163 (number)
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163 is the natural number following one hundred sixty-two and preceding one hundred sixty-four.
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| Ordinal | One hundred [and] sixty-three |
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| 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 
.
163 is a strictly non-palindromic number.
163 is a Heegner number. That is, the ring of integers of the field 
has unique factorization for a = 163. The only other such integers are a = 1,2,3,7,11,19,43,67.
[edit] 
The square root of 163 occurs in several interesting pieces of mathematics.
The function f(n) = n2 + n + 41 gives prime values for all values of n between 0 and 39, and for n < 107 approximately half of all values are prime. 163 appears as a result of solving f(n) = 0, which gives 
.
appears in the Ramanujan constant, in which 
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...
[edit] Other occurrences
One hundred sixty-three is also:
- The first number that cannot be shot with three darts on a standard dart board.
- The year AD 163 or 163 BC.
[edit] Reference
- Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (pp. 141 - 142). London: Penguin Group.
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