127
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Number
$127$ (one hundred and twenty-seven) is:
- The $31$st prime number
- The $2$nd obstinate number after $1$.
- The $4$th Mersenne number and $4$th Mersenne prime after $3$, $7$, $31$:
- $127 = 2^7 - 1$
- The $5$th Friedman number base $10$ after $25$, $121$, $125$, $126$:
- $127 = 2^7 − 1$
- The $7$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$:
- $127 = 1 + 6 + 12 + 18 + 24 + 30 + 36 = 7^3 - 6^3$
- The index of the $11$th Mersenne number after $1$, $2$, $3$, $5$, $7$, $13$, $17$, $19$, $31$, $67$ which Marin Mersenne asserted to be prime
- (note that he missed $89$ and $107$)
- The index of the $12$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $17$, $19$, $31$, $61$, $89$, $107$:
- $M_{127} = 2^{127} - 1 = 170 \, 141 \, 183 \, 460 \, 469 \, 231 \, 731 \, 687 \, 303 \, 715 \, 884 \, 105 \, 727$
- The $26$th lucky number:
- $1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $63$, $67$, $73$, $75$, $79$, $87$, $93$, $99$, $105$, $111$, $115$, $127$, $\ldots$
Also see
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- Previous ... Next: Prime Gaps of 14
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Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $127$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $127$