Riesel Sieve

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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[edit]

At the start of the project in August 2003, there were 101 k less than 509203 for which no prime k × 2n − 1 was known. As of September 2008, 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,[1] and it is known that for none of the remaining k is there 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.

Riesel Sieve maintains lists of the primes that have been found[2] and the k whose status is still unknown.[3]

From 2010 onward, the investigation has been taken over by another distributed computing project, PrimeGrid.[4]

References[edit]

  1. ^ Riesel Sieve Project at The Prime Pages. Retrieved 2008-08-04.
  2. ^ Riesel Sieve, Project Prime Finder Hall of Fame.
  3. ^ PrimeGrid, Current k Status.
  4. ^ "Definition and status of the problem". Prothsearch.net. Retrieved 2011-02-20. 

External links[edit]