15

Number
$15$ (fifteen) is:


 * The first product of two different odd primes:
 * $3 \times 5$


 * The $5$th triangular number after $1, 3, 6, 10$:
 * $15 = 1 + 2 + 3 + 4 + 5 = \dfrac {5 \left({5 + 1}\right)} 2$


 * The $3$rd hexagonal number after $1, 6$:
 * $15 = 1 + 5 + 9 = 3 \left({2 \times 3 - 1}\right)$


 * The $6$th lucky number:
 * $1, 3, 7, 9, 13, 15, \ldots$


 * The magic constant of the order $3$ magic square.


 * The largest $n$ for which the Ramanujan-Nagell equation $x^2 - 7 = 2^n$ has an integral solution:
 * $181^2 - 7 = 32 \, 768 = 2^{15}$

Also see

 * Magic Constant of Order 3 Magic Square
 * Solutions of Ramanujan-Nagell Equation