EVIDENCE
One possible conjecture is that their sum is 27. The conjecture is patently false, but that does not stop it being a conjecture.
You can make a conjecture by conducting research or experiments that come out to be unproven. It can appear to be correct but it is actually unproven.
Usually not. If you do use conjectures, you should make it quite clear that the proof stands and falls with the truth of the conjecture. That is, if the conjecture happens to be false, then the proof of your statement turns out to be invalid.
You can make whatever conjecture that you want: it does not have to be true or even logical. You could conjecture that the relationship is like the one between the Sun and the Earth!
My conjecture is that the sum is 67. A conjecture does not have to be true, or even plausible. You should be able to test it. If it is found to be true then in is no longer a conjecture, if it is found to be false, it is rejected - and so no longer a conjecture. If it cannot be proved either way, it remains a conjecture.
The future tense of "conjecture" is "will conjecture."
Any conjecture you want; a conjecture is merely an opinion or conclusion based on given information. Whether the conjecture is true or not is left to be proved (if provable at all). One opinion (conjecture) could be that the sum is "blue". It's a totally nonsense conjecture, but its a conjecture none the less. A sensible conjecture might be that the sum is odd. This can be tested and found to be true or false by summing the first 46 odd numbers (a mechanical method that is fairly easy in this case), or by the mathematical manipulation of axioms via algebra (a mathematical proof).
Infrencing
Goldbach's conjecture states that every even integer which is greater than 2 can be expressed as the sum of two prime numbers.
The Poincaré Conjecture.
a conjecture
A conjecture should be testable. You test it and if it fails the test, it is a false conjecture.