Two Fun Factorizations

I recently came across the following pair of numbers, quite close to one another, and with similar-looking prime factorizations:

4061 = 31*131
4069 = 13*313

We can explain the proximity of these two numbers by expanding the products as follows:

4061 = (3*10 + 1*1)(1*100 + 3*10 + 1*1) = 3*1000 + 9*100 + 1*100 + 3*10 + 3*10 + 1*1 4069 = (1*10 + 3*1)(3*100 + 1*10 + 3*1) = 3*1000 + 9*100 + 1*100 + 3*10 + 3*10 + 3*3

Notice that only the last terms are different, leading to the difference 3*3 - 1*1 = 8 between the two numbers.

The same sort of argument shows that products of the aba...ba*ba and bab...ab*ab differ only by a*a - b*b, where a and b are any two digits. However, a computer search yields no other examples where all of these numbers are prime, besides the above, up to at least a googol.