(Meta comment: Congrats to Andre Nicolas! I am happy for Andre Nicolas that he is second ranked now. Also he has 3001 answers with no questions. That is good. I am also glad to see Arturo Magidin has been online yesterday.)
Now my question is the following: What prime numbers have the sum of their digits as a prime number? We know that $3001$ (could be Andre's $3001$ answers) is a prime number with the sum of its digits a composite number. How many primes are there such that their sum of their digits is prime?