A necessary distinction is between a "normal" thesis and a "thesis by papers". In the latter, the thesis is really just and intro and conclusion wrapped around

A necessary distinction is between a "normal" thesis and a "thesis by papers". In the latter, the thesis is really just and intro and conclusion wrapped around already-published papers. In some universities in Ireland and in some other European countries, the student can choose either. In the case of thesis by papers, the required number of first-author journal papers is 3. I haven't heard of any special dispensation for the case where the student has 1 paper proving P != NP. But the student is not obliged to choose "thesis by papers" so there is no problem.