if f(`x`) and g(`x`) are functions which are integrable on [`a`,`b`]. *[6]*

**2.** Consider the polynomial h(`x`) = `x`^{2} - `x` + 41. Note that h(1) = 41, h(2) = 43, h(3) = 47, h(4) = 53, and h(5) = 61 are all prime numbers. (An integer `n` > 1 is a *prime number* if its only positive integer divisors [*i.e.* factors] are 1 and `n` itself. For example 5 is prime, but 6 = 2 times 3 isn't.) Is h(`x`) always a prime number if `x` is a positive integer? Why or why not? *[4]*

**Bonus.** Is there any (other?) polynomial which always gives you prime numbers? *[2]*

Solution to Assignment #6

Department of Mathematics Trent University

Maintained by Stefan Bilaniuk. Last updated 1998.08.22.