In a polynomial $p (x) = x^{2} + x + 41$ put different values of x and find $p (x)$ . Can you conclude after putting different values of x that $p (x)$ is prime for all. Is x an element of N? Put $x = 41$ in $p (x)$ . Now what do you find?

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Solution

Conjecture is false because you can not find a composite number for $x = 41$ .

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