How many of the sequential primeconcatenations are prime?

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  • 2 is a prime. 3 is the next prime. 23 is also a prime.
  • 31 is a prime. 37 is the next prime. 3137 is also a prime.

Can we estimate or prove how many $XY$ are prime if $X$ and $Y$ are primes nr $n$ and $n+1$?

I know this is dependent on basis. I will for this question assume basis 10.

(Optional question) Can we prove whether lower or higher basis will increase or decrease occurrance?