23

Number
$23$ (twenty-three) is:


 * The $9$th prime number, after $2, 3, 5, 7, 11, 13, 17, 19$


 * The $5$th Sophie Germain prime after $2, 3, 5, 11$:
 * $2 \times 23 + 1 = 47$, which is prime.


 * The index of the $3$rd repunit prime after $R_2, R_{19}$:
 * $R_{23} = 11 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111$


 * The $1$st of the first pair of consecutive prime numbers which differ by $6$:
 * $23, 29: 29 - 23 = 6$


 * The $3$rd Woodall number after $1, 7$, and $2$nd Woodall prime after $7$:
 * $23 = 3 \times 2^3 - 1$


 * The $3$rd Thabit number after $(2), 5, 11$, and $4$th Thabit prime:
 * $23 = 3 \times 2^3 - 1$


 * The $6$th happy number after $1$, $7$, $10$, $13$, $19$:
 * $23 \to 2^2 + 3^2 = 4 + 9 = 13 \to 1^2 + 3^2 = 1 + 9 = 10 \to 1^2 + 0^2 = 1$


 * The $1$st of the only two positive integers needing as many as $9$ positive cubes to express it:
 * $23 = 2^3 + 2^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3$
 * The other is $239$.


 * The number of digits in its factorial:
 * $23! = 25 \, 852 \, 016 \, 738 \, 884 \, 976 \, 640 \, 000$
 * which has $23$ digits


 * The $4$th of $5$ primes of the form $2 x^2 + 5$:
 * $2 \times 3^2 + 5 = 23$


 * The smallest integer greater than $1$ which is not the sum of two Ulam numbers.


 * The $4$th positive integer $n$ after $5, 11, 17$ such that no factorial of an integer can end with $n$ zeroes.


 * The $12$th positive integer which is not the sum of $1$ or more distinct squares:
 * $2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, \ldots$


 * The number of unit rods required to brace a unit square when rods may not cross.

Also see

 * Numbers not Expressible as Sum of Less than 9 Positive Cubes
 * Smallest Integer not Sum of Two Ulam Numbers
 * Square-Bracing Problem: Non-Crossing Rods