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Riesel Sieve is a distributed effort to prove that k=509203 is the smallest Riesel number. These numbers do not produce primes for any n in the function k*2^n-1

Riesel Sieve project URL; http://boinc.rieselsieve.com/

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Riesel Sieve

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In 1956, mathematician Hans Riesel proved that there are numbers k, when plugged into the function k*2^n-1 do not produce any primes. When choosing k=3 for example 3*2^3-1 = 23 which is prime, so 3 is not a Riesel number. Mr. Riesel also discovered a number which produces only composites, and this number is 509203. He cojectured this was the smallest Riesel number there is. To prove this conjecture, one must find an n for all odd k < 509203, so k*2^n-1 is prime.

Finding primes

To find primes of the form k*2^n-1, where 2^n is larger than k, there is a very easy test, developed by Edouard Lucas,  Derrick Henry Lehmer and Hans Riesel (LLR). This test starts with a number determined by k and n, and keeps sqauring it and reducing it by 2. This is done n-2 times. When the candidate divides this large number, the number being tested is prime. To find out more about this test, see this article on Wikipedia.

Sieving

It would take a very long time to LLR all numbers, so another method is used to eliminate numbers. One simply starts taking the first odd prime, 3, and removes all candidates divisible by this prime. Then the next prime is 5, and all numbers divisible by 5 are removed. This will eliminate a lot of candidates and these do not have to be LLR-ed. 

Status

The status of Riesel Sieve is unknown at the moment. The founder of the project has disappeared and the project is offline. The admin stated he had contact with the founder, and things will resume in the future. Right now it is not possible to crunch for the project.

Video about Prime Number Sieve and the Ulam Spiral

This video is not about the Riesel Sieve project. Its about the Ulam Spril which was publicized by Stanislaw Ulam in 1963. The spiral can be generated using the sieve of Eratosthenes to etch out prime numbers.

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