8191

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Number

$8191$ (eight thousand, one hundred and ninety-one) is:

The $1028$th prime number

The $2$nd of the $2$ known numbers (with $31$) expressible as the sum of successive powers starting from $1$ in in $2$ different ways:

$8191 = 1 + 90 + 90^2 = 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9 + 2^{10} + 2^{11} + 2^{12}$

The $5$th Mersenne prime after $3$, $7$, $31$, $127$:

$8191 = 2^{13} - 1$

The $6$th Mersenne number after $3$, $7$, $31$, $127$, $2047$:

$8191 = 2^{13} - 1$

Also see

• Previous: Sum of Successive Powers in 2 ways
• Previous  ... Next: Mersenne Prime
• Previous  ... Next: Mersenne Number
• Previous  ... Next: Prime Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $8191$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2^{8191} - 1$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $8191$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2^{8191} - 1$