KVPY 2019 SA Exam Previous Papers

Question : 64 of 80

Marks: +1, -0

A prime number p is called special if there exist primes

p_1, p_2, p_3, p_4

such that

p = p_1 + p_2 = p_3 -p_4

The number of special primes is :

Solution:

Obviously

p_4 = 2

& one of

p_1, p_2

is also 2 (say p

_2

)
so

p = p_1 + 2 = p_3 -2

⇒

p_1, p, p_3

are 3 consecutive odd numbers
⇒ atleast one of them is divisible by 3
⇒

p_1 = 3 ⇒ p_2 = 5 \and p_3 = 7

Hence only one special prime exists.

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