It is well known that multiplying two large primes to get their product is easy, and factoring the result to get the prime factors is hard, such that if someone has published a large number and says it's the product of two primes, and then tells you the two factors, this is fairly conclusive evidence that they are the one who originated the product.
However, consider a slightly modified problem: The person presenting you with the two prime factors doesn't have to have their product equal the pre-existing number; they only need to generate a result which is nearly correct, as if the published number had a typo in it. It must otherwise appear to be a standard private-key claim, such that if the 'typo' was corrected it would be the standard known-difficult problem and therefore a strong proof of being the original author.
To specify this formally, say that the product of the two large primes they present must have edit distance one to the published number. (Of the well-known edit distance metrics, the most natural would be Damerau-Levenshtein distance, which allows insertion, deletion, substitution, and transposition of adjacent characters, though the context where this came to my attention was actually considering solely transposition of adjacent digits.)
How difficult is this problem? I am interested in the answers for considering the two numbers as strings in base 10 and in base 2, and of course a generalization for arbitrary bases would be even more interesting.