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The growing interest in peer-to-peer applications has underlined the importance of scalability in modern distributed systems. Not surprisingly, much research effort has been invested in gossip-based broadcast protocols. These trade the traditional strong reliability guarantees against very good "scalability" properties. Scalability is in that context usually expressed in terms of throughput and delivery latency, but there is only little work on how to reduce the overhead of membership management on a large scale. The paper presents Lightweight Probabilistic Broadcast (lpbcast), a novel gossip-based broadcast algorithm which preserves the inherent throughput scalability of traditional gossip-based algorithms and adds a notion of membership management scalability: every process only knows a random subset of fixed size of the processes in the system. We formally analyze our broadcast algorithm in terms of scalability with respect to the size of individual views, and compare the analytical results both with simulations and concrete measurements.