Definition: The $n$th Smarandache-Wellin number in base $m$, denoted $S_n^m$ (or just $S_n$ for $m=10$), is the concatenation of the first $n$ base-$m$ primes.
So, for example, we would have $S_4 = 2357,$ or $S_7 = 235791113$.
Sometimes, the Smarandache-Wellin numbers are prime; for instance 2, 3, and 2357. There are currently 7-8 Smarandache-Wellin primes known - but are there infinitely many?
Of course this is almost certainly an open problem, but googling Smarandache-Wellin surprisingly says nothing even remotely about whether there are infinitely many. Are the numbers just not well-studied enough to even ask the question?