Conjectures are often based on inference from a few cases.
A famous example is the Riemann Hypothesis which states that all zeros of the zeta function have real part 1/2. All the zeros that we've found on the zeta functions had real part 1/2.
In the same fashion, the abc conjecture has been verified for a lot of large cases.
Can you think of any conjecture true for a "large" number of cases but was still proved wrong?