Primality testing of A052007(11) onwards

[Alonso Del Arte]

I'm wondering if anyone has tried to ascertain whether the terms after
317 in A052007, numbers n such that 2^n + n is prime, are really prime
or just strong pseudoprimes.

Mathematica has a special PrimeQ that the Help describes as being a
slower algorithm but which gives a much more certain result. The
regular PrimeQ takes a second to answer True to all 2^n + n of the
sequence, but I hesitate to try out the special PrimeQ because I have
no idea if by slower they mean that it would take an hour or a year.

AL