Primula x polyantha is listed as an accepted name in The Plant List, which is woefully obsolete and usually incorrect. GRIN and ITIS also list it as an accepted name, but their data date back to 2005 and 2011. The Catalogue of Life, last updated on 4/21/2015, recognizes Primula polyantha only as a synonym.
Primula x polyantha was supposed to have been a cross of P. veris x P. vulgaris, but many of the P. veris subtaxa are now synonyms for subspecies of P. elatior and P. acaulis, and Primula vulgaris and all of its subspecies are now synonyms for a variety of other Primula species, so the name of this hybrid taxon (P. x polyantha) is no longer valid.
If the polyanthus primrose cultivars in our database are known to be hybrids of mixed origin, they should not have a species listed at all, and should be identified as polyanthus primroses only by their common names.