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If n= p^2-p+17, is n prime?

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Zarrolou
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If n= p^2-p+17, is n prime? [#permalink] New post   13 May 2013, 13:53
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If \(n= p^2-p+17\), is \(n\) prime?

1)\(p\) is prime

2)\(p\) is an integer less than \(17\)


Hi guys this is a question I just created. OE here
As always any feedback is appreciated
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C
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Bluelagoon
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Re: If n= p^2-p+17, is n prime? [#permalink] New post   13 May 2013, 19:52
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Zarrolou wrote:
If \(n= p^2-p+17\), is \(n\) prime?

1)\(p\) is prime

2)\(p\) is an integer less than \(17\)


Hi guys this is a question I just created. If you want give it a try: Kudos to the correct solution!
As always any feedback is appreciated



The correct answer is C.
A) If you pick p =17. Than n is not prime.
if you pick p=2. Than n is prime.
Insufficient.

B) From the above reasoning an integer less than 17 can be negative also.
If you take p=-17 than n is not prime. if you take p=2 than n is prime.

Hence , if you take both , then a prime number less than 17 will surely make n prime.

Hence, answer is C.
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Re: If n= p^2-p+17, is n prime? [#permalink] New post   13 May 2013, 22:35
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Well done Bluelagoon, you're correct!

Official Explanation

\(n=p^2-p+17\)

1)p is prime

if \(p = 17\), then \(n=17^2-17+17= 17(17-1+1)\) is divisible by 17
if \(p=2\) then n is prime.
Not sufficient

2)p is an integer less than 17

This seems to solve the problem because p cannot be 17. But now p can be -17, and we have a similar situation as above

if \(p= -17\), then n=\(17*17+17+17=17(17+1+1)\) is divisible by 17
if \(p=2\) then n is prime

1+2) Now we are sure that 17 or -17 is not an option, so the numbers will have no "common factor" and n will be prime
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Re: If n= p^2-p+17, is n prime? [#permalink] New post   13 May 2013, 19:53
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srcc25anu wrote:
N = p^2 - P + 17
N = P(P-1) + 17
Is N prime?

St1: P = Prime Number
if p = 2, 2*1 + 17 = 19 Prime
If p = 17, 17*16 + 17 = a multiple of 17. hence Not Prime
Insufficient

ST2: P = Integer < 17
True for all integers.
Product of any 2 consecutive integers + 17 will yield a prime number.
if p = 3, 3*2+17 = 23 (prime)
if p = 6, 6*5 + 17 = 47 (prime)
same for all integers less than 17.
SUFFICIENT

Ans B


In B you are not considering negative numbers. If p=-17, than B is not sufficient.
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Re: If n= p^2-p+17, is n prime? [#permalink] New post   13 May 2013, 19:00
N = p^2 - P + 17
N = P(P-1) + 17
Is N prime?

St1: P = Prime Number
if p = 2, 2*1 + 17 = 19 Prime
If p = 17, 17*16 + 17 = a multiple of 17. hence Not Prime
Insufficient

ST2: P = Integer < 17
True for all integers.
Product of any 2 consecutive integers + 17 will yield a prime number.
if p = 3, 3*2+17 = 23 (prime)
if p = 6, 6*5 + 17 = 47 (prime)
same for all integers less than 17.
SUFFICIENT

Ans B
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Re: If n= p^2-p+17, is n prime? [#permalink] New post   17 Jun 2014, 03:37
I think the answer is E?

If p = 11 (prime), then p^2 - p + 17 = 121 - 11 + 17 = not prime.
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Re: If n= p^2-p+17, is n prime? [#permalink] New post   17 Jun 2014, 03:39
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pretzel wrote:
I think the answer is E?

If p = 11 (prime), then p^2 - p + 17 = 121 - 11 + 17 = not prime.


121 - 11 + 17 = 127 = prime.
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Re: If n= p^2-p+17, is n prime? [#permalink] New post   24 Jan 2023, 21:42
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Re: If n= p^2-p+17, is n prime? [#permalink]
24 Jan 2023, 21:42
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