That's an uncompressed Bloom filter with a single hash function. To get a false-positive probability of p with a single hash function you need 1/p bits per entr

That's an uncompressed Bloom filter with a single hash function. To get a false-positive probability of p with a single hash function you need 1/p bits per entry. But that's the uncompressed filter. It compresses way, way down: to about 8 bits per entry. That gives 400KB of data, still with a 1/1024 false-positive rate. Much better than 3MB. If you consider (uncompressed) Bloom filters with arbitrarily many hashes, the best you can do for a false-positive rate of 1/1024 is about 14 bits per entry.