A prime number has only 2 factors: 1 and itself. Factor 1 is the key. 

Make one of the factor (in bracket) be 1, or -1   

(X-17)(X-3).

Let X =18: (18-17)(18-3) = 15 (not prime)

Let x=2: (2-17)(2-3) = 15 (not prime)

let x=4: (4-17)(4-3)=-13 (is “negative” prime a prime number?)

let X=16: (16-17)(16-3)=-13 (“negative” prime)

Answer is 4 and 16 (?)

#BigDevil: ok thanks, changed above. if negative prime is not a prime, then I have no solution too.

#Chief: Got it. Just to show a positive example (literally and figuratively) to have peace with my ownself:

x2 -22x + 85=(X-17)(X-5)

Let x=18: (18-17)(18-5)= 13 (definitely prime)

Let x=4: (4-17)(4-5) = 13 (definitely prime)

let x=16: (16-17)(16-5) =-11 (arguably not prime)

let x=6: (6-17)(6-5) =-11 (arguably not prime)

Answer is 18 and 4 (definitely correct)

I do believe the above method is what the setter is looking for. Now I am at peace. 😀

Yep…I was thinking along the same line as well, and

I googled. Negative numbers are not prime numbers.

You made a slight mistake with x = 16                                                                                                                    (16 – 17)(16 – 3) = -13, not 13.

So both x = 4, and x = 16 are not acceptable.

For the life of me, I can’t think of any other possibilities. So I am strongly suspecting this question is a mistake?

I think the jury is out on whether prime numbers can be negative.  While mostly used in the positive domain, there are plausible arguments for negative primes too.  Within the context of the question, I suspect the answer is yes, prime numbers can indeed be negative.

DD’s teacher had confirmed that the question was indeed a mistake.

I guess why a negative number cannot be considered a prime number is because of the definition of prime number: a number which can only be evenly divided by 1 and itself.

A negative number, eg -5, is divisible by -5, -1, 1, 5; which does not meet the definition of prime and thus not considered to be a prime number.

Appreciated for following up and updating. Guess my son also can sleep tonite, since I posted this question to him.

The question did not cause any sleepless nights for my daughter… but it had been bugging me instead! lol