Re: Largest CPAP differences
- I have followed Jens lead, and on Christmas day, discovered a
CPAP-5 with a gap of 2310. This number is:
with n from 0 to 4 and
x632 = 29453397765450271545399188085266
Now, we need a CPAP-6 :) Any takers?
--- In firstname.lastname@example.org, "Jens Kruse Andersen"
> 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:
> Jens Kruse Andersen
- Jim Fougeron wrote:
> I have followed Jens lead, and on Christmas day, discovered aCongratulations.
> CPAP-5 with a gap of 2310. This number is:
> 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
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