  We construct the q-discrete Painleve I and II equations and their higher
order analogues by virtue of periodic cluster algebras. Using particular (k,k)
exchange matrices, we show that the cluster algebras corresponding to k=4 and 5
give the q-discrete Painleve I and II equations respectively. For k=6,7,..., we
have the higher order discrete equations that satisfy an integrable criterion,
the co-primeness property.
