For example, 13 is not a weakly prime since changing its last digit into 7 we obtain another prime, 17. The smallest weakly prime is 294001, indeed changing any of its digits results in a composite number.

A composite number which cannot be turned into a prime by changing a single digit is called unprimeable.

Terence Tao has proved that there are infinite weakly primes.

The first weakly primes are 294001, 505447, 584141, 604171, 971767, 1062599, 1282529, 1524181, 2017963, 2474431, 2690201 more terms

A few extremely weakly primes are known, i.e., prime that become composite if any digit is removed, changed, or inserted. They are 40144044691, 58058453543, 89797181359, 185113489357, 213022025663, and 222498988079.

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here