Catabolizes diadenosine 5',5'''-P1,P4-tetraphosphate (Ap4A) into ADP and ATP. It does not catalyze the reverse phosphorolysis reaction. The optimum substrates are dinucleoside polyphosphates containing four or five phosphate residues. ADP + ATP + H(+) = P(1),P(4)-bis(5'-adenosyl) tetraphosphate + phosphate Binds 1 divalent metal ion per subunit. Mn(2+) is the most efficient metal, but can also use Co(2+), Ca(2+) and Mg(2+). Optimum pH is 8. Optimum temperature is 30 degrees Celsius. The activity completely disappears after treatment at 65 degrees Celsius for 10 min. Homotetramer. Rv2613c is a unique Ap4A phosphorylase with a primary structure homologous to that of Ap4A hydrolase rather than typical Ap4A phosphorylases. Was identified as a high-confidence drug target.