The Sieve of Eratosthenes is a well known algorithm for computing primes, but suffers from space requirements. The Incremental Sieve solves that problem.
Vibrating cantilevers has a long history of being used as sensors, but almost always in the micro-domain. The cantilever is frequently etched into silicon or other substrate. The weight of even single molecules can be measured or detected. The idea is fairly simple. Change the distribution of weight on the cantilever, and the frequency of vibration will change. It can even be used as a motion detector since acceleration in the same plane as the natural vibration will either start the cantilever vibrating or will change the frequency of the vibration.