105 is a triangular number and a 12-gonal number as well as a sphenic number and a Zeisel number. It comes in the middle of the prime quadruplet (101, 103, 107, 109). The only other such odd numbers less than a thousand are 15, 195 and 825. 105 is also a pseudoprime to the prime bases: 13, 29, 41, 43, 71, 83 and 97.
One hundred five is also a number n for which n - 2k is prime, for k < log2(n). (This even works up to k = 8, ignoring the negative sign.)