2022/007) If, $n^2−33,n^2−31$ and $n^2−29$ are prime numbers, then what is the number of possible values of n where n is an integer

 $n^2−33,n^2−31$ and $n^2−29$ are 3 consecutive even numbers or 3 consecutive odd numbers

they cannot be 3 consecutive even numbers as all cannot be prime

so they are 3 cosecutive odd numbers.

so one of them is divisible by 3.

so the number has to be 3 otherwise it is not prime.

so 3 numbers are 3 , 5, 7 and $n^2-33 = 3$ giving $n = \pm 6$ or number of values of n = 2