The remainder obtained when any prime number greater than 6 is divided by 6 must be :

Let the required prime number be p.
Let p when divided by 6 give n as quotient and r as remainder. Then p = 6n + r, where 0 $$ \leqslant $$ r < 6
Now, r = 0, r = 2, r = 3 and r = 4 do not give p as prime.
∴ r $$ \ne $$ 0, r $$ \ne $$ 2, r $$ \ne $$ 3, and r $$ \ne $$ 4
Hence, r = 1 or r = 5