Riesel Sieve

Riesel Sieve was a volunteer computing project, running in part on the BOINC platform. Its aim was 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

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 May 2018, 52 of these k had been eliminated by Riesel Sieve or outside persons; the largest prime found by this project is 502,573 × 27,181,987 − 1 of 2,162,000 digits,[1] and it is known that for none of the remaining k 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[2] and the k whose status is still unknown.[3]

From 2010, the investigation has been merged with another BOINC project, PrimeGrid as a sub-project.[4]

References
  1. Riesel Sieve Project Archived 2006-09-10 at the Wayback Machine at The Prime Pages. Retrieved 2008-08-04.
  2. Riesel Sieve, Project Prime Finder Hall of Fame (Archived with Wayback Machine).
  3. PrimeGrid, Current k Status Archived 2010-11-28 at the Wayback Machine.
  4. "Definition and status of the problem". Prothsearch.com. Archived from the original on 2017-04-10. Retrieved 2016-01-14.


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