It's fun to see this. I investigated these on my own as an undergrad, but I called them solid primes. Originally I wrote a visual basic program (it was a long t

It's fun to see this. I investigated these on my own as an undergrad, but I called them solid primes. Originally I wrote a visual basic program (it was a long time ago) to find all the solid primes in base ten, which obviously involved writing a big num implementation. It ran for three days, only half solved the problem and then ran out of memory. Recoding it in Mathematica took 6 lines, ran in 20 minutes and found all of them. Plotting the distribution gives a nice curve which you can model quite well with the prime number theorem. From memory it looks like x^2*e^-x. Then plotting in different bases is also interesting.