- Hi all,

Third time lucky

2^5900 + 469721931951

2^5900 + 469721934831

2^5900 + 469721937711

2^5900 + 469721940591

form a CPAP4 each with 1777 digits and difference 2880

Cheers

Ken--- In primeform@yahoogroups.com, "Ken Davis" <kradenken@...> wrote:

>

> Hi Jim,

> Having thought about it over the lt couple of days I had come to

the

> same conclusion.

> The prp testing is fine and the original sieving wasn't by pfgw.

> I hv ealreadyhad 123 AP-3's of which 113 were reported as CPAP-3. I

> never bothered verifying them as it was an AP4 I am searching for.

> I'l continue on then

> Thanks

> Ken

>

> --- In primeform@yahoogroups.com, "jim_fougeron" <jfoug@> wrote:

> >

> > I have started looking into the cpap format (the JF CPAP-??

format)

> > file processing.

> >

> > What is happening, is that "internally", the program (once it

finds

> a

> > AP of probable size), it quickly performs a pretty shallow (first

> 10k

> > primes) window'd SoE over the range (tracking which factors are

> > found), and on the candidates left, it performs a PRP test. If

> none

> > of these PRP test result in a PRP, then it is written out as a

CPAP

> > result.

> >

> > However, the code doing the SoE is totally broken (as listed by

> > Jens). I do not know if/when this code was working, but it is

> > obviously broken.

> >

> > However, all of the "found" AP's are still valid. It is just the

> > verification that is busted. Thus, if you have other AP's found,

> > they are valid. If there are no other AP-4's found, then there

> were

> > no others in your test data. Thus, there are no missed AP's,

> > just "falsely" listed CPAP's.

> >

> > Jim.

> >

> >

> > --- In primeform@yahoogroups.com, "Jens Kruse Andersen"

> > <jens.k.a@> wrote:

> > >

> > > Ken Davis wrote:

> > > > pfgw cpap4.in -lcpap4.log

> > > > with cpap.in =

> > > >

> > > > JF CPAP-5 2^5900

> > > > 172518140307 3150

> > >

> > > I have no previous experience with the JF format and have not

> seen

> > > it documented. I don't know how to fix it but will just observe

> > what

> > > goes wrong using PFGW 1.2.0.

> > >

> > > I made cpap4abc.in with this:

> > > ABC2 2^5900+172518140307+$a

> > > a:from 0 to 9450 step 2

> > >

> > > pfgw -f cpap4abc.in -lcpap4abc.log

> > > gives this in cpap4abc.log (factors verified by PARI/GP):

> > > 2^5900+172518140307+2398 is 3-PRP! (0.1490s+0.0554s)

> > > 2^5900+172518140307+2400 has factors: 127

> > > 2^5900+172518140307+2402 has factors: 3

> > > 2^5900+172518140307+2404 is composite: [57EBE58EC2D21DD]

> > (0.1374s+0.0701s)

> > > ...

> > > 2^5900+172518140307+2422 has factors: 5

> > > 2^5900+172518140307+2424 is composite: [160E5E697CE17556]

> > (0.1350s+0.0593s)

> > > 2^5900+172518140307+2426 has factors: 3

> > > 2^5900+172518140307+2428 is 3-PRP! (0.1349s+0.0514s)

> > >

> > > cpap4.log from Ken's JF file has very different content:

> > > 2^5900+172518140307+2398 has factors: 5

> > > 2^5900+172518140307+2400 has factors: 3

> > > 2^5900+172518140307+2402 is composite: [2EDEDA40E91BFEED]

> > (0.1378s+0.0031s)

> > > 2^5900+172518140307+2404 is composite: [57EBE58EC2D21DD]

> > (0.1415s+0.0005s)

> > > ...

> > > 2^5900+172518140307+2422 has factors: 14747

> > > 2^5900+172518140307+2424 has factors: 3

> > > 2^5900+172518140307+2426 has factors: 17

> > > 2^5900+172518140307+2428 has factors: 5

> > >

> > > So trial factoring went completely wrong with the JF format.

> > > It found false factors and overlooked real factors.

> > >

> > > --

> > > Jens Kruse Andersen

> > >

> >

> - Ken Davis wrote:
> 2^5900 + 469721931951

Congratulations!

> 2^5900 + 469721934831

> 2^5900 + 469721937711

> 2^5900 + 469721940591

>

> form a CPAP4 each with 1777 digits and difference 2880

http://hjem.get2net.dk/jka/math/cpap.htm is updated with

the first proven CPAP record since March 2005.

--

Jens Kruse Andersen - Hi Jens,

I think it also qualifies for largest differnce for a CPAP4 also

cheers

Ken

--- In primeform@yahoogroups.com, "Jens Kruse Andersen"

<jens.k.a@...> wrote:>

> Ken Davis wrote:

> > 2^5900 + 469721931951

> > 2^5900 + 469721934831

> > 2^5900 + 469721937711

> > 2^5900 + 469721940591

> >

> > form a CPAP4 each with 1777 digits and difference 2880

>

> Congratulations!

> http://hjem.get2net.dk/jka/math/cpap.htm is updated with

> the first proven CPAP record since March 2005.

>

> --

> Jens Kruse Andersen

> - Ken Davis wrote:
>> > form a CPAP4 each with 1777 digits and difference 2880

Right! Thanks for pointing that out. The record page is updated.

> I think it also qualifies for largest differnce for a CPAP4 also

--

Jens Kruse Andersen