RNA polymerase that catalyzes the synthesis of short RNA molecules used as primers for DNA polymerase during DNA replication. Can use NTPs but not dNTPs. Binds DNA. Also part of the exosome, which is a complex involved in RNA degradation. Acts as a poly(A)-binding protein that enhances the interaction between heteromeric, adenine-rich transcripts and the exosome. ssDNA + n NTP = ssDNA/pppN(pN)n-1 hybrid + (n-1) diphosphate. Binds two Mg(2+) per subunit. kcat is 0.033 min(-1). Optimum temperature is 70 degrees Celsius. Forms a ternary complex with MCM helicase and DNA. Component of the archaeal exosome complex. Interacts with Csl4 but not with Rrp4. Belongs to the archaeal DnaG primase family.