After nearly 5 days of 29 computers work I have found a CC15, which
sets 15 Simultaneous Primes record:

CC15, 2nd kind: 28320350134887132315879689643841 (32 digits)

There were 9 maximal (i.e. not extendable to longer CC) CC14 found
during the search, the largest 2 being:

CC14, 2nd kind: 36027516322668108492823293067201 (32 digits)
CC14, 2nd kind: 35461680947014037576372182070401 (32 digits)

but the upper CC14 contained in the CC15 is the largest.
There was one 33-digit maximal CC13 found:

CC13, 2nd kind: 243753092403308369115790643493121 (33 digits)

out of total number of 73 maximal CC13's found.

Jarek