Prime numbers of the form $2357111317...$

Yes there are others.

From the corresponding list in OEIS we can find the sublist of primes. Unfortunately, tough,

The next term is the 355-digit number 2357111317192329313741434753...677683691701709719 which is too large to include here.

There other interesting lists linked there, like this one, that is the list of "Numbers $n$ such that the concatenation of the first $n$ primes is a prime."

These numbers are called Smarandache–Wellin numbers, and if they happen to be prime, they are called Smarandache–Wellin primes. There are many known primes of this form, and the first one after $2357$ is $m_{128}=235711\dots719$ (ending with prime $719$).