11,213

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Number

$11 \, 213$ (eleven thousand, two hundred and thirteen) is:

The $1357$th prime number


The index of the $23$rd Mersenne prime after $2$, $3$, $5$, $7$, $13$, $\ldots$, $2203$, $2281$, $3217$, $4253$, $4423$, $9689$, $9941$:
$M_{11 \, 213} = 2^{11 \, 213} - 1 \approx 2 \cdotp 814 \times 10^{3375}$


Also see

  • Previous  ... Next: Index of Mersenne Prime
  • Previous  ... Next: Prime Number


Historical Note

The Mersenne number $M_{11 \, 213} = 2^{11 \, 213} - 1$ was demonstrated to be a Mersenne prime by Donald Bruce Gillies on $2$ June $1963$ at the University of Illinois.

The University celebrated this event by using a special postmark to frank its letters.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2^{11213} - 1$
  • 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Mersenne numbers or Mersenne primes
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2^{11,213} - 1$
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