[QUOTE=Batalov;402038]The last operation x^b may be a bit tricky; the usual exponentiation relies on x being small: lots of squarings with some mul by x.
When x is as large as the whole residue, the long mul will need to be implemented.[/QUOTE]

Squaring is done normally by:
* FFT
* point-wise squaring
* inv FFT
* carry adjustment.
During the carry adjustment, any mutliplication by the PRP-base can also be included.

For multiplication by a large X, we just need to repeat this operation once more (instead of doing it in carry propagation step) where we'll do point-wise multiplication by X (which would already be in FFT form). Since this would only be for a few 100 bits, the additional step doesn't matter in terms of speed. Should be very straightforward to implement.

[I don't know how this new-fangled Z transform works, but should be similar in principle).

Re: CycloSv: New version 0.6 (02-28-2015)
 

[QUOTE=axn;394904]New version 0.5:

Fixed ETA calculation. Was off by a factor of 50% (if it said 1hr, it would actually take 1.5hr).
Changed ETA update frequency from once every 3 seconds to 10 seconds


Attached are the source, win32 exe (CUDA 3.2), and compile scripts for windows and linux.[/QUOTE]

[quote=axn;primesearchteam.com;11000]New version 0.6

CPU usage has been reduced, so fewer instances should be able to keep the GPUs fed (especially slower CPU/faster GPU combinations). You may want to retest which combinations of instances & B values gives most thruput.

There should be minor increase in overall thruput as well, as a result.

Share your experiences here.[/quote]
Reposting from the other forum where sieving has been briefly run ~15 months ago and then was simply shut down and the effort discontinued.

[B]axn[/B], perhaps you could comment; maybe you have a code repository (at assembla?)

I updated the cyclosv0.6.zip code to sieve for cyclotomics of the second type (Phi(3,-b[SUP]3*2^n[/SUP])) and will run the Phi(3,-b[SUP]49152[/SUP]) for a short time. There should be perhaps a dozen primes there for b<1,500,000.
___________________
Phi(3,-b[SUP]3^m*2^n[/SUP]) with m>1 are less effective to run (at least on CPU) because only 3*2^n and 9*2^n FFT patterns are currently implemented in gwnum; the 9*2^n FFT is perfect for Phi(3,-b[SUP]49152[/SUP]). A clever extension to CycloOCL code may change that.

With Ryan P., we've run the Phi(3,-b^98304) series, too.
And now continuing with Phi(3,-b^196608) -- which will produce a string of 2-million digit primes. :rolleyes:

Oh, it is so nice to have resources! :rolleyes:

Current tally is:
[CODE]
32768 27 (max = 1164012)
49152 18 (max = 1373894)
65536 18 (max = 1181782)
98304 8 (max = 1202113)
131072 3+1 (max = 1082083)
[/CODE]

Plus assorted primes for 34992, 36864, 41472, 46656, 78732.

Even more small ones:
[CODE]1 2592
849 4096
5 5184
1 5832
355 8192
[COLOR=DimGray]1 13122[/COLOR]
107 16384
[COLOR=Blue]... 24576[/COLOR]
48 32768
[COLOR=DimGray]1 34992
2 36864
2 41472
1 46656[/COLOR]
[COLOR=Blue]27 49152
[/COLOR][COLOR=DimGray][COLOR=SeaGreen]1 59049 (3^10, Zhou)[/COLOR]
[/COLOR]18 65536
[COLOR=DimGray]1 78732[/COLOR]
[COLOR=Blue]8 98304[/COLOR]
4 131072
[COLOR=Blue]2 196608[/COLOR]
2 262144
[COLOR=Blue]1 393216[/COLOR]
1 524288
[/CODE]

[QUOTE=Batalov;450429]With Ryan P., we've run the Phi(3,-b^98304) series, too.
And now continuing with Phi(3,-b^196608) -- which will produce a string of 2-million digit primes. :rolleyes:

Oh, it is so nice to have resources! :rolleyes:[/QUOTE]

Congrats for [URL="http://primes.utm.edu/primes/page.php?id=122698"]this one[/URL]!

Thanks!

Writing the modified sieve was fun. I had to implement a modular cubic root again (but I already had an innoculation with [URL="http://mersenneforum.org/showthread.php?p=436289#post436289"]this small diversion[/URL]; this time I didn't need Adleman-Manders-Miller's; with the cyclotomic restrictions all cubic roots were easy).
And then the PhiExtension for P95 proved itself useful -- ...we still don't have a supernumeral-3 version of Cyclo{OCL|CPU}.

Congrats to Serge and Ryan for this [URL="http://primes.utm.edu/primes/page.php?id=122722"]2,259,865 digit prime[/URL] :banana: :banana:

[QUOTE=Batalov;450429]With Ryan P., we've run the Phi(3,-b^98304) series, too.
And now continuing with Phi(3,-b^196608) -- which will produce a string of 2-million digit primes. :rolleyes:

Oh, it is so nice to have resources! :rolleyes:[/QUOTE]

Who has greater resources , you or him? :)

Congratulation on this huge prime.

Wow! [URL="http://primes.utm.edu/primes/page.php?id=122736"]3,068,389 decimal digits[/URL]. Congrats to Ryan and Serge again.

:banana: :banana: :banana: