97

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Number

$97$ (ninety-seven) is:

The $25$th prime number

The larger of the $1$st pair of primes whose prime gap is $8$:

$97 - 89 = 8$

The $6$th Proth prime after $3$, $5$, $13$, $17$, $41$:

$97 = 3 \times 2^5 + 1$

The $8$th emirp after $13$, $17$, $31$, $37$, $71$, $73$, $79$

The $9$th long period prime after $7$, $17$, $19$, $23$, $29$, $47$, $59$, $61$:

$\dfrac 1 {97} = 0 \cdotp \dot 01030 \, 92783 \, 50515 \, 46391 \, 75257 \, 73195 \, 87628 \, 86597 \, 93814 \, 43298 \, 96907 \, 21649 \, 48453 \, 60824 \, 74226 \, 80412 \, 37113 \, 40206 \, 18556 \, \dot 7$

The $13$th permutable prime after $2$, $3$, $5$, $7$, $11$, $13$, $17$, $31$, $37$, $71$, $73$, $79$

The $15$th prime $p$ after $11$, $23$, $29$, $37$, $41$, $43$, $47$, $53$, $59$, $67$, $71$, $73$, $79$, $83$ such that the Mersenne number $2^p - 1$ is composite

The $15$th left-truncatable prime after $2$, $3$, $5$, $7$, $13$, $17$, $23$, $37$, $43$, $47$, $53$, $67$, $73$, $83$

The $19$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $28$, $31$, $32$, $44$, $49$, $68$, $70$, $79$, $82$, $86$, $91$, $94$:

$97 \to 9^2 + 7^2 = 81 + 49 = 130 \to 1^2 + 3^2 + 0^2 = 1 + 9 + 0 = 10 \to 1^2 + 0^2 = 1$

The $35$th odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime

$1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $73$, $77$, $83$, $89$, $97$, $\ldots$