- if p=2n+1 ,where p2,p is prim, than p-1=2n and n=(p-1)/2
- so for n=k than k=(p-1)/2 so 2k=p-1 so
2k=(2n+1)-1 so 2k=2n /divide both sides by 2
so k=n
- from this result that for every natural numbers
n=1 exist one p prim such that n=(p-1)/2
true or false ?

Question

- if p=2n+1 ,where p>2,p is prim, than p-1=2n and n=(p-1)/2
- so for n=k than k=(p-1)/2 so 2k=p-1 so 
2k=(2n+1)-1 so 2k=2n /divide both sides by 2
so k=n
- from this result that for every natural numbers 
n>=1 exist one p prim such that n=(p-1)/2
true or false ?

mr.math · Answer

False. Take $n=4$ for example, that would give $p=9$ which is not a prime.