The odd looking prime

Number Theory Level 1

I've calculated the difference between 2 consecutive prime numbers, and it turns out that the result is also a prime number!

What is this resultant prime number?

The answer is 2.

3 solutions

Zach Abueg
Jul 29, 2017

Note that $2$ and $3$ are the only consecutive primes, and their difference, $1$ is not prime.

Every other prime $p > 2$ is odd, so the difference between any two consecutive primes is always even:

$\displaystyle (2m + 1) - (2n + 1) = 2(m - n)$

Now, the only even prime is $2$ , so $\boxed{2}$ is the only possible prime difference between two primes.

Oh, how is this wrong? @Pi Han Goh

Zach Abueg - 3 years, 10 months ago

Just saw Marta's report! I didn't think of that!

Zach Abueg - 3 years, 10 months ago

I've added the word "consecutive." Yayyy!!!

Pi Han Goh - 3 years, 10 months ago

@Pi Han Goh – Sounds good! Thanks :)

Zach Abueg - 3 years, 10 months ago

Mohammad Khaza
Aug 10, 2017

$5-3=2$ ..........................[all of them are primes]

You have only demonstrated that 2 can be an answer, but you didn't show that it is a unique answer.

Pi Han Goh - 3 years, 10 months ago

if the difference between two prime number is 2, then ,all of them are primes.

suppose, 7-5=2......[all of them are primes]

Mohammad Khaza - 3 years, 10 months ago

That makes no sense. You have only demonstrated that 5-3= 2 and 7-5 = 2, but how do you know that there doesn't exists another pair of primes such that their difference is not 2?

Pi Han Goh - 3 years, 10 months ago

@Pi Han Goh – if the difference is more than 2,then all of the three will not be prime.

because, if you want to get, odd primes, then you have to subtract a even number from an odd number.

Mohammad Khaza - 3 years, 10 months ago

Janesh G
Sep 12, 2017

How can this be two consecutive means. A number and the next one only

The odd looking prime

The answer is 2.

3 solutions

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