False
That is false. Two is a prime number and two is even.
False. An enormous number of them are divisible by three.
This is far outside my own field of knowledge. All I can do is to point you toward a secondary source.
All prime numbers are rational.
false
The statement is false.
False.
False
False
That is false. Two is a prime number and two is even.
No because 2 is an even number which is also a Prime number that has only two factors which are itself and one.
False. An enormous number of them are divisible by three.
To be true a Conjecture must be true for all cases.
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).
Goldbach's conjecture
Two composite numbers may or may not be relatively prime, depending on their factors. Relatively prime numbers are sets of two or more numbers having 1 as their greatest common factor (gcf). All even numbers have 2 as a common factor, so no even number is relatively prime with any other even number.