1031
This number is a prime.
The number of ones that form the fifth known repunit prime. (The next and currently largest known contains 49081 ones.)
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.
Starts the first group of four emirps formed from the same
digits: 1031, 1301, 1103, 3011. [Silva]
The smallest 4-digit 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]
The number of cells of the male C. elegans -- a
nematode worm, small enough that you can barely see an
adult unless it’s placed right up against your eye. [Post]
One approach to "quantum gravity" is string theory: a mathematical description of particles and forces at scales
1031 times smaller than a proton. [Annemberg]
The smallest prime which cannot be expressed as the
difference of two palindromes. [Gudipati]