331

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


 * The $67$th prime number


 * 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 $5$th obstinate number after $1, 127, 149, 251$.


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


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


 * 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 $M$.

Also see

 * Existence of n such that M - 2^n or M + 2^n has no Prime factors less than 331


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