521
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Number
$521$ (five hundred and twenty-one) is:
- The $98$th prime number
- The $8$th Lucas prime after $2$, $3$, $7$, $11$, $29$, $47$, $199$.
- The $13$th Lucas number after $(2)$, $1$, $3$, $4$, $7$, $11$, $18$, $29$, $47$, $76$, $123$, $199$, $322$:
- $521 = 199 + 322$
- The index of the $13$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $17$, $19$, $31$, $61$, $89$, $107$, $127$:
- $M_{521} = 2^{521} - 1 \approx 6 \cdotp 865 \times 10^{156}$
- The smaller of the $25$th pair of twin primes:
- $523 - 521 = 2$
Also see
- Previous ... Next: Index of Mersenne Prime
- Previous ... Next: Lucas Prime
- Previous ... Next: Lucas Number
- Previous ... Next: Twin Primes
- Previous ... Next: Prime Number
Historical Note
The Mersenne number $2^{521} - 1$ was proven to be the $13$th Mersenne prime on $30$th January $1952$, on the Standards Western Automatic Computer.
The program used was written by Raphael Mitchel Robinson over the Christmas period of $1951$, using an implementation of the Lucas-Lehmer Test.
This and the $14$th Mersenne prime $2^{607} - 1$ were thus discovered after a mere few hours.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2^{521} - 1$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $521$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2^{521} - 1$