Via the (C,F)-construction we produce a 2-fold simple mixing transformation which has uncountably many non-trivial proper factors and all of them are prime.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm139-1-3, author = {Alexandre I. Danilenko and Anton V. Solomko}, title = {Simple mixing actions with uncountably many prime factors}, journal = {Colloquium Mathematicae}, volume = {139}, year = {2015}, pages = {37-54}, zbl = {06419982}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm139-1-3} }
Alexandre I. Danilenko; Anton V. Solomko. Simple mixing actions with uncountably many prime factors. Colloquium Mathematicae, Tome 139 (2015) pp. 37-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm139-1-3/