Future directions

paulunderwood · 2015-01-02, 07:59

When I started this little project, I hadn't expected the Batalov Effect. We are grateful to Serge for his huge crunching efforts and he has been rewarded with finding those 4 primes for base 10 and expoenent 388080. It is a pity about the dearth for exponent 471240.

The use of generic modular reduction for such large exponents and bigger ones is a big disadvantage to the project. However I have a few ideas about what to do next:

(A) Shelve the project.

(B) Do another sub-million exponent for base 10 -- will require a few weeks of Ksieve.

(C) Do a mega exponent for base 10 using the magic formula which leaves a lot in the sieve -- will require quite a while with Ksieve.

(D) Do base 10 with exponent 1000000.

(E) Do a base 2 search using the magic formula -- can be engineered to leave a lot in the sieve; has a bigger domain to search, with more primes per exponent. Fast at sub-semi-mega bigger-than-PG-twin-search.

(F) Choose another base such as 3 or 2015 etc.

(G) Go for a world record prime -- fanciful.

(H) Search for NeRDs which use only special modular reduction.

My favourites are (A) or (E).

VBCurtis · 2015-01-02, 08:40

C, E, and H all sound good. I haven't contributed yet, but I like to sieve, so I'd be willing to help with that for the next step in the project.

paulunderwood · 2015-01-02, 08:51

Is there a sieve for (H)

paulunderwood · 2015-01-02, 09:47

Code:

? 2^5*3^2*5*7*11*13*log(2)/log(10)
433916.67694988905402889179241167322850
? 2^5*3^2*5*7*11*13
1441440

So 2^1441440-2^k-1 might be a candidate for (E), where 360360<=k<1441440.

Batalov · 2015-01-02, 17:45

Someone else is apparently thinking about F), independently.

Batalov · 2015-01-02, 17:52

I think about A), and possibly redirecting the CPU power into the soon to emerge "Cyclo"tomic-based project. It is similar to F)+H), and indeed, only focuses on numbers for which special FFT exists.

Initially, it will probably be on PrimeGrid's PRPnet, as most budding projects are. I can provide my LLR implementation for their CPU participants, and Cyclo is OpenCL so it will run on any modern* GPU.
______________
*this excludes only very old and cheap cards that don't have double float.

rogue · 2015-01-02, 19:12

Quote:

Originally Posted by Batalov

I think about A), and possibly redirecting the CPU power into the soon to emerge "Cyclo"tomic-based project. It is similar to F)+H), and indeed, only focuses on numbers for which special FFT exists.

Initially, it will probably be on PrimeGrid's PRPnet, as most budding projects are. I can provide my LLR implementation for their CPU participants, and Cyclo is OpenCL so it will run on any modern* GPU.
______________
*this excludes only very old and cheap cards that don't have double float.

I believe that putting this onto PRPNet would require a new server type. I presume that Cyclo would run on the client side and do the PRP testing. That would require additional changes to the client. As PRPNet is open source (via sourceforge) if someone wants to work on it, let me know now I'll give you access to the repository.

Batalov · 2015-01-07, 02:26

They will probably take care of that (or it can be disguised as a flavor of the genefer[OCL]-search).

Initially they will have a sieving period which is mostly manual (and only Windows sieve existed so far, just like for GNF-Sv).
They have an existing worked-out way of coordinating that. The sieve is data-less, and they have a result collection upload server.

2015-01-02, 07:59	#1
paulunderwood Sep 2002 Database er0rr 2·2,243 Posts	Future directions When I started this little project, I hadn't expected the Batalov Effect. We are grateful to Serge for his huge crunching efforts and he has been rewarded with finding those 4 primes for base 10 and expoenent 388080. It is a pity about the dearth for exponent 471240. The use of generic modular reduction for such large exponents and bigger ones is a big disadvantage to the project. However I have a few ideas about what to do next: (A) Shelve the project. (B) Do another sub-million exponent for base 10 -- will require a few weeks of Ksieve. (C) Do a mega exponent for base 10 using the magic formula which leaves a lot in the sieve -- will require quite a while with Ksieve. (D) Do base 10 with exponent 1000000. (E) Do a base 2 search using the magic formula -- can be engineered to leave a lot in the sieve; has a bigger domain to search, with more primes per exponent. Fast at sub-semi-mega bigger-than-PG-twin-search. (F) Choose another base such as 3 or 2015 etc. (G) Go for a world record prime -- fanciful. (H) Search for NeRDs which use only special modular reduction. My favourites are (A) or (E). Last fiddled with by paulunderwood on 2015-01-02 at 08:02

2015-01-02, 09:47	#4
paulunderwood Sep 2002 Database er0rr 4486₁₀ Posts	Code: ? 2^53^2571113log(2)/log(10) 433916.67694988905402889179241167322850 ? 2^53^25711*13 1441440 So 2^1441440-2^k-1 might be a candidate for (E), where 360360<=k<1441440.

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2015-01-02, 08:40	#2
VBCurtis "Curtis" Feb 2005 Riverside, CA 12775₈ Posts	C, E, and H all sound good. I haven't contributed yet, but I like to sieve, so I'd be willing to help with that for the next step in the project.

2015-01-02, 08:51	#3
paulunderwood Sep 2002 Database er0rr 2·2,243 Posts	Is there a sieve for (H)

2015-01-02, 17:45	#5
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2743₁₆ Posts	Someone else is apparently thinking about F), independently.

2015-01-02, 17:52	#6
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 19·23² Posts	I think about A), and possibly redirecting the CPU power into the soon to emerge "Cyclo"tomic-based project. It is similar to F)+H), and indeed, only focuses on numbers for which special FFT exists. Initially, it will probably be on PrimeGrid's PRPnet, as most budding projects are. I can provide my LLR implementation for their CPU participants, and Cyclo is OpenCL so it will run on any modern* GPU. ______________ *this excludes only very old and cheap cards that don't have double float.

2015-01-07, 02:26	#8
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 19×23² Posts	They will probably take care of that (or it can be disguised as a flavor of the genefer[OCL]-search). Initially they will have a sieving period which is mostly manual (and only Windows sieve existed so far, just like for GNF-Sv). They have an existing worked-out way of coordinating that. The sieve is data-less, and they have a result collection upload server.