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Let be a square-free odd integer and the integer residue ring modulo . This paper studies the distinctness of primitive sequences over modulo 2. Recently, for the case of , a product of two distinct prime numbers and , the problem has been almost completely solved. As for the case that is a product of more prime numbers, the problem has been quite resistant to proof. In this paper, a partial proof is given by showing that a class of primitive sequences of order over is distinct modulo 2, where is a positive integer. Besides as an independent interest, this paper also involves two distribution properties of primitive sequences over , which are related closely to our main results.

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