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The number of ones that form the fifth and largest known repunit prime. It was first proven prime in 1985. (The next few that could possibly be prime are those with 49081, 86453, 109297, and 270343 digits.) 1031 = 2*3*5 + 7*11*13. [Capelle] Halloween falls on "ten thirtyone" (10/31) each year. It is a crossquarter date, approximately midway between an equinox and a solstice. The final bid for an Erdős number on eBay (April 30, 2004) was $1031. Note that the bidding was for an Erdős number of 5. [McCranie] The lesser of the smallest twin emirps. Their reversals are also twins and reflective. [Punches] The only emirp among the subscripts p of all known repunit primes R_{p} = (10^{p} 1)/9, as of August 2009. [Beedassy] Simon Plouffe collected and published 1031 formulas that were generated by a computer program in 1992. Starts the first group of four emirps formed from the same digits: 1031, 1301, 1103, 3011. [Silva] The smallest 4digit emirp p whose the reversal of square is equal to the square of the reversal of p, i.e., 1031^2=1062961 and 1301^2=1692601. [Loungrides]
(There are 3 curios for this number that have not yet been approved by an editor.)
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