4253
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Number
$4253$ (four thousand, two hundred and fifty-three) is:
- The $583$rd prime number
- The index of the $19$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $17$, $19$, $31$, $61$, $89$, $107$, $127$, $521$, $607$, $1279$, $2203$, $2281$, $3217$:
- $M_{4253} = 2^{4253} - 1 \approx 1 \cdotp 908 \times 10^{1280}$
Also see
- Previous ... Next: Index of Mersenne Prime
- Previous ... Next: Prime Number
Historical Note
The Mersenne number $M_{4253} = 2^{4253} - 1$ was demonstrated to be a Mersenne prime by Alexander Hurwitz on $3$ November $1961$, using an IBM 7090, along with $M_{4423}$, whose primality was similarly demonstrated in the same computer run.
These were the first titanic primes ever discovered.
It is a moot question which one was actually discovered first.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2^{4253} - 1$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2^{4253} - 1$