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In this note we compare some notions of primeness for modules existing in the literature. We characterize the prime left R-modules such that the left annihilator of every element is a (two-sided) ideal of R, where R is an associative ring with unity, and we prove that if M is such a left R-module then M is strongly prime. These two notions are studied by Beachy [B 75]. Furthermore, if M is projective as left R/(0: M)-module then M is B-prime in the sense of Bican et al.[BJKN]. On the other hand, if M is faithful then M is (strongly) prime if and only if M is strongly prime (or an SP-module) in the sense of Handelman-Lawrence [HL] if and only if M is torsionfree and R is a domain. In particular this happens if R is commutative.