A small RNA molecule, 22-23 nt in size, that is the product of a longer RNA. The production of priRNAs is independent of dicer and involves binding of RNA by argonaute and trimming by triman. In fission yeast, priRNAs trigger the establishment of heterochromatin. PriRNAs are primarily generated from centromeric transcripts (dg and dh repeats), but may also be produced from degradation products of primary transcripts.