- Jim Fougeron wrote:

> I have a 2004 addition for CPAP-4 (yes, it was very easy to find)

I also chose to search an easy improvement with a "special" d:

>

> 78006074.883#+k*2004+R is prime for k = [0...3]

>

> Using the special crafted R of:

>

> R=211456......

>

> This is 379 decimal digit CPAP-4 with d=2004 (d chosen for the

> year of finding).

46313478 * 1201#/1302643 + x498 + 2310n, for n = 0..3

Using the special crafted x498 at the site.

d = 2310 = 11# is the smallest possible d for a CPAP-11.

Only 7 more primes and a few trillion GHz years to go!

(Yes, I checked the CPAP-4 doesn't extend)

PrimeForm/GW prp'ed and Marcel Martin's Primo proved.

This record is going fast. I added a record history to keep up:

http://hjem.get2net.dk/jka/math/cpap.htm#difference_history

--

Jens Kruse Andersen - I have followed Jens lead, and on Christmas day, discovered a

CPAP-5 with a gap of 2310. This number is:

9400734826*1499#+x632+2310n

with n from 0 to 4 and

x632 = 29453397765450271545399188085266

55368252378620585099496385650600431498269661083903

16211042912735310776015757228962737061429256177227

59452435429488328389328281466289664367352954006161

79207095576921259775792175026579617936878099659414

32837668975308693630297479962123616982055909919099

17025496933775418577095695897932136276184735064982

12549583475520940170609152997656163627242028405951

20483292467767923352271563327090757509953181908766

84457108535835673100713235902439791043089273743933

82074800677693506138530042890392327727580262290580

36426781990814418117965800120148977404531919575260

38333320588240996195703518136355252551601080488639

Now, we need a CPAP-6 :) Any takers?

Jim.

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

<jens.k.a@g...> wrote:> Jim Fougeron wrote:

>

> > I have a 2004 addition for CPAP-4 (yes, it was very easy to find)

> >

> > 78006074.883#+k*2004+R is prime for k = [0...3]

> >

> > Using the special crafted R of:

> >

> > R=211456......

> >

> > This is 379 decimal digit CPAP-4 with d=2004 (d chosen for the

> > year of finding).

>

> I also chose to search an easy improvement with a "special" d:

>

> 46313478 * 1201#/1302643 + x498 + 2310n, for n = 0..3

>

> Using the special crafted x498 at the site.

>

> d = 2310 = 11# is the smallest possible d for a CPAP-11.

> Only 7 more primes and a few trillion GHz years to go!

> (Yes, I checked the CPAP-4 doesn't extend)

>

> PrimeForm/GW prp'ed and Marcel Martin's Primo proved.

> This record is going fast. I added a record history to keep up:

> http://hjem.get2net.dk/jka/math/cpap.htm#difference_history

>

> --

> Jens Kruse Andersen - Jim Fougeron wrote:

> I have followed Jens lead, and on Christmas day, discovered a

Congratulations.

> CPAP-5 with a gap of 2310. This number is:

>

> 9400734826*1499#+x632+2310n

>

> Now, we need a CPAP-6 :) Any takers?

Thanks for your interest in the new record category.

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

Note that it is also easily the second largest overall CPAP-5, only beaten by

Jim himself who has the whole top-10.

For a CPAP-6 with difference 2310, I think I would search around 560 digits.

For comparison, the largest known 6 simultaneous primes is a 418-digit CC-6 by

Dirk Augustin: http://hjem.get2net.dk/jka/math/simultprime.htm#records

Around 16 AP-6's at 560 digits are expected before hitting a CPAP-6 with my

program.

It looks pretty hard. I estimate perhaps 5 GHz years if my deep sieve is

improved to manage sparse forms better.

I don't have plans to make such a hard CPAP-6 search.

--

Jens Kruse Andersen