SOLUTION: Can you please explain this problem to me. I have given some of the solutions I have tried but do not know if I am doing it right. To prove or disprove the following: The expres

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Question 619418: Can you please explain this problem to me. I have given some of the solutions I have tried but do not know if I am doing it right.
To prove or disprove the following: The expression n2 - n + 41 produces a prime number for every positive integer n. (Hint: try the following numbers 1, 10, and 41).
I have tried this in two seperate ways-The first reading the 2 as a power of. Therefore making the problem n^2 -n + 41. The second attempt was n(2) -n +41.
n^2 - n + 41 = 1^2 - 1 + 41 = 1 - 1 + 41 = n=41
n(2) - n + 41 = 1(2) - 1 + 41 = 2 - 1 + 41 = 1 + 41 = 41
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Try n = 1

n^2 - n + 41

1^2 - 1 + 41

1 - 1 + 41

41

Which is prime. So it works so far.

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Try n = 2

n^2 - n + 41

2^2 - 2 + 41

4 - 2 + 41

43

Which is prime. So it works so far.

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Try n = 41

n^2 - n + 41

41^2 - 41 + 41

41(41 - 1 + 1)

41(41)

Which is NOT prime since we can write the final expression as a product of two primes. So this is where the formula breaks down.