We are
looking for solutions of the first type where a
equals +/-1, b is even and n, n+/-b are prime.

Several of our puzzler’s, but mainly Patrick de
Geest and Giovanni Resta, have contributed these
sequences.

Integer sequences A030465 and A054214 solve
type b. for a=1 and a=-1 respectively.

Trying
to solve Q2 for twin primes p,q:

p.q =
n(10^d+1) – 1 gives:

m^2=n(10^d+1) (using p=m-1,q=m+1)

So a
solution to type b. with even m and m+/-1 prime
would be nice.

Checking the even solutions of A102567 will
not give our sought solutions.

I
studied solutions to pq=n(10^d+1)+r with |r|>0
and |r| as close to 1 as possible.

My
best solution is (r=-4):

81818181817,81818181821,6694214876166942148757