In this letter we evaluate whether the gravitational wave background recently
observed by a number of different pulsar timing arrays could be due to merging
primordial supermassive black hole binaries. We find that for homogeneously
distributed primordial black holes this possibility is inconsistent with strong
cosmological and astrophysical constraints on their total abundance. If the
distribution exhibits some clustering, however, the merger rate will in general
be enhanced, opening the window for a consistent interpretation of the PTA data
in terms of merging primordial black holes.Comment: 8 pages, 3 figure