163 (number)

163 is the natural number following 162 and preceding 164.

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 figures in an approximation of "e", in which $e\; approx\; \{163\; over\; 3cdot4cdot5\}\; approx\; 2.7166dots$.

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$a\; =\; 1,\; 2,\; 3,\; 7,\; 11,\; 19,\; 43,\; 67$.

$sqrt\{163\}$

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 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...

Other occurrences

One hundred sixty-three is also:
* The least number that cannot be shot with three darts on a standard dart board.
* The year AD 163 or 163 BC.

References

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

ee also

* 163 (disambiguation)

External links

* [http://math.arizona.edu/~mcleman/CoolNumbers/CoolNumbers.html The coolest number is 163!]