Question

prove that there exists no prime such that p-q=97,if p and q are prime

Answer 1

when p and q are both not equal to 2 then,
p and q are both odd numbers and difference of two odd number is an even number so
one of them has to be even.
Now, when p=2 then 2-q=97 ==> q=-95 [not prime]
when q=2 then p-2=97 ===>p=99[not prime]
Thus, there exists no prime such that p-q=97,if p and q are prime

Answer 2

great thanks I just have to formalize it

Answer 3

What can I say now..

I can just say that @sauravshakya is right...

Answer 4

lol thanks

Answer 5

Ha ha ha ha..