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 k × 2n − 1 for all odd k smaller than 509,203.
Progress of the project
At the start of the project in August 2003, there were 101 k less than 509,203 for which no prime k × 2n − 1 was known. As of September 2008[update], 37 of these k had been eliminated by Riesel Sieve or outside persons; the largest prime found by this project is 485,767 × 23,609,357 − 1 of 1,086,531 digits, and it is known that for none of the remaining k there is a prime with n < 2,000,000.
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.
- The official Riesel Sieve home page (Riesel Sieve is now part of Primegrid)
- Definition and status of the problem