35

Number
$35$ (thirty-five) is:


 * $5 \times 7$


 * The $13$th semiprime after $4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34$:
 * $35 = 5 \times 7$


 * The $5$th pentagonal number after $1, 5, 12, 22$:
 * $35 = 1 + 4 + 7 + 10 + 13 = \dfrac {5 \left({3 \times 5 - 1}\right)} 2$


 * The $5$th tetrahedral number, after $1, 4, 10, 20$:
 * $35 = 1 + 3 + 6 + 10 + 15 = \dfrac {5 \left({5 + 1}\right) \left({5 + 2}\right)} 6$


 * The $4$th pentatope number after $1, 5, 15$:
 * $35 = 1 + 4 + 10 + 20 = \dfrac {4 \left({4 + 1}\right) \left({4 + 2}\right) \left({4 + 3}\right)} {24}$


 * The number of distinct hexominoes, up to reflection.


 * The maximum length of a non-crossing knight's tour on a standard chessboard.


 * $35$ and $4374$ have the same prime factors between them as $36$ and $4375$, that is: $2$, $3$, $5$ and $7$.


 * The $4$th integer after $7, 13, 19$ the decimal representation of whose square can be split into two parts which are each themselves square:
 * $35^2 = 1225; 1 = 1^2, 225 = 15^2$


 * The $19$th after $1, 2, 4, 5, 6, 8, 9, 12, 13, 15, 16, 17, 20, 24, 25, 27, 28, 32$ of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes.


 * The $25$th integer $n$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{35} = 34 \, 359 \, 738 \, 368$


 * The $1$st positive integer $n$ such that $\sigma \left({n}\right) = \dfrac {\phi \left({n}\right) \times \tau \left({n}\right)} 2$:
 * $\sigma \left({35}\right) = 48 = \dfrac {\phi \left({35}\right) \times \tau \left({35}\right)} 2$


 * The $5$th integer $n$ after $1, 3, 15, 30$ with the property that $\tau \left({n}\right) \mathrel \backslash \phi \left({n}\right) \mathrel \backslash \sigma \left({n}\right)$:
 * $\tau \left({35}\right) = 4$, $\phi \left({35}\right) = 24$, $\sigma \left({35}\right) = 48$

Also see

 * 35 Hexominoes
 * Maximum Length of Non-Crossing Knight's Move
 * Prime Factors of 35, 36, 4734 and 4735