A small conjecture and its counterexample

A prime is an integer greater than 1 with no positive divisors other than 1 and itself. Test a formula that seems to make primes and find the one counterexample that overturns the claim.

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1 · Predict before revealing the answer

Substituting n = 0 through 10 into n² + n + 41 produces 11 prime values. Does the formula produce a prime for every non-negative integer n?

Conjecture, then test farther