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One possible conjecture is that each square number up to 1000 has 4 factors. The conjecture is manifestly false, but it is still a conjecture.
There is no logical conjecture that can be made for what could be an irregular polygon with an unknown number of sides. Of course, you could always conjecture anything. For example, that they will taste of strawberries. A conjecture that, I guess, will be disproved quite easily.
2 would be a counterexample to the conjecture that prime numbers are odd. 2 is a prime number but it is the only even prime number.
Goldbach's conjecture says that every even number greater than two can be expressed as the sum of 2 primes. If 30 could not be expressed as the sum of two primes, then this would disprove the conjecture. As it is, 30 can be expressed as the sum of two primes. You can express it as 11+19. Thus, Goldbach's conjecture holds in this case.
There is not "the" conjecture: there are several. The oldest and probably best known unsolved conjecture in number theory is the Goldbach conjecture. According to it every even integer greater than two can be expressed as the sum of two prime numbers.