You know that no matter how many examples you give to show that a conjecture is true, it does not prove the conjecture. It takes just one counterexample to disprove a conjecture. Describe 3 conjectures you thought were true based on many examples, but that turned out to be false based on a counterexample. The conjectures do not have to be mathematical.

Question

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conjecture: the formula n^2 - n + 41 is a prime number generating formula . I tested n = 1,2,3,... 40  up to 40

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is it true for all n?  (hint: test n = 41)