## [PrimeNumbers] Re: Largest CPAP differences

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• ... 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
Message 1 of 6 , Dec 3, 2004
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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
• 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
Message 2 of 6 , Dec 30, 2004
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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
• ... Congratulations. 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
Message 3 of 6 , Dec 31, 2004
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Jim Fougeron wrote:

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

Congratulations.
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
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