163 (number)

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162 163 164
Cardinal one hundred and 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[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]

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163 is also:

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