What is the value of prime number p?

Question

What is the value of prime number  p ?
1)  p=n^2-1  where  n  is a positive integer
2)  p ,  p+2 , and  p+4  are all prime

Loser94 · Answer

What is the value of prime number p ?

State 1
p=n^2-1=(n-1)*(n+1) so for every value of n except for 2 this will be a even number means it will have more than 1 factors.
so putting n=2 gives p=3
Sufficient

2) p, p+2, p+4 are prime this can happen if p=3 and p=11 both prime number holds the equation so not sufficient .

IMO-A

yashikaaggarwal · Answer

To find: What is the value of prime number p?

Solution:
1) p=n^2-1 where n is a positive integer
P = n^2-1 
P = (n+1) (n-1) 
So P is a product of two consecutive no. Situated at even consecutive distance. 
And P is prime so it's one (lowest) factor has to be 1.
So n-1 = 1
N = 2
So P = 1*3 = 3
(Sufficient)

2) p, p+2, and p+4 are all prime
Odd+even = odd
And since the prime triplets are at even consecutive distance. 
Which is by default only 3,5&7. 
So P value is 3
(Sufficient)

Answer is D

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TestPrepUnlimited · Answer

Statement 1:

p = n^2 - 1 = (n - 1)*(n + 1)  so p cannot be prime unless (n - 1) = 1. In that case we have n = 2 and p = 3. Then p = 3 is the only possible prime input. Sufficient.

Statement 2:

If we look at the divide by 3 world, these values are consecutive in that world with p, p + 2 and p + 4 -> p + 1. Since we have 3 consecutive values, one of them must be divisible by 3 and cannot be prime. Then we cannot have any large p's where p, p+2 and p+4 are all prime. However we have a special case of 3, 5, 7 so p = 3 is the only possible scenario. Sufficient.

Ans: D

Mo2men · Answer

When p=11 then p+4=11+4=15 which is NOT prime number.

Gauravji21 · Answer

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Hi..
I understand that if we have three consecutive numbers then one of them will be divisible by 3. But in the questions we have P, P+2, P+4. how come these three numbers can be considered consecutive numbers.

rajatchopra1994 · Answer

In statement 2
As you quoted When P=11, 
P+4 will be 15 which is not a prime number.
The only value which satisfies the condition when P=3

Tonkotsu · Answer

I was confused by this 'consecutive' thing also, but looked up some math properties.

We know already that  P, P + 2, P + 4   is a small list of 3 consecutive odd integers.
If we want to see it another way, can rewrite this equation here   2n + 1, 2n + 3, 2n + 5   where n is an integer.

This shows us that either the first, second, or third number can be divisible by 3 just by nature of being 3 odd numbers apart.
Any integer n (or p in the earlier equation) you plug in will always result in being divisible by three.

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What is the value of prime number p?

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What is the value of prime number p?

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