163 (number) Article Index for
163
Shopping
163
 

Information About

163 (number)






Ordinal One hundred {Link without Title}
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 .


<MATH>\SQRT{163}</MATH>


The Square Root of 163 occurs in several interesting pieces of mathematics.

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, 163.

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. 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...


OTHER OCCURRENCES


One hundred sixty-three is also: