73 (seventy-three) is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.

It is the 21st prime number and the fourth star number. It is also the eighth twin prime, with 71.

73 is the 21st prime number, and emirp with 37, the 12th prime number. It is also the eighth twin prime, with 71. It is the largest minimal primitive root in the first 100,000 primes; in other words, if p is one of the first one hundred thousand primes, then at least one of the numbers 2, 3, 4, 5, 6, ..., 73 is a primitive root modulo p. 73 is also the smallest factor of the first composite generalized Fermat number in decimal: ${\displaystyle 10^{4}+1=10,001=73\times 137}$, and the smallest prime congruent to 1 modulo 24, as well as the only prime repunit in octal (111₈). It is the fourth star number.

Where 73 and 37 are part of the sequence of permutable primes and emirps in base-ten, the number 73 is more specifically the unique Sheldon prime, named as an homage to TV character Sheldon Cooper and defined as satisfying "mirror" and "product" properties, where:

73 and 37 are also consecutive star numbers, equivalently consecutive centered dodecagonal (12-gonal) numbers (respectively the 4th and the 3rd). They are successive lucky primes and sexy primes, both twice over, and successive Pierpont primes, respectively the 9th and 8th. 73 and 37 are consecutive values of ${\displaystyle g(k)}$ such that every positive integer can be written as the sum of 73 or fewer sixth powers, or 37 or fewer fifth powers (and 19 or fewer fourth powers; see Waring's problem).

73 and 37 are consecutive primes in the seven-integer covering set of the first known Sierpiński number 78,557 of the form ${\displaystyle k\times 2^{n}+1}$ that is composite for all natural numbers ${\displaystyle n}$, where 73 is the largest member: ${\displaystyle \{3,5,7,13,19,37,73\}.}$ More specifically, ${\displaystyle 78,557\times 2^{n}+1}$ modulo 36 will be divisible by at least one of the integers in this set.^{[citation needed]}

Consider the following sequence ${\displaystyle A(n)}$:

Known such index values ${\displaystyle n}$ where ${\displaystyle p}$ is equal to 73 as the largest member of such covering sets are: ${\displaystyle \{1,6,9,12,15,16,21,22,24,27\}}$, with 37 present alongside 73. In particular, ${\displaystyle A(n)}$ ≥ 73 for any ${\displaystyle n}$.