Prime ideals of Moh and the characteristic of the field

We reprove and generalize a result of Moh which bounds the minimal number of generators of an ideal in a power series ring in three variables over a field. As a consequence, we obtain minimal generating sets for the first prime of Moh, proving that the minimal number of generators might decrease depending on the field characteristic. This contradicts an statement of Sally. Finally, we show that these minimal generating sets are standard basis with the negative degree reverse lexicographic order.