a theorem
There is no conjecture about the sum of the first 30 positive even numbers. The answer can be derived and proven. A statement that has been proven is no longer a conjecture.
A conjecture is an unproven statement or hypothesis that is proposed based on observations or patterns. When a conjecture is proven true through logical reasoning or mathematical proof, it becomes a theorem. For example, the conjecture that "the sum of the angles in a triangle is always 180 degrees" is a statement that can be proven true in Euclidean geometry.
There have been many attempts to try and prove it but so far none of these succeeded
From Wikipedia ("Prime triplet"): "Similarly to the twin prime conjecture, it is conjectured that there are infinitely many prime triplets." So, it seems that nobody really knows for sure. "It is conjectured" means that it seems reasonable to suppose that there are infinitely many, but that it hasn't been proven yet.
Never
theorem
a theorem
It is a proposition that is believed to be true but has not [yet] been proven to be true. Clearly, if proven to be false it would no longer be a conjecture.
There is no conjecture about the sum of the first 30 positive even numbers. The answer can be derived and proven. A statement that has been proven is no longer a conjecture.
theorem
A conjecture is an unproven statement or hypothesis that is proposed based on observations or patterns. When a conjecture is proven true through logical reasoning or mathematical proof, it becomes a theorem. For example, the conjecture that "the sum of the angles in a triangle is always 180 degrees" is a statement that can be proven true in Euclidean geometry.
There are no proven dangers, only rumor and conjecture.
Theorem
It is a proposition or a belief that has not yet been proven.
There is need for a conjecture. It is an easily proven fact that an even number minus an even number is always an even number.
There have been many attempts to try and prove it but so far none of these succeeded