I have found a 60351-digit 3-Carmichael number, namely
N=P*Q*R, where
P=X*Y+1 is a 15092-digit prime,
Q=16*X*Y+1 is a 15093-digit prime,
R=X*Y*(Q+16)/9266506659322630097+1 is a 30166-digit prime,
X is the product of the first 2762 primes and
Y is the 4315-digit integer in the Pari-GP code at:

http://physics.open.ac.uk/~dbroadhu/cert/3carm.txt

X enabled OpenPFGW proofs that each of {P,Q,R} is prime.
Pari-GP showed that N=1 mod LCM(P-1,Q-1,R-1)
and hence that N is a 3-Carmichael number,
with b^N=b mod N for all integer b.

The previous record was set by Phil Carmody at 30052 digits:

http://listserv.nodak.edu/scripts/wa.exe?A2=ind0211&L=nmbrthry&P=R623

I thank Phil for his generous encouragement to exploit
the Chinese remainder theorem as fully as he has done.

David Broadhurst