Explain why every odd prime q is of one of the forms 12n1 12

Explain why every odd prime q is of one of the forms 12n+1, 12n+5, 12n+7, or 12n+11.

We will one by one rule out other cases

12n+2 would be even so cannot be odd prime

12n+3 is possible for n=0. Not clear what is the range of n. If n is a natural number then 12n+3 cannot be prime as it would be multiple of 3

12n+4 is also even

12n+6 is also even

12n+8 is even

12n+9 is multiple of 3

12n+10 is even

12n is even

Hence only the given cases are left out for q to be odd prime