▁pr imes . ▁ ▁Note ▁that ▁there ▁are ▁rational ▁pr imes ▁which ▁are ▁not ▁Gaussian ▁pr imes . ▁A ▁simple ▁example ▁is ▁the ▁rational ▁prime ▁ 5 , ▁which ▁is ▁fact ored ▁as ▁ ▁in ▁the ▁table , ▁and ▁therefore ▁not ▁a ▁Gaussian ▁prime . ▁ ▁Con vent ions ▁The ▁second ▁column ▁of ▁the ▁table ▁contains ▁only ▁integers ▁in ▁the ▁first ▁quadr ant , ▁which ▁means ▁the ▁real ▁part ▁x ▁is ▁positive ▁and ▁the ▁imag inary ▁part ▁y ▁is ▁non - negative . ▁The ▁table ▁might ▁have ▁been ▁further ▁reduced ▁to ▁the ▁integers ▁in ▁the ▁first ▁oct ant ▁of ▁the ▁complex ▁plane ▁using ▁the ▁symmetry ▁. ▁ ▁The ▁factor izations ▁are ▁often ▁not ▁unique ▁in ▁the ▁sense ▁that ▁the ▁unit ▁could ▁be ▁absor bed ▁into ▁any ▁other ▁factor ▁with ▁exponent ▁equal ▁to ▁one . ▁The ▁entry ▁, ▁for ▁example , ▁could ▁also ▁be ▁written ▁as ▁. ▁The ▁entries ▁in ▁the ▁table ▁resolve ▁this ▁ambigu ity ▁by ▁the ▁following ▁convention : ▁the ▁factors ▁are ▁pr imes ▁in ▁the ▁right ▁complex ▁half ▁plane ▁with ▁absolute ▁value ▁of ▁the ▁real ▁part ▁larger ▁than ▁or ▁equal ▁to ▁the ▁absolute ▁value ▁of ▁the ▁imag inary ▁part . ▁ ▁The ▁entries ▁are ▁sorted ▁according ▁to ▁increasing ▁norm ▁ ▁. ▁ ▁The ▁table ▁is ▁complete ▁up ▁to ▁the ▁maximum ▁norm ▁at ▁the ▁end ▁of ▁the ▁table ▁in ▁the ▁sense ▁that ▁each ▁composite ▁or ▁prime ▁in ▁the ▁first ▁quadr ant ▁appears ▁in ▁the ▁second ▁column . ▁ ▁Gaussian ▁pr imes ▁occur ▁only ▁for ▁a ▁subset ▁of ▁norm s , ▁detailed ▁in