As in the beginning, Prime Minister was an unofficial title in eRepublik, some countries, such as the United Kingdom, Australia, New Zealand and Canada, choose to call their President, "Prime Minister", in order to stick with real life national political systems. It became a political title after it being proposed by one of the citizens.
India and Slovakia
Some countries, notably India and Slovakia, had Prime Ministers being the head of a Cabinet, however it was not the Chief Executive (e.g. President) of the country. Effectively the Prime Minister in this situation took on a Deputy role of the Nation.
Apart from having a President, Prime Minister was a separate job in the (United) Netherlands where the title Prime Minister was used for the head of the Cabinet, which was defacto also head of state. Cabinets were formed after congress elections and the leader of the biggest party forms a coalition with other parties to form a Cabinet. This coalition decided who would be Prime Minister. This position was considered more than or equally important as Country President. The president was more seen as a military and symbolic position. After a year of debating and experimenting in October 2010 this position was disbanded when the last Prime Minister Daniel Parker changed the constitution in favor of a semi-CP-government (CP is head of government, but his powers are limited by the congress).
Croatia and Italy