Where can you see the Al Bhed Primers which you have collected?

Solution 1:

I believe you can see the ones you have already collected via the Key Items list. You might have to scroll to the very bottom though.

As you mentioned, your rank is based on the number of primers collected:

Rank                            Primers
---------------------------------------
Al Bhed Hujela (Novice)         1
Al Bhed Pakehhan (Beginner)     4
Al Bhed Typpman (Dabbler)       7
Al Bhed Maynhan (Learner)       10
Al Bhed Cbaygan (Speaker)       13
Al Bhed Hydeja (Native)         16
Al Bhed Unydun (Orator)         19
Al Bhed Medanyde (Literati)     22
Al Bhed Sycdan (Master)         26

And just for information, Al Bhed Primers XIX, XX, XXI and XXII are miss-able, so be careful if you want to collect them all in one play-through.

Source.

Solution 2:

I scrolled to the bottom of the "Key Items" list and found them. There are blank spaces in between.

You have to select "Key Items" from your "Items" screen, and then scroll to the bottom to see them. They probably won't be visible from the top of the list, even if you see empty spaces underneath the items you can see.