationprime
Prime38th
Divisors1, 163
Roman numeralCLXIII
Binary101000112
Ternary200013
Quaternary22034
Quinary11235
Senary4316
Octal2438
Duodecimal11712
HexadecimalA316
Vigesimal8320
Base 364J36

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

In mathematics[edit]

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. 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 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.


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, 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[edit]

In the US military[edit]

In American sports[edit]

In transportation[edit]

In other fields[edit]

163 is also:

See also[edit]

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