Catalyzes the interconversion of glucose 1-phosphate and glucose 6-phosphate, and the interconversion of mannose 1-phosphate and mannose 6-phosphate. Also displays low activity with deoxyribose 1-phosphate and glucosamine 1-phosphate. alpha-D-glucose 1-phosphate = alpha-D-glucose 6-phosphate alpha-D-mannose 1-phosphate = D-mannose 6-phosphate Can also use Ni(2+), Mn(2+) and Zn(2+), to a lesser extent. kcat is 575 sec(-1) with glucose 1-phosphate as substrate. kcat is 330 sec(-1) with mannose 1-phosphate as substrate. kcat is 190 sec(-1) with 2-deoxyribose 1-phosphate as substrate. Optimum pH is 7.0 for PGM activity. Optimum temperature is 90 degrees Celsius for PGM activity. Homotetramer. Up-regulated in the presence of starch. Activated by phosphorylation. Belongs to the phosphohexose mutase family.