163 (number)
Encyclopedia : 1 : 16 : 163 : 163 (number)
163 is the natural number following one hundred sixty-two and preceding one hundred sixty-four.
| |||
| 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 \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(\sqrt)] has unique factorization for [a=163]. The only other such integers are [a = 1, 2, 3, 7, 11, 19, 43, 67].
[\sqrt]
The square root of 163 occurs in several interesting pieces of mathematics.
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 ) / 2].
[\sqrt] appears in the Ramanujan constant, in which [e^}] 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...
Other occurrences
One hundred sixty-three is also:
Reference
- Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (pp. 141 - 142). London: Penguin Group.
From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.