86,243
Number
$86 \, 243$ (eighty-six thousand, two hundred and forty-three) is:
- The $8384$th prime number
- The index of the $28$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $\ldots$, $2203$, $2281$, $3217$, $4253$, $4423$, $9689$, $9941$, $11 \, 213$, $19 \, 937$, $21 \, 701$, $23 \, 209$, $44 \, 497$:
- $M_{86 \, 243} = 2^{86 \, 243} - 1 \approx 5 \cdotp 369 \times 10^{25 \, 961}$
Also see
- Previous ... Next: Index of Mersenne Prime
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Historical Note
The Mersenne number $M_{86 \, 243} = 2^{86 \, 243} - 1$ was demonstrated to be a Mersenne prime on $25$ September $1982$ by David Slowinski, using a CRAY-1 supercomputer.
Working at $150$ megaflops, it took $1$ hour, $3$ minutes and $22$ seconds for this calculation to be performed, but several months of preliminary work to establish that this number was indeed likely to be prime.
According to David Wells, writing in Curious and Interesting Numbers in $1986$, a mere $150$ megaflops was already old hat by then, and the more recent models available at that time could work at anything up to $1000$ megaflops.
In a final sentence of gosh-wowery, his jaw drops to the floor to report that the Cray-3 was expected to reach the order of $10$ gigaflops.
However, that machine was never commercially available, and the line was discontinued.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2^{86243} - 1$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2^{86,243} - 1$