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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