Looks like comets with 26000 year orbits, do exist, Anons.
How many more are there?
Comets with 26000 Year Orbits
C/2012 CH17 is a comet with a barycentric aphelion epoch of 26000 AU in the year 1800, which corresponds to an orbit of approximately 26,000 years. This comet is known for its extremely long orbital period, placing it among the long-period comets that originate from the Oort Cloud, a spherical cloud of icy bodies extending far beyond the Kuiper Belt. These comets can be perturbed by passing stars and the galactic tides, leading them into orbits that bring them closer to the Sun.