163 (number)

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 area = 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 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 = 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!]


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