My general thoughts here:

• The first ~half of the conjectures, up to and including "Is 65537 the largest Fermat prime", I very strongly expect to be true. Any of them being false would be a big shock, likely resulting in a fundamental change in my (and undoubtedly many others') outlook to number theory.

  • I guess it is conceivable that "by chance" there is a further Fermat prime, for example, but standard heuristics and numerical calculations suggest this to be extremely improbable.

  • (I'm less sure of the Agoh-Giuga conjecture, I don't know much about that)

  • Note that Schinzel's Hypothesis H would imply all of those other conjectures, with the exception of the ones on Fermat numbers and Agoh-Giuga (and the Levy conjecture only "morally", I guess). Many of the conjectures stand and fall together

• I do not know much about Busy Beaver numbers. I do expect BB(5) = 47176870. I really do not know what to expect of the decidability of BB(20). I do not know about BB(6) either. As far as I am concerned, those could resolve either way.

• The Riemann hypothesis falls to the category of "if this is wrong, I have been very fundamentally wrong about something". So does the question of P = NP.

• Having no technical knowledge of the other Millenium problems, I fall back to "these are well-known conjectures that are expected to be true, that means that they are very likely true" and "if I did go and read about them more, I would very likely be as confident about them as I'm about the number theoretic conjectures, so better update now"

• Don't know much about Graph Isomoprhism, but apparently it being NP-complete would collapse the polynomial hierarchy and the exponential time hypothesis would fail. This seems very unlikely.

• Not an expert on abc-conjecture, but seems again likely true on the basis of being a famous conjecture.