For how many positive integers n is n^2-3n+2 a prime number?

(D) more than two, but finitely many

2002 AMC 12B Problem 3

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For how many positive integers

n

n^2-3n+2

a prime number?

none

one

two

more than two, but finitely many

infinitely many

Factor

n^2-3n+2

(n-1)(n-2)

is a product of two integers; for it to be prime one factor must equal

1

Factor

n^2-3n+2=(n-1)(n-2).

For

n\ge4

both factors exceed

1,

so the value is composite. Checking

n=1,2,3

gives

0,

0,

and

2.

Only

n=3

yields a prime, so there is exactly one such

n.

Thus, the correct answer is B.