73

Number
$73$ (seventy-three) is:


 * The $21$st prime number, after $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71$


 * The $2$nd of the $8$th pair of twin primes, with $71$


 * The $6$th emirp after $13, 17, 31, 37, 71$


 * The $11$th permutable prime after $2, 3, 5, 7, 11, 13, 17, 31, 37, 71$.


 * The $17$th lucky number:
 * $1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 73, \ldots$


 * The $1$st of the $2$nd ordered quadruple of consecutive integers that have sigma values which are strictly increasing:
 * $\sigma \left({73}\right) = 74$, $\sigma \left({74}\right) = 114$, $\sigma \left({75}\right) = 124$, $\sigma \left({76}\right) = 140$


 * In the smallest equilateral triangle with sides of integer length ($112$) which contains a point which is an integer distance from each vertex, the distance from that point to its furthest vertex (the other two being $57$ and $65$).


 * The $14$th positive integer $n$ after $5, 11, 17, 23, 29, 30, 36, 42, 48, 54, 60, 61, 67$ such that no factorial of an integer can end with $n$ zeroes.


 * The $1$st of the $17$ positive integers for which the value of the Euler $\phi$ function is $72$:
 * $73, 91, 95, 111, 117, 135, 146, 148, 152, 182, 190, 216, 222, 228, 234, 252, 270$


 * Every positive integer can be expressed as the sum of at most $73$ $6$th powers.

Also see

 * Hilbert-Waring Theorem for $6$th Powers
 * Smallest Equilateral Triangle with Internal Point at Integer Distances from Vertices





Observation
Sheldon Cooper:


 * $73$ is the best number:


 * $73$ is the $21$st prime number.


 * Its mirror $37$ is the $12$th prime number.


 * Its mirror $21$ is the product of multiplying, hang on to your hats, $7$ by $3$.

Leonard Hofstadter:


 * So $73$ is the Chuck Norris of numbers!

Sheldon Cooper:


 * Chuck Norris wishes.


 * In binary, $73$ is a palindrome: $1001001$, which is the same backwards as forwards.


 * All Chuck Norris gets you backwards is Sirron Kcuhc!

It may be worth adding the following observation about the Hilbert-Waring Theorem:
 * Every positive integer can be expressed as the sum of at most $37$ positive $5$th powers.

and:
 * Every positive integer can be expressed as the sum of at most $73$ (positive) $6$th powers.