58

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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

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• Previous: Powers of 5 with no Zero in Decimal Representation

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• Previous  ... Next: Non-Square Positive Integers not Sum of Square and Prime

• Previous  ... Next: Noncototient

• Previous  ... Next: Semiprime Number