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 (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 (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]
To link to this page use http://primes.utm.edu/curios/page.php?number_id=97
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