$:$ Senderov V.A.

Does there exist a number $n$ such that the numbers

a) $n-96, n, n+96$

b) $n-1996, n, n+1996$

are prime? (All prime numbers are considered positive.)
a) For example, when $n=101$, we get the prime numbers 5, 101, 197.

b) Since 1996 is not divisible by 3, one of the numbers $n-1996$, $n$, and $n+1996$ is divisible by 3, hence $n-$ $1996=3$. But then $n+1996=3995$ is a composite number.

## Answer

a) Exists; b) does not exist.