Problem #12

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?

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