A prime number p is called a digitally delicate prime in base \(b \ge 2\) ; if any single digit of the base b expansion is replaced by any other digit \(0,1,..,b-1\) , the resulting number is composite. Tao showed that there is a positive proportion of digitally delicate primes in base \(b \ge 2\) . M. Filaseta raised a question about primes, which are not digitally delicate primes. We are going to discuss those prime numbers that are not digitally delicate primes. We prove there are infinite numbers of primes that are not digitally delicate primes.