# Thread: Prime number of a form

1. ## Prime number of a form

Find all primes of the form 2^(2^n)+5, where n is a nonnegative integer

Thanks very much!!

2. Originally Posted by suedenation
Find all primes of the form 2^(2^n)+5, where n is a nonnegative integer

Thanks very much!!
Only n=0
Because if n>0 then you have
none, all these numbers are divisible by three.
Proof
~~~
We know that,
2 = -1 (mod 3 )
Then,
2^(2^n) = (-1)^(2^n) (mod 3)
But,
(-1)^(2^n)=1 because exponent is even.
Thus,
2^(2^n) = 1