Thank you for the candled views. These contrasts are what I'd expect from natural pearls. Viewed from several axis, there's no visible geometry from a bead. Also, this pearl presents with typical contrasts which are eccentric, random and mottled. Moreover, the contrasts appear at different depths, meaning the pearl has likely burst from it's sac more than once during it's formation. That's a good thing, because each time this happens, a juvenile layer or aragonite forms on the outer surface.
You have an extraordinary pearl, kyratango.
And yes, Sophie. This is a large baroque drop.
La Peregrina originated from the Gulf of Panama in Central America. It's just a guess, but I'd suspect this one did as well and it's reasonable to consider it may be older than 19th century.
I highly recommend this pearl be sent to the lab for certification. Not because of doubt, but for confirmation and insurable valuation. It's possible they'd waive the cost of the examination in trade for retaining the record on file.