This number is a prime.
The largest known prime tribonacci number is element number 4201 in the sequence, which has 1112 digits. Eric W. Weisstein found this in March 2004, after examining the first 10^4 tribonacci numbers. Note that Dr. Weisstein neglected to point out that 4201 is itself prime. [Post]
The only prime of form p*q*r+2 where p, q, r, are consecutive double-digit primes. [Loungrides]
The largest distinct-digit prime whose all the digits, as exponents in the form 2^x+3^x, create primes, i.e., 2, 5, 13, 97. [Loungrides]