43

Number
$43$ (forty-three) is:


 * The $14$th prime number, after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$


 * The $2$nd of the $6$th pair of twin primes, with $51$


 * The lower end of the $4$th record-breaking gap between twin primes:
 * $59 - 43 = 16$


 * The $12$th lucky number:
 * $1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $\ldots$


 * The index of the $1$st non-integer term of Göbel's sequence.


 * The $5$th of $11$ primes of the form $2 x^2 + 11$:
 * $2 \times 4^2 + 11 = 43$


 * The $19$th positive integer which is not the sum of $1$ or more distinct squares:
 * $2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $23$, $24$, $27$, $28$, $31$, $32$, $33$, $43$, $\ldots$


 * The $26$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $26$, $29$, $30$, $31$, $32$, $33$, $37$, $38$, $42$ which cannot be expressed as the sum of distinct pentagonal numbers.

Also see

 * Non-Integral Value of Göbel's Sequence