The largest known Mersenne prime exponent (as of 23 August 2008): see 2^43112609-1.
Mersenne prime M47, i.e. 2^43112609-1 contains the exponent of (the larger) Mersenne prime M50, i.e. 77232917. [Harrison]
(There is one curio for this number that has not yet been approved by an editor.)