Is the expression x² + x + 41 prime for all non-negative integers x?

0² + 0 + 41 = 41 (prime)

1² + 1 + 41 = 43 (prime)

2² + 2 + 41 = 47 (prime)

3² + 3 + 41 = 53 (prime)

4² + 4 + 41 = 61 (prime)

5² + 5 + 41 = 71 (prime)

etc. (?)

Note: this sequence can also be obtained by starting with 41, then add on 2, then add on 4, then 6, then 8,...

Extra credit (+3 GOE): Can you settle this question without a calculator?

MM

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