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

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If n= p^2-p+17, is n prime? [#permalink]  13 May 2013, 12:53
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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
[Reveal] Spoiler: OA

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Kudos [?]: 14 [0], given: 17

Re: If n= p^2-p+17, is n prime? [#permalink]  13 May 2013, 18:00
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]  13 May 2013, 18:52
2
KUDOS
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

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.

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Kudos [?]: 136 [1] , given: 12

Re: If n= p^2-p+17, is n prime? [#permalink]  13 May 2013, 18:53
1
KUDOS
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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Kudos [?]: 1611 [1] , given: 219

Re: If n= p^2-p+17, is n prime? [#permalink]  13 May 2013, 21:35
1
KUDOS
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]  16 Jun 2014, 11:47
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Re: If n= p^2-p+17, is n prime? [#permalink]  17 Jun 2014, 02:37
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]  17 Jun 2014, 02:39
Expert's post
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] 17 Jun 2014, 02:39
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