216,091
Number
$216 \, 091$ (two hundred and sixteen thousand and ninety-one) is:
- The $19 \, 292$nd prime number
- The index of the $31$st Mersenne prime after $2$, $3$, $5$, $7$, $13$, $\ldots$, $11 \, 213$, $19 \, 937$, $21 \, 701$, $23 \, 209$, $44 \, 497$, $86 \, 243$, $110 \, 503$, $132 \, 049$:
- $M_{216 \, 091} = 2^{216 \, 091} - 1 \approx 7 \cdotp 461 \times 10^{65 \, 049}$
Also see
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Historical Note
David Wells, in his Curious and Interesting Numbers of $1986$, announces that the Mersenne number $M_{261 \, 092} = 2^{261 \, 092} - 1$ was discovered by researchers at Chevron Geosciences of Houston, Texas, running performance tests on their Cray X-MP, in preparation for its use in oil prospecting.
It took $3$ hours, at $400$ million operations per second, to accomplish this feat, although the preliminary preparation to determine its possible primeness had taken several months beforehand.
An announcement about this was made on $18$ September $1985$, and, according to David Wells, was broadcast to Britain on BBC Radio.
However, it appears that David Slowinski had already discovered this fact on $1$ September $1985$, probably using the same (or a similar) configuration of the CRAY-1 he had used for previous searches.
Further research is needed into the exact details.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2^{216091} - 1$