The expression n^2 + n + 41 is prime for n = 0, 1, 2, ldots, 39. For n = 40 its value is 1681 = 41^2. This shows that:

  1. 40 cases make a proof
  2. 1681 is prime
  3. the expression is always prime
  4. a pattern can fail even after many cases, so it needs a proof
Answer

D) a pattern can fail even after many cases, so it needs a proof

Forty examples worked, yet n = 40 is a counterexample. SLO M-09-B-13 · Knowledge

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