Torbjörn Alm and I have found the largest known CPAP-4 (4 consecutive primes
in arithmetic progression) at 1284 digits:

4919761805*3000# + 6673 + 30n, for n = 0, 1, 2, 3

First Michael Bell and Jim Fougeron's APSieve sieved for an AP-6:
k*3000# + 6673 + 30n, n=0..5
The form avoids factors below 3000.

For each surviving k, the number with n=3 was prp tested with PrimeForm/GW.
Each found prp simultaneously gave 3 AP-4 chances: n=0..3, n=1..4, n=2..5
This reduced the expected number of prp tests to around 1/3.

It was checked that the found AP-4 had consecutive primes and these were
proved with Marcel Martin's Primo.
The Primo certificates are at the largest known CPAP's:
http://hjem.get2net.dk/jka/math/cpap.htm

The expected time for a 1333 MHz Athlon alone would have been around 23 days.
We used 3 computers and were a little above expectation.

--
Jens Kruse Andersen