This number is a prime.
In the April 1975 issue of Scientific American, Martin Gardner wrote (jokingly) that Ramanujan's constant (e^(π*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]
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]
The smallest score impossible to make using up to but not more than 3 darts. [Geach]
The smallest prime p whose pth power pp contains a pandigital substring: 163163 = 38599...(5941863207)...95547. Note that π(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]
Some Major League Baseball seasons consists of 163 games. [Post]
163 and 631 are two primes consisting of the same distinct digits, (1, 3, 6), such that one of these digits is twice the product of the other two, i.e., 6 = 2*(1*3). Note that a concatenation of these primes creates a Cyclops prime, i.e., 6310163. [Loungrides]
The largest squarefree integer n such that the ring of integers of the field Q(sqrt(-n)) has unique factorization. [Luen]
CD163 is a protein encoded by the CD163 gene in humans. [Ford]