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

Answer 1

n is natural number
p is prim number the form of 6n +/- 1

prove that 12n + p always give a prime number

Answer 2

prove this by math induction

Answer 3

Here's something that might come in hand,

Answer 4

consider n=3
p = 6*3+1= 19
p is a prime of the given format

But 12n+p = 12*3+19 = 55 is not a prime number.

Answer 5

yes @imqwerty true so sorry but i ve made a mistake there bc. the n from 12n is not the same n from 6n +/- 1

so let be in place of n in case of 12n an m in this way let be 12m with m natural number

Answer 6

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
m is natural number
p is prim number the form of 6n +/- 1

prove that 12m + p always give a prime number
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 7

@Vocaloid how you think please can be this proven by math induction ?

Answer 8

so i have wrote the proof of ... but i m not sure that is acceptably or not ... ???

Answer 9

"prove that 12m + p always give a prime number"

but you can still consider the case where n = 3 & m = 3.

Answer 10

yes @imqwerty this is true but i ve thought on a different cases - sorry i need re-edit this posted question ... and i will re-post it
ty. all your contribution

Answer 11

okie