How many of the following mathematical predictions will have surprising results? (That is, resolve other than as currently expected.)
N/A results are not expected for any of these.
This is a derivative market; it will resolve exactly in accordance with the underlying markets.
/PlasmaBallin/is-the-first-hardylittlewood-conjec(Expected Yes)
/PlasmaBallin/is-the-second-hardylittlewood-conje (No)
/PlasmaBallin/are-there-infinitely-many-composite (Yes)
/PlasmaBallin/is-levys-conjecture-true (Yes)
/PlasmaBallin/are-there-infinitely-many-prime-tri (Yes)
/PlasmaBallin/are-there-infinitely-many-cousin-pr (Yes)
/PlasmaBallin/is-de-polignacs-conjecture-true (Yes)
/IsaacKing/is-artins-conjecture-on-primitive-r (Yes)
/IsaacKing/is-the-bunyakovsky-conjecture-true (Yes)
/IsaacKing/are-there-infinitely-many-balanced (Yes)
/IsaacKing/are-there-any-answers-to-brocards-p (No)
/IsaacKing/is-the-agohgiuga-conjecture-true (Yes)
/PlasmaBallin/is-schinzels-hypothesis-h-true (Yes)
/PlasmaBallin/is-dicksons-conjecture-true (Yes)
/PlasmaBallin/are-all-fermat-numbers-squarefree (Yes)
/PlasmaBallin/are-there-infinitely-many-fermat-pr (No)
/PlasmaBallin/is-65537-the-largest-fermat-prime (Yes)
/BoltonBailey/is-there-a-5state-binary-tape-turin (No)
/BoltonBailey/is-the-20th-busy-beaver-number-inde (No)
/EvanDaniel/is-the-bb6-machine-the-kropitz-2022 (No)
/NcyRocks/is-the-riemann-hypothesis-correct (Yes)
/NcyRocks/does-a-smooth-navierstokes-solution (No)
/IsaacKing/does-p-np (No)
/NcyRocks/is-the-hodge-conjecture-true (Yes)
/NcyRocks/is-the-birch-and-swinnertondyer-con (Yes)
/NcyRocks/is-the-abc-conjecture-correct (Yes)
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.