This number is a composite.
Both 1!+3!+5! and 1!!+3!!+5!! are primes. [Jevtic]
135 is the 4th term (found by Shyam Sunder Gupta) in the following sequence: a(n) is the height (continuous number of rows) of a palindromic prime pyramid (starting with 2) of step size n, where each palindromic prime p is the smallest p that contains p in the row above. The sequence begins 3, 11, 26, 135, 828, ... . Can you find a(6) ?