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 k × 2ⁿ − 1 for all odd k smaller than 509,203.

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 2016^[update], 51 of these k had been eliminated by Riesel Sieve or outside persons; the largest prime found by this project is 502,573 × 2^7,181,987 − 1 of 2,162,000 digits, and it is known that for none of the remaining k there is a prime with n < 8,000,000. (For k = 342,847 and 444,637, there is even no prime with n < 10,000,000.

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 and the k whose status is still unknown.

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

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