A Number of Reasonable Length

A concatenation of numbers is where you smush them together. For example, if I were to smush 1 and 1 together, I would get 11. Now, if you were to smush primes together, in chronological order, like this:

2, 23, 235, 2357, 235711, and so on,

you would have what is known as a Smarandache-Wellin number. Here is a link to their entry on the Online Encyclopedia of Integer Sequences.

Most of these numbers end up being composite, with very, very, very few primes. Sadly, OEIS states that the fourth prime is to large to list. To rectify this issue, I have taken it upon myself to do the noble act of posting the first four Smarandache-Wellin primes on this here page. Now we can finally appreciate them together in all their glory!

The first four decimal Smarandache-Wellin primes are 2, 23, 2357, and 2357111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193197199211223227229233239241251257263269271277281283293307311313317331337347349353359367373379383389397401409419421431433439443449457461463467479487491499503509521523541547557563569571577587593599601607613617619631641643647653659661673677683691701709719.