I have set Cunningham chain records for length 5 and 6 with my sieve.
Only the smallest prime in each chain is listed below.
CC5, 1st kind: 510482336*1181# + 10487557079, 503 digits
CC5, 2nd kind: 496391760*1277# + 325305140161, 540 digits
CC6, 1st kind: 9270784*647# + 44010196229, 277 digits
CC6, 2nd kind: 703632724*787# + 94265010841, 336 digits
In each case I sieved for a CC9 to a relatively low limit, and only prp'ed the
middle number at first. A chain can be extended in both directions so each prp
gave 5 CC5 and 4 CC6 chances.
Torbjörn Alm has found the longest CC by my sieve:
CC15, 2nd kind: 1081574468532104336791, 22 digits
He now holds 13 CC records.
All prp tests were performed by the GMP (GNU Multiple Precision) library.
All primes were proved by Marcel Martin's Primo.
Dirk Augustin has updated the record list:
A funny coincidence (maybe less funny to Thomas Wolter): Dirk Augustin, Thomas
Wolter and I all beat an old CC6 record from January 2003 within 5 days, without
knowing others were working on it.
Augustin's was largest of the 3 but I improved it further later (OK, I'm
greedy). Wolter's was smallest so he doesn't even make the updated top-3 list,
and it was last so he never had the record. Bad luck!
Jens Kruse Andersen