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

[Hugo Pfoertner]

David Wilson wrote:
> 
> 
> Can someone please verify A033189(13).  I would have expected A033189 to be
> increasing, but it ain't necessarily so.
a(k)>a(k-1) would of course be true without the condition in A033188
"minimum difference". Only if this difference is the same for a(k-1) and
a(k) (as for the 3 "199" terms, which all have difference 210) then the
occurrence of a longer progression starting earlier would be
impossibible. But since A033188(12)=2310 and A033188(13)=30030 it's
quite plausible that a progression with smaller difference may start
later then a longer one with bigger difference. BTW, I've ckecked that
14933623 is indeed the start of 13 primes 14933623+k*30030 k=0...12 and
that 14933623+13*30030 is composite.

Hugo Pfoertner