Primes in A000670; prime ordered Bell numbers; prime Fubini numbers

[Jonathan Post]

I'd no sooner said that "primes of the form xxx" is usually not an
interesting sequence, when I started to wonder about:

Primes in A000670
1, 13, 541, 47293, 7087261, 526858348381

njas gives the table of first 100 values of A000670.

n such that A000670(n) is prime begin 2, 3, 5, 7, 9, 13.

Is there something obvious about this which is staring me in the face?