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 $9$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$:
 * $35 = \dfrac {5 \left({3 \times 5 - 1}\right)} 2$


 * 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 $4375$:
 * $35 = 5 \times 7$, $4374 = 2 \times 3^7$; $36 = 2^2 \times 3^2$, $4375 = 5^4 \times 7$


 * 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 $\tau \left({n}\right) \mathrel \backslash \phi \left({n}\right) \mathrel \backslash \sigma \left({n}\right)$:
 * $\tau \left({35}\right) = 4$, $\phi \left({35}\right) = 24$, $\sigma \left({35}\right) = 48$


 * The number of pairs of twin primes less than $1000$

Also see

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