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+ A prime whose reversal is another prime (19) squared. [Trigg]

+ In the April 1975 issue of Scientific American, Martin Gardner wrote (jokingly) that Ramanujan's constant (e^(pi*sqrt(163))) is an integer. The name "Ramanujan's constant" was actually coined by Simon Plouffe and derives from the above April Fool's joke played by Gardner. The French mathematician Charles Hermite (1822-1901) observed this property of 163 long before Ramanujan's work on these so-called "almost integers." [Aitken]

+ The largest Heegner number. [Croll]

+ 163 = "is a prime number" by adding the letters in the alphabet code, i.e., a = 1, b = 2, c = 3, etc. [Necula]

+ 163 is the smallest prime number that is a factor of more than one number of the form p# - 1 (163 divides both 67# - 1 and 79# - 1).

+ Let the cs(p) be the cumulative digit sum of all the primes 2 to p (e.g., cs(11)=2+3+5+7+1+1=19). There are the only four known primes such that cs(p)=2p; they are 5, 23, 47 and 163. [Vrba]

+ 163 = 1+2*3^4. [Oliver-Lafont]

+ 163 is the only known number m (up to 3*10^10) such that m + 4*n^2 for n = 0, 1, 2, ... , 19 are prime. [Firoozbakht]

+ Conjectured to be the largest prime that can be represented uniquely as the sum of three squares (1^2 + 9^2 + 9^2). Note that squares are allowed to be zero. [Noe]

+ The smallest score impossible to make using up to but not more than 3 darts. [Geach]

+ The sum 37 + 59 + 67 of all 2-digit irregular primes. [Poo Sung]

+ The smallest prime p whose pth power pp contains a pandigital substring: 163163 = 38599...(5941863207)...95547. Note that pi(163) is a semiprime with larger prime factor 19 which is the smallest prime q whose qth power qq is pandigital, and that the concatenations 16319 and 19163 are also primes. [Beedassy]

+ According to Cam McLeman, 163 is the coolest number in existence.

+ 163 is the least number k such that decimal representation of 1/k has period of length 81. It is one of a few exceptions to the rule that k=3^(n+2) is the least number with 1/k having period 3^n. [Noe]

+ The smallest 3-digit prime whose absolute value of the differences between any two of its digits are also prime. [Green]

(There are 12 curios for this number that have not yet been approved by an editor.)




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