A probable CPAP-3 with d=17676
- 9337#+835401121+n*17676, n=0,1,2
is a _probable_ 4003-digit CPAP-3, which, when proved prime*, would fit
into the top-10 of this type of prime constellations (as of 5 Sep 2004).
But what is more interesting (at least to me) is the fact that d=17676
is the largest known common difference for any CPAP-k (k > 2) that has
ever been discovered, as far as I know.
I dare to conjecture that within one year from now (5 Sep 2004) on*, no
one will find a larger value of d for any CPAP-k. Note that the average
prime gap length for the form 9337#+k by testing k from 1 to 840000001
* The Primo certifications of primality will follow within due time.