The difficulty on the primecoin network has been stuck at 10.95-10.98 (give or take) for months. It only seems to be increasing in response to miner efficiency.
I doubt they will be seeing any new records for a while.
Unlike Riecoin, Primecoin makes it possible to submit POW well above the current difficulty. The present Primecoin record is a 2nd kind Cunningham chain of length 14 from May this year (when the difficulty was 10.96)
http://primecoin.io/index.phphttp://primerecords.dk/Cunningham_Chain_records.htmThat's true: there is the possibility that, by chance, a primecoin POW will be a chain of greater length than what's specified by the difficulty. However this happens "by luck", and since they are limited on the size of their primes, I agree with bsunau7 that they won't be seeing much new records for a while.
On the other hand, Riecoin cannot find sextuplets above difficulty (as you said)... BUT, analogous to what you decribed with primecoin, RIC can find sextuplets that are also part of septuplets or octuplets. The records for septuplets are much lower than those of sextuplets, so we may have broken some of those already! wow, I haven't realized this before... I'll have to make a script to test it, but with 120000 sextuplets there's a chance one of those is also a septuplet (and a world record breaking one)! the numbers are so large that the chance may be too small, but we have to test it...
Am I crazy, or should we not expect to have a few tens of septuplets already? Perhaps I'm mis-thinking the math -- 1/ln(2^1700) ~= 1/1200 chance of a sextuplet being a septuplet?