The spaceship has really good life support/recycling The spaceship is self-repairing and draws power from interstellar hydrogen

That requires a MTTF of 3^^^3 years, or a per-year probability of failure of roughly 1/3^^^3.

I've discovered the Universe will last at least another 3^^^3 years

This implies that physical properties like the cosmological constant and the half-life of protons can be measured to a precision of roughly 1/3^^^3 relative error.

To me it seems like both of those claims have prior probability ~ 1/3^^^3. (How many spaceships would you have to build and how long would you have to test them to get an MTTF estimate as large as 3^^^3? How many measurements do you have to make to get the standard deviation below 1/3^^^3?)