SOLUTION: Mathematicians have been searching for a formula that yields prime numbers. One such formula was x2 - x + 41. Select some numbers for x, substitute them in the formula, and see

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Question 157975: Mathematicians have been searching for a formula that yields prime numbers. One such formula was x2 - x + 41. Select some numbers for x, substitute them in the formula, and see if prime numbers occur. Try to find a number for x that when substituted in the formula yields a composite number. All of the first number are squared such as 1 squared (not 12), 2 squared, 3 squared, etc.
12 - 1 + 41 = 0 + 41 = 41
22 – 2 + 41 = 16 – 2 + 41 = 14 + 41 = 55
32 – 3 + 41 = 9 – 3 + 41 = 47
42 – 4 + 41 = 16 – 4 + 41 = 65
52 – 5 + 41 = 25 – 5 + 41 = 61
62 – 6 + 41 = 36 – 6 + 41 = 73
72 – 7 + 41 = 49 – 7 + 41 = 83
82 – 8 + 41 = 64 – 8 + 41 = 97
92 – 9 + 41 = 81 – 9 + 41 = 113
I say there is no number you can put into this equation and get a composite number. Is that correct?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
It may seem like every number you try will yield a prime number, but it is not a good idea to generalize like that (you need to prove it somehow). If you try x=41, then


%2841%29%5E2-41%2B41=41%5E2%2B0=41%5E2=41%2A41=1681


So this shows that plugging in x=41 gives you a composite number (since 41 is a factor of 1681).