Riesel Sieve
Encyclopedia
Riesel Sieve is a distributed computing
project, running in part on the BOINC platform. Its aim is to prove that is the smallest Riesel number
, by finding a prime of the form for all odd smaller than .
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
.
Distributed computing
Distributed computing is a field of computer science that studies distributed systems. A distributed system consists of multiple autonomous computers that communicate through a computer network. The computers interact with each other in order to achieve a common goal...
project, running in part on the BOINC platform. Its aim is to prove that is the smallest Riesel number
Riesel number
In mathematics, a Riesel number is an odd natural number k for which the integers of the form k·2n − 1 are composite for all natural numbers n....
, by finding a prime of the form for all odd smaller than .
Progress of the project
At the start of the project in August 2003, there were less than 509203 for which no prime was known. , 37 of these had been eliminated by Riesel Sieve or outside persons; the largest prime found by this project is of 1,086,531 digits, and it is known that for none of the remaining is there a prime with .The project proceeds in the same way as other prime-hunting projects like GIMPS or Seventeen or Bust
Seventeen or Bust
Seventeen or Bust is a distributed computing project started in March 2002 to solve the last seventeen cases in the Sierpinski problem.-Goals:...
: 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
PrimeGrid
PrimeGrid is a distributed computing project for searching for prime numbers of world-record size. It makes use of the Berkeley Open Infrastructure for Network Computing platform...
.
External links
- The official Riesel Sieve home page (Riesel Sieve is now part of PrimegridPrimeGridPrimeGrid is a distributed computing project for searching for prime numbers of world-record size. It makes use of the Berkeley Open Infrastructure for Network Computing platform...
) - Definition and status of the problem