# 43

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

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

- The $6$th prime $p$ after $11$, $23$, $29$, $37$, $41$ such that the Mersenne number $2^p - 1$ is composite

- The $2$nd of the $6$th pair of twin primes, with $41$

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

- The $17$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
- $3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $\ldots$

- 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 $21$st odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
- $1$, $3$, $5$, $7$, $\ldots$, $35$, $37$, $41$, $43$, $\ldots$

- 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

*Previous ... Next*: Lucky Number

*Previous ... Next*: Prime Number*Previous ... Next*: Sequence of Indices of Composite Mersenne Numbers

*Previous ... Next*: Twin Primes

## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $43$