Determining the total numbers of any population is a technically difficult exercise. Insofar as the RoC has not undertaken any population census in the north (for obvious reasons), by definition the RoC and Piratis have no idea what that population number is nor how it is composed.
The consequence of this is that the effective administration of the north, whether you call that TRNC or Turkey, have conducted population censuses, the latest being that of 2006.
The PRIO report, of which I have a copy in front of me, uses data from a number of different sources and is a model of how one can try to test the reliability of population data through using different techniques and methods. The PRIO report also uses census data produced by RoC and by its central governmental statistical agency. It also uses UN, EU an dother international organisations material (most of which tends to come from national authorities anyway)
Unless Piratis has conducted other surveys or population censuses - in which case let him share those with us and PRIO - then my money is with PRIO's report as being the most reliable currently on offer. That does not mean that the PRIO report is not without problems, but it does mean that we can test the robustness of PRIO data and conclusions. All those people, including on other threads now, who just say 'well I think the population is X' or 'I think there are Y thousand illegals' are simply making things up.
A separate but related question is how one classifies different parts of a population into, for example, immigrant, temporary resident, resident, etc. How one classifies clearly has a political component to it and we have to always be wary or cautious about classifications. Having said that, there are UN classification and reporting systems which reporting agencies - for example national statistical authorities - are requested/required to comply with. This means that to a great extent, with relatively minor margins of error, population data can be meaningfully compared across the world. The problems of classification which north Cyprus or RoC are dealing with are not peculiar to these places and it is mistaken to reduce it to a question of propaganda or crude anti-politics. For example, who one includes in the category 'temporary worker' or 'resident' is keenly debated by tax authorities, immigration authorities, police, education and trade unions and so on across the world. TRNC and RoC are no exception.