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 ?

Answer 1

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