Riesel Sieve
Riesel Sieve is a distributed computing project, running in part on the BOINC platform. Its aim is to prove that 509,203 is the smallest Riesel number, by finding a prime of the form for all odd smaller than 509,203. Progress of the project. At the start of the project in August 2003, there were less than 509,203 for which no prime was known. , 52 of these had been eliminated by Riesel Sieve or outside persons; the largest prime found by this project is 502,573 × 2 − 1 of 2,162,000 digits, and it is known that for none  of the remaining there is a prime with "n" <= 10,000,000 (As of February 2020). The project proceeds in the same way as other prime-hunting projects like GIMPS or Seventeen or Bust: sieving eliminates pairs ("k", "n") with small factors, and then a deterministic test, in this case the Lucas-Lehmer-Riesel test based on the Lucas-Lehmer test, is used to check primality of numbers without small factors. Users can choose whether to sieve or to run LLR tests on candidates sieved by other users; heavily-optimised sieving software is available. Riesel Sieve maintains lists of the  primes that have been found and the "k" whose status is still unknown. From 2010 onward, the investigation has been taken over by another distributed computing project, PrimeGrid.