No. A residence permit for students is not the basis of a permanent residence permit. If you have only had a student permit, you cannot apply for a permanent residence permit.

If you stay in Iceland after finishing your studies, on a residence permit that may be the basis of a permanent residence permit, for example, a permit for work requiring expert knowledge, you can apply for a permanent residence permit after two years on such a permit.

In order to fulfil this exemption, an individual must have been in Iceland for a continuous period of four years, first on a student permit for at least two years and then on a residence permit, which can be the basis of a permanent residence permit, for at least another two years.