John Forum moderator Project scientist Send message Joined: Feb 21 06 Posts: 1560 ID: 2449 Credit: 357,929 RAC: 0
Over the past nine months, six new projects (4 primality and 2 sieves) have been added to PrimeGrid. As mentioned in this post, \"the primary focus was on simplicity...how easily could a new sub-project be implemented within PrimeGrid and BOINC.\"
We will soon be adding three new projects...all primality testing (LLR). Simplicity of implementation is still a driving factor right now. However, we may explore adding other primality programs in the future and add prime searches with increasing variety.
Sieving was conducted over the past several months and has been completed for the first project and ongoing for the other two projects.
Sophie Germain Prime Search
A prime number p is called a Sophie Germain prime if 2p + 1 is also prime. For example, 5 is a Sophie Germain prime because it is prime and 2 × 5 + 1 = 11, is also prime. They are named after Marie-Sophie Germain, an extraordinary French mathematician.
We\'ll be searching the form k*2^n-1. If it is prime, then we\'ll check k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1. We are able to do this because a quad sieve was performed for this search. This sieve ensured that k*2^n-1, k*2^n+1, k*2^(n-1)-1, & k*2^(n+1)-1 do not have any small prime divisors.
As you can see, a twin prime is also possible from this search although we expect to find a Sophie Germain prime first. Here are some stats for the search:
k range: 1<k<41T
n=666666
sieve depth: p=200T
candidates remaining: 34,190,344
Probability of one or more significant pair = 80.1%
Probability of one or more SG = 66.7%
Probability of one or more Twin = 42.3%
3*2^n+1
This will be a sister project to the already established 3*2^n-1 project. We hope to eventually have both projects at the same n value. We have reserved k=3 from the ProthSearch site. Our initial goal will be like 3*2^n-1, tested up to n=5M. However, sieving is currently being conducted beyond that.
Here are some stats for the search:
k=3
sieved n range: 1<n<5M
sieve depth: p=500T (ongoing)
3*2^n+1 will be a double check effort for even n up to ~1.8M and for odd n up to ~2.6M. Beyond that will be new primes, although there may be a small chance of a missed prime in the lower ranges.
+1 Prime Search
This search will be looking for primes in the form of k*2^n+1. With the condition 2^n > k, these are often called the Proth primes. We will be coordinating our effort through the ProthSearch site. This project will also have the added bonus of possibly finding Generalized Fermat Numbers (GFN) factors. Each k*2^n+1 prime found may be a GFN factor. As this requires PrimeFormGW (PFGW) (a primality-testing program), once PrimeGrid finds a prime, it will then be manually tested outside of BOINC for GFN divisibility.
Our initial goal will be to double check all previous work up to n=300K for k<1200 and to fill in any gaps that were missed. Primes found in this range will not make it into the Top 5000 Primes database (currently n>333333). However, the work is still important as it may lead to new GFN or "classical" Fermat number factors. While there are many GFN factors, currently there are only about 270 "classical" Fermat number factors known.
Here are some stats for the search:
k range: 4<k<1200
n range: 1<n<5M
sieve depth: currently at p=10T (ongoing)
Once the initial goal is reached, we\'ll advance to n<400K and then n<500K. Afterwards, we\'ll turn our focus to smaller k values and higher n values. For example, k<32 complete to n=2M, k<64 complete to n=1M and so on. Primes found in these ranges will definitely make it into the Top 5000 Primes database.
Generalized Cullen/Woodall Search: This is similar to our current Cullen/Woodall search except a base other than 2 will be selected. The form of these primes are as follows:
Generalized Fermat Prime Search: This searches for primes in the form b^2^n+1. A previous project has already completed a substantial amount of work. It can be found here: Generalized Fermat Prime Search. We may be able to double check all completed work and then help the previous project extend their search.
Wieferich prime: There is now an established effort for this search which can be found here: http://www.elmath.org/
Another thought: will participation in these projects require selecting each project individually in our account settings each time it is added? Maybe I\'d like to accept new projects by default and unselect them whenever necessary. This would be just a checkbox on the web page. OTOH it is yet another checkbox, which doesn\'t necessarily mean an improvement.
____________
?SYNTAX ERROR
READY.
Rytis Forum moderator Project administrator Send message Joined: Jun 22 05 Posts: 2426 ID: 1 Credit: 1,229,526 RAC: 64
Maybe I\'d like to accept new projects by default and unselect them whenever necessary. This would be just a checkbox on the web page.
Sadly, this is not possible with the current BOINC implementation. You can either select no projects (which would send you work from any of available ones), or you can select the ones you\'d like.
____________
