7777/2861 is the fraction with the smallest prime denominator closer to e than 1650/607.
The largest known prime number that cannot be expressed as
the sum of 3 pentagonal numbers. [Capelle]
The smallest prime which prefixed by the concatenation of two
perfect numbers. [Firoozbakht]
Magnus Carlsen's peak rating is 2861, the highest in chess history.
(There is one curio for this number that has not yet been approved by an editor.)