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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^(*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 (18221901) observed this property of 163 long before Ramanujan's work on these socalled "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. [OliverLafont] 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 2digit irregular primes. [Poo Sung] The smallest prime p whose pth power p^{p} contains a pandigital substring: 163^{163} = 38599...(5941863207)...95547. Note that (163) is a semiprime with larger prime factor 19 which is the smallest prime q whose qth power q^{q} 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 3digit prime whose absolute value of the differences between any two of its digits are also prime. [Green] The largest squarefree integer n such that the ring of integers of the field Q(sqrt(n)) has unique factorization. [Luen] The prime number 163 contains only the three positive triangular digits, as does the 163rd triangular number (13366). [Gaydos]
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