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Mathematician: 3 is prime, 5 is prime, 7 is prime, the rest follows from induction.

Physicist: 3 is prime, 5 is prime, 7 is prime, 9...that's probably an experimental error..., 11 is prime, 13 is prime. The law of nature in question is backed-up by experiment well enough.

Engineer: 3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime, 13 is prime...