somebody good in math induction proof ?

so prove that always there exist a prim number p the form of 6n +/- 1 what adding to the number of 12g , where g is a number from this set 1,2,3,5,7,10,12,17,.... , so from this sum always result at least one prim number

for example :

1. 12*1 + 5 or 7 = 17 - 19
2. 12*2 + 5 or 7 = 29 - 31
3. 12*3 + 5 or 7 = 41 - 43
4. 12*5 + 11 or 13 = 71 - 73

- so i think maybe this proven by math induction

Question

somebody good in math induction proof ?

so prove that always there exist a prim number p the form of 6n +/- 1 what adding to the number of 12g , where g is a number from this set 1,2,3,5,7,10,12,17,.... , so from this sum always result at least one prim number

for example :

1. 12*1 + 5 or 7  = 17 - 19
2. 12*2 + 5 or 7 = 29 - 31
3. 12*3 + 5 or 7 = 41 - 43
4. 12*5 + 11 or 13 = 71 - 73

- so i think maybe this proven by math induction

Imagine · Answer

Are you asking us to solve this?

jhonyy9 · Answer

yes for any idea to solve it by math induction or ... there exist other one method to prove it ?

jhonyy9 · Answer

@imqwerty now is posted correct - any idea ? ty.

imqwerty · Answer

So the set $g$ only contains 1,2,3,5,7,10,12,17 ? no other numbers in set g?

jhonyy9 · Answer

no - this set is - i think -  infinity

imqwerty · Answer

how can I generate more numbers of this set? How do I get the $n^{th}$ number in this set