## 6913-digit AP5

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• 2799788209*16001#/5+1 2813053969*16001#/5+1 2826319729*16001#/5+1 2839585489*16001#/5+1 2852851249*16001#/5+1
Message 1 of 9 , Jun 23 9:53 PM
2799788209*16001#/5+1
2813053969*16001#/5+1
2826319729*16001#/5+1
2839585489*16001#/5+1
2852851249*16001#/5+1
• 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
Message 2 of 9 , Jun 24 3:36 AM
>
> 2799788209*16001#/5+1
> 2813053969*16001#/5+1
> 2826319729*16001#/5+1
> 2839585489*16001#/5+1
> 2852851249*16001#/5+1

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.

Phil
• ... Indeed. This was a consolation prize for a failed triplet search. I had 175591 singlets, 540 twins and hence the probability of failure was
Message 3 of 9 , Jun 24 6:01 AM
--- In primeform@yahoogroups.com, Phil Carmody <thefatphil@...> wrote:

> 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

Indeed. This was a consolation prize for a failed triplet
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: 25841
> 2839585489*16001#/5-1 has factors: 572332339

David

PS: There would have been a tedious ECPP job if the triplet
• Congratulations to you, David ! Have you try to make a PRP-Test of your 540 twins - k*16001#/5 -5 ? Best wishes Norman
Message 4 of 9 , Jun 24 7:18 AM
Congratulations to you, David !

Have you try to make a PRP-Test of your 540 twins - > k*16001#/5 -5 ?

Best wishes

Norman
• ... Yes 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
Message 5 of 9 , Jun 24 8:06 AM
--- In primeform@yahoogroups.com, "nluhn" <nluhn@...> wrote:

> k*16001#/5-5

Yes 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.

Do your really expect to use Primo
at 10k digits, if your find a PRP?

David
• ... 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. ... Hm, yes I try it.
Message 6 of 9 , Jun 24 8:42 AM
> 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 Primo
> at 10k digits, if your find a PRP?

Hm, yes I try it. I hope my new Phenom system can verify this 10k digit
number in 6-8 months, but it is a lot of manuell work.

Norman
• ... Here s a slightly smaller AP5 668285521*16001#/5+1 1101157031*16001#/5+1 1534028541*16001#/5+1 1966900051*16001#/5+1 2399771561*16001#/5+1 Puzzle for Phil
Message 7 of 9 , Jun 24 9:16 AM
>
> 2799788209*16001#/5+1
> 2813053969*16001#/5+1
> 2826319729*16001#/5+1
> 2839585489*16001#/5+1
> 2852851249*16001#/5+1

Here's a slightly smaller AP5

668285521*16001#/5+1
1101157031*16001#/5+1
1534028541*16001#/5+1
1966900051*16001#/5+1
2399771561*16001#/5+1

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
• ... Congratulations! http://hjem.get2net.dk/jka/math/aprecords.htm is updated. ... I never got around to making a public version of APTreeSieve but if you want
Message 8 of 9 , Jun 24 12:58 PM
> 2799788209*16001#/5+1
> 2813053969*16001#/5+1
> 2826319729*16001#/5+1
> 2839585489*16001#/5+1
> 2852851249*16001#/5+1

Congratulations!
http://hjem.get2net.dk/jka/math/aprecords.htm is updated.

> 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.

I never got around to making a public version of APTreeSieve but if you want
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
memory use.

--
Jens Kruse Andersen
• ... Thanks for the offer, but I ll stick to nix boxes, and leave that Windoze advantage to Ken. David (ever a light siever)
Message 9 of 9 , Jun 24 1:22 PM
--- In primeform@yahoogroups.com, "Jens Kruse Andersen"
<jens.k.a@...> wrote:

> I never got around to making a public version of APTreeSieve
> but if you want a Windows DOS-box alpha version...

Thanks for the offer, but I'll stick to 'nix boxes,
and leave that Windoze advantage to Ken.

David (ever a light siever)
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