# 331

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## Number

$331$ (three hundred and thirty-one) is:

The $67$th prime number

The number below which it can be guaranteed that no prime factors of $M - 2^n$ or $M + 2^n$ exist for a certain positive integer $n \in \Z_{\ge 0}$ for any integer $M$.

The larger of the $3$rd pair of primes whose prime gap is $14$:
$331 - 317 = 14$

The $5$th obstinate number after $1$, $127$, $149$, $251$

The $11$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $169$, $217$, $271$:
$331 = 1 + 6 + 12 + 18 + 24 + 30 + 36 + 42 + 48 + 54 + 60 = 11^3 - 10^3$

The $53$rd happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $226$, $230$, $236$, $239$, $262$, $263$, $280$, $291$, $293$, $301$, $302$, $310$, $313$, $319$, $320$, $326$, $329$:
$331 \to 3^2 + 3^2 + 1^2 = 9 + 9 + 1 = 19 \to 1^2 + 9^2 = 1 + 81 = 82 \to 8^2 + 2^2 = 64 + 4 = 68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$