The Prime Sierpinski Problem

We look at a special class of prime numbers called proth numbers which have the general formula k*2^n+1. We further specialize our search by looking at numbers for which k is prime in k*2^n+1. Furthermore it has been proven that there exists an infinite number of prime k's such that k*2^n+1 can never be prime. These k's are called prime sierpinski numbers.

The smallest proven prime Sierpinski number is 271129. We are looking at all prime k's below this number and trying to prove that they are not sierpinski numbers. The easiest way to prove that a k is not a prime sierpinski number is to find a prime for that k.

There are currently 11 such candidates remaining for which we need to find a prime. We have already found 18 large primes, several of which made it into the top 100 largest known prime number list.

Before testing numbers for primality, we sieve out all those numbers where it is easy to find a factor, so that they cannot be prime. This is called "sieving". We are currently sieving up to n=50 million, which limit was chosen for efficiency reasons. The sieving stage of the project is currently finished.

When a k is proved that it is not a sierpinski number the k is eliminated. This means that we no longer have to test that k for primality nor find factors for this k.

If you have any questions please ask them on our forum here.

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**How is the project organized?**
To solve the Prime Sierpinski Problem we need to find 11 primes for the k's listed at the end of this thread. 3 of these k's are reserved by

www.seventeenorbust.com, an other project searching for primes for these 3 k's, the rest of the 8 k's are reserved by us. In order to prove the primality of a number we need to perform a primality test called PRP. This test takes very long; hence to reduce the time of the project we look for numbers with small factors and remove these numbers from our primality-testing list. This process is called sieving (currently over). The PRP testing method is not 100 % efficient, that is, it can make errors. On the other hand once a factor is found for a number, we can be 100 % sure that, that number is not prime. All numbers that are checked by PRP need to be double-checked. Since the probability of finding a prime is higher than having made an error and missing a prime, we are not currently pursuing the double check of numbers actively.

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**How to participate?**
**BOINC** Just download the client from

http://www.primegrid.com and select The Prime Sierpinski Problem as your active project.

If you have some computers that can help PSP but you are running into problems, please ask on the forum. There might be a solution to your problem, such that you would be able to run your machines.

**AND FINALLY HAPPY PRIME HUNTING!**
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**List of k's we are searching currently!**
79309

79817

152267

156511

168451

222113

225931

237019

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**List of Primes already found!**
87743*2^212565+1 is prime! (found by Morris Cox on 11/18/03)

224027*2^273967+1 is prime! (found by FootMaster on 12/12/03)

203761*2^384628+1 is prime! (found by FootMaster on 01/05/04)

122149*2^578806+1 is prime! (found by FootMaster on 01/19/04)

247099*2^484190+1 is prime! (found by FootMaster on 02/05/04)

172127*2^448743+1 is prime! (found by Citrix on 02/05/04)

159503*2^540945+1 is prime! (found by FootMaster on 02/07/04)

263927*2^639599+1 is prime! (found by FootMaster on 02/20/04)

261917*2^704227+1 is prime! (found by ltd on 03/08/04)

161957*2^727995 + 1 is prime! (found by FootMaster on 03/22/04)

216751*2^903792+1 is prime ! (found by ltd on 5/10/2004)

241489*2^1365062+1 is prime! (found by Citrix on 1/25/2005)

149183*2^1666957+1 is prime! (found by ltd on 10/7/2005)

214519*2^1929114+1 is prime! (found by ltd on 1/2/2006)

222361*2^2854840+1 is prime! (found by Shy24 on 31/8/2006)

265711*2^4858008+1 is prime! (found by Sloth on 05/04/2008)

258317*2^5450519+1 is prime! (found by Sloth on 28/7/2008)

90527*2^9162167+1 is prime! (found by Bold_Seeker on 19/6/2010)

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Project Coordinators: -

Citrix: - Project Admin

Ltd: - Database and Stats maintainer.

(Instead of emailing the admin's about the problems you have, please post your problem on the forum so someone can help you out faster.)