Question

If p, q, r are prime numbers such that r=q+2 and q=p+2,then the number of triplets of form p, q, r is

Answer 1

Answer:

(3 , 5 , 7)

Step-by-step explanation:

If p, q, r are prime numbers such that r=q+2 and q=p+2,then the number of triplets of form p, q, r is

r = q + 2

q = p + 2

=> r =p + 4

three numbers are

p , p + 2 , p + 4

Let say p = 3k

Then

3k , 3k + 2  , 3k + 4

3k , 3k + 3 , 3(k + 1) + 1

out of Three number  one must be multiple of 3

so k = 1 only Satisfies this

p = 3  q = 5 r = 7

the number of triplets of form p, q, r  is  only one

(3 , 5 , 7)