A023394 and the smallest undiscovered Fermat factor

[Max A.]

SeqFans,

A023394 claims that it is "complete up to a(19) = 1214251009".
Can we be confident with the higher listed terms and remove the quoted
claim from A023394 description?

I've found an old discussion on the topic
http://www.fermatsearch.org/forum/messages/52.html
where Phil Moore suggested that "there are probably no more
undiscovered Fermat factors
less than 5704689200685129054721, the larger factor of F7". That was
almost 5 years ago. What is the current sutiation?

Max