question about A033188 (Conjectural) minimum difference of an increasing arithmetic progression of n primes.

[N. J. A. Sloane]

I'm (exceptionally) sending this to the whole list,
because several people have been involved.

Look at this:

%S A033188 1,1,2,6,6,30,150,210,210,210,2310,2310,30030,30030,30030,30030,
%T A033188 510510,510510,9699690,9699690,9699690,9699690,223092870,223092870,
%U A033188 223092870,223092870,223092870,223092870,6469693230,6469693230
%N A033188 (Conjectural) minimum difference of an increasing arithmetic progression of n primes.
%D A033188 Computed by David W. Wilson
...
%F A033188 David W. Wilson conjectures that a(n) = n# (n primorial, A034386) for n >= 8.
%A A033188 Eric W. Weisstein (eric(AT)weisstein.com)

and

%S A033189 2,2,3,5,5,7,7,199,199,199,60858179,147692845283,14933623,834172298383,
%T A033189 894476585908771,1275290173428391,259268961766921,1027994118833642281
%N A033189 Smallest first term of arithmetic progression of n primes with difference A033188(n).
%C A033189 a(18) found by Gusev and Andersen.
...
%A A033189 Eric W. Weisstein (eric(AT)weisstein.com)
%E A033189 More terms from David W. Wilson (davidwwilson(AT)comcast.net)
%E A033189 a(14) corrected by Gennady Gusev, Jul 07 2004
%E A033189 Oct 05 2004: Gennady Gusev (gennady.gusev(AT)npo-saturn.ru) reports that Jens Kruse Andersen found a(15), and Gennady Gusev and Jens Kruse Andersen together found a(16) and a(17).


In view of the great interest in these matters, I think
it is important that these two sequences say which terms are
known to be correct and which are just conjectures.

Can David or Eric or Hugo or ... respond?

Thanks

Neil