33333...33333 (10000-digits)

This number is a probable-prime (likely to be a prime but we have not (re-)proven it on this site).

The number (10¹⁰⁰⁰⁰ - 1)/3 - 10⁶³³³ is probably the smallest gigantic near-repdigit (other than near-repunit) prime. [Wesolowski]