2400

This number is a composite.

The smallest number n such that both n and n+1 are cube root-free smooth. The largest prime factor of both 2400 and 2401 is less than its cube root. [Gudipati]

The number of 2400-bit primes with one off bit -- i.e, of form 2²⁴⁰⁰ - 2^k - 1 with k = 1 to 2398 -- is 19, breaking the record (for 168 bits) of 17. [Merickel]