eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2015-10-26 3 4 97 103 10.12691/tjant-3-4-2 TJANT2015342 article Idir Sadani sadani.idir@yahoo.fr 1 Department of Mathematics, University of Mouloud Mammeri, Tizi-Ouzou. Algeria We study the properties of prime number sequences obtained using a well-defined equivalence relation . It will be seen that the elements of each class of are all prime numbers which constitute the fundamental object of our study. The number of prime numbers of each class less than or equal to a given quantity , the number of the different equivalence classes and some other results will be deduced. http://pubs.sciepub.com/tjant/3/4/2/tjant-3-4-2.pdf distribution of prime numbers equivalence relation iteration asymptotic formula