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## Re: LLRP4 Version 3.3 now available !

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• The following is posted on behalf of Jean Penne who sent his reply to primenumbers-owner instead of primenumbers by mistake. Cheers Ken ... pfgw ... the
Message 1 of 6 , Dec 1, 2004
The following is posted on behalf of "Jean Penne" who sent his reply
to "primenumbers-owner" instead of "primenumbers" by mistake.
Cheers
Ken
--- In primenumbers@yahoogroups.com, "pminovic" <pminovic@y...>
wrote:
>
> > I am not surprised if LLPP4 deterministic test is slower than
pfgw
> PRP
> > one, because the "Computing U0" loop is more time consuming than
the
> > LL loop...
>
> This is true, it takes about 50 minutes to compute U0, I'll
> append the lresults.txt file tomorrow.
>

Thanks by advance !

> > Is the deterministic pfgw test also faster ?
>
> No! To prove primality of a PRP using "pfgw -tp" is very slow.
> Again I don't have exact timings handy but I think at least an
> hour in comparison to less than 18 minutes to find that
> (2^110615+1)^2-2 is 3-PRP.
>

I am also not surprised : Deterministic pfgw pays for its more
general algorithms than those of LLR.

> > Second question : with composite candidates, you found different
> > residues with pfgw and with LLRP4, it may be normal, or it may be
> > still an LLR bug...
>
> The input is different too, n=240068 and n=240065. The survival
> rate of Kynea (and Carol) is high and there are so many
> candidates to test that I simply cannot afford to process the
> same number twice :-)) Will try the same number later using
> smaller exponents.
>

My fault ! I did'nt see the inputs were different...

> BTW, testing k*2^n+1, n~180,000, both the new LLR and PRP3
> could process one number in almost exactly the same time, about
> 66 sec on 2.4GHz P-4.
>

Again, I am not surprised, PRP3 and LLRP4 use exactly the same code
to do squarings, the only difference is that, for Proth deterministic
tests, LLR computes the base "a" for each number, although PRP3 sets
always "a" = 3, but all that is done outside the loops.

Regards,
Jean
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