Erdős proved that there are infinitely many weakly
prime numbers (also called (digitally) delicate primes),
i.e., prime numbers such that changing any single one of the digits,
in a given base, with any other digit
always results in a composite number. Tao proved that weakly prime
numbers constitute a positive
proportion of all prime numbers. In this talk, we are going to discuss
further quantitative refinements
on the distribution of weakly prime numbers.