Yes, or, no! Sorry, but it depends on which primulas you mean. Most of the Asiatic primulas, candelabra or drumstick etc, will do fine in ericaceous compost but most of the European ones, auricula or xpubescens types, prefer a limey soil. On the positive side, all will grow very nicely in a regular compost!

Cowslips (Primula veris) need calcium from chalky or limey soils, they would struggle in very acid conditions.

That explains a lot! Thanks BA and Landgirl, and Dee for asking. I have shoved all my Primulas in my neutral to slightly acidic soil. Some..drumsticks in particular are thriving. The cowslips are awful...all leaf and tiny rubbishy flowers. The auriculas are mostly struggling although a couple are ok. The ones that grow close to the ground are all struggling. It's a mixed bag. I must pay more attention, and get on with making a trough for the lime lovers!