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 thirty-one" (10/31) each year. It is a cross-quarter 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
Rp = (10p -1)/9, as of August 2009. [Beedassy]
Simon Plouffe collected and published 1031 formulas that were generated
by a computer program in 1992.
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