Not all Paphs interbreed EASILY, and there may be some fertility issues in the hybrids, but it is generally recognized that they all probably can be crossed. Chromosome number is not always a good indication if species can be crossed. Completely unrelated species could incidentally have the same chromosome number, and there are cases where different chromosome numbers have been documented within a species. it is rarely a simple question, especially in orchids.

Not counting a few unnamed hybrids from 1899, there are 8 registered Phramipaphium (Phragmipedium x Paphiopedilum) hybrids. They date from 1912 to several from one breeder in 2002-2004. I've seen pictures of some of the alleged hybrids, but none have been completely convincing at least to me. You may find some with an image search. The most reliable information I've heard, based on my personal knowledge of the source, is that sometimes there is germination but seedlings do not live long even in flask. If these plants do exist I would assume someone would widely distribute the pictures and documentation, rather than keep them nearly secret.

Now, if someone was serious about producing intergeneric hybrids in the Cypripedioideae just to prove it could be done, I would suggest trying Selenipedium x Cypripedium.