58

Number
$58$ (fifty-eight) is:
 * $2 \times 29$


 * The $3$rd non-square positive integer which cannot be expressed as the sum of a square and a prime:
 * $10$, $34$, $58$, $\ldots$


 * The $4$th Smith number after $4$, $22$, $27$:
 * $5 + 8 = 2 + 2 + 9 = 13$


 * The $5$th positive integer which cannot be expressed as the sum of a square and a prime:
 * $1$, $10$, $25$, $34$, $58$, $\ldots$


 * The $6$th noncototient after $10$, $26$, $34$, $50$, $52$:
 * $\nexists m \in \Z_{>0}: m - \map \phi m = 58$
 * where $\map \phi m$ denotes the Euler $\phi$ function


 * The $16$th (and probably largest) integer $n$ after $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $9$, $10$, $11$, $17$, $18$, $30$, $33$ such that $5^n$ contains no zero in its decimal representation:
 * $5^{58} = 34 \, 694 \, 469 \, 519 \, 536 \, 141 \, 888 \, 238 \, 489 \, 627 \, 838 \, 134 \, 765 \, 625$


 * The $21$st semiprime after $4$, $6$, $9$, $10$, $14$, $15$, $21$, $22$, $25$, $26$, $33$, $34$, $35$, $38$, $39$, $46$, $49$, $51$, $55$, $58$:
 * $58 = 2 \times 29$

Also see