- Posted by: "David Broadhurst"
>I know in some of your previous sets, the /5 (or /30, or whatever) has been there to shrink a larger pattern to be the right size for a tuplet/CPAP, but I don't see why you've included such a construction here. What would have been wrong with a simple k*p#+1 search?
Well found, anyway.
- --- In firstname.lastname@example.org, Phil Carmody <thefatphil@...> wrote:
> I know in some of your previous sets,Indeed. This was a consolation prize for a failed triplet
> the /5 (or /30, or whatever)
> has been there to shrink a larger pattern to be the
> right size for a tuplet/CPAP
search. I had 175591 singlets, 540 twins and hence the
probability of failure was
exp(-540^2/175591) = 19%
but I drew that short straw. Then I realized that (since I
had triple sieved) there might be ways of turning this
failure into an AP5 success. So I took all threesomes of
the form (a+k*d)*16001#/5+1 for which three of the integers
k=0,1,2,3,4 had given primes and tested for the two holes,
which had not been tested in the triplet search, since
NewPGen had found that the corresponding numbers
(a+k*d)*16001#/5-1 and/or (a+k*d)*16001#/5+5 were composite.
In the AP5 the two holes were at k=1 and k=3 and
have cognate factors that
pfgw -f -e1000000000
can quickly recover
> 2813053969*16001#/5+5 has factors: 25841Thanks for your interest,
> 2839585489*16001#/5-1 has factors: 572332339
PS: There would have been a tedious ECPP job if the triplet
search had succeeded.
- --- In email@example.com, "nluhn" <nluhn@...> wrote:
> k*16001#/5-5Yes Norman, I tried those too, but with no luck:
grep fact pfgw.out | wc
190 760 8616
grep comp pfgw.out | wc
350 1750 26767
grep prime pfgw.out | wc
0 0 0
Here, of course, the prospect of failure is larger
exp(-exp(Euler)*540*log(16001)/log(10^6913)) = 56%
as opposed to
exp(-540^2/175591) = 19%
for the channel sieved by NewPGen.
The probability of a double failure was thus
0.19*0.56 = 11%.
which quantifies my lack of luck for the triplet search.
It's a pity that NewPGen doesn't have an option to sieve
all 4 of the cases k*n#/5 +/- 1 and k*n#/5 +/- 5.
Then the prospect of success would have been
1-exp(-2*540^2/175591) = 96.4%
for this amount of effort.
How's your 10k-digit search going?
Do your really expect to use Primo
at 10k digits, if your find a PRP?
> How's your 10k-digit search going?Good.
Up to date, I have found 67 gigantic (k*2^33333 +/- 1 , +5) twins
between k=1 and 5000*10^9.
I will stop newpgen at p=4*10^14.
> Do your really expect to use PrimoHm, yes I try it. I hope my new Phenom system can verify this 10k digit
> at 10k digits, if your find a PRP?
number in 6-8 months, but it is a lot of manuell work.
- --- In firstname.lastname@example.org, "David Broadhurst"
>Here's a slightly smaller AP5
Puzzle for Phil et al:
Which were the two NewPGen holes in this case?
[Note that I'm not telling you whether pfgw -f
is the best way of solving this. How about
GMP-ECM, for example? Or some other factoring
algorithm? All you know is that at least
2 and at most 4 of 10 cognate numbers have a
factor found by NewPgen.]
- David Broadhurst wrote:
http://hjem.get2net.dk/jka/math/aprecords.htm is updated.
> It's a pity that NewPGen doesn't have an option to sieveI never got around to making a public version of APTreeSieve but if you want
> all 4 of the cases k*n#/5 +/- 1 and k*n#/5 +/- 5.
a Windows DOS-box alpha version with poor user interface and documentation
then I could mail it. It can sieve k*a+b+c_i for k < 2^32, any a, b, and as
many simultaneous c_i < +/-2^31 as anybody could want. It uses 1 bit per k.
There is no option to sieve the first part in different runs and then reduce
Jens Kruse Andersen
- --- In email@example.com, "Jens Kruse Andersen"
> I never got around to making a public version of APTreeSieveThanks for the offer, but I'll stick to 'nix boxes,
> but if you want a Windows DOS-box alpha version...
and leave that Windoze advantage to Ken.
David (ever a light siever)