29

Number
$29$ (twenty-nine) is:


 * The $10$th prime number, after $2, 3, 5, 7, 11, 13, 17, 19, 23$


 * The $7$th Lucas number after $(2), 1, 3, 4, 7, 11, 18$:
 * $29 = 11 + 18$


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


 * The $3$rd number such that $2 n^2 - 1$ is square, after $1$ and $5$:
 * $2 \times 29^2 - 1 = 2 \times 841 - 1 = 1681 = 41^2$


 * The first of $29$ primes of the form $2 x^2 + 29$:
 * $2 \times 0^2 + 29 = 29$


 * The $4$th of $11$ primes of the form $2 x^2 + 11$:
 * $2 \times 3^2 + 11 = 29$

Also see

 * Hilbert-Waring Theorem: Cubes
 * Smallest Integer not Sum of Two Ulam Numbers
 * Square-Bracing Problem: Non-Crossing Rods