A number (written in base 10) is said to be weakly prime if it is
prime, but all the numbers obtained by changing one of its digits are not
prime. [For the record: 1 is not prime.] For example, 17 is not weakly
prime, since changing the first digit to 0 gives 07 which is prime.
Are there any weakly prime numbers? If so, what is the smallest?
What about weakly prime numbers in other bases?