Question 557458: Mathematicians have been searching for a formula that yields prime numbers. One such formula was x^2-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.
I'm not sure of the steps to complete this problem...Please explain.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The polynomial  was supposed to yield prime numbers.
You are expected to try a few values for x , and find the corresponding P(x).
It is likely to be a prime number. Here are a few:
P(0)=41, P(1)=41, P(2)=43, P(3)=47, P(4)=53, P(5)=61, P(6)=71, P(7)=83, P(8)=97, P(9)=113, P(10)=131 P(20)=421, P(30)=971, P(40)=1601.
All of those (and  for the  values in between) are prime numbers.
It was a nice try, the design of P(x) ensured that iy could not be a multiple of 2, 3, 5, 7.
However,
 , so if or  were a multiple of 41, would be a multiple of 41. So,
 , and so on
There are other values of P(x) that are not prime, too, like
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