[seqfan] What is the next prime p after 2 such that concatenating p values of A00043 is a prime, and p is itself in A000043?

[Jonathan Post]

235713171931618910712752160712792203228132174253442396899941112131993721701232094449786243110503132049216091
=
= 17581 * 497 672557 * 539043 454964 280391 * 49977 302050 968765
471356 702102 783655 170292 824326 347428 341036 466200 073082 434053
(Composite)
The above composite number concatenates the first 31 values of A000043
 Primes p such that 2^p - 1 is prime. 2^p - 1 is then called a
Mersenne prime.

The first 2 values concatenate to the prime 23, and 2 is an element of
A000043.  Concatenating the first 3, 5, 7, 13, 17, or 19 values gives
a composite.  What is the next prime p after 2 such that concatenating
p values of A00043 is a prime, and p is itself in A000043?