*Problem #12*

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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?