Similar to: Does there exist a prime that is only consecutive digits starting from 1?
Let $b_n=\overline{a_1a_2a_3\dots a_n}$ and $a_n=n$. For example $b_{11}= 1234567891011$. I have a couple of questions about the primes in the sequence $b_n$.
- What is the lowest number $n$ such that $b_n$ is prime (if there is is an $n$)?
- Are there infintely many primes in the sequence $b_n$?
- Do these primes have a name?
The first question was an excercise in Clifford Pickover's A Passion For Mathematics. I don't know if there is a way to find the answer to the first question without using a computer.
Like in Does there exist a prime that is only consecutive digits starting from 1?, $n$ cannot be an even number (or else $b_n$ would be even). Thanks.