2
$\begingroup$

Let's observe following number :

$ 4517\cdot 2^{332192811}+1$

I have noticed :

If $k\cdot 2^{2n+1}+1$ is prime number then $\gcd(k-1,3)=1$ , where $k,n \in Z^{+}$ , so

$\gcd(k-1,3)=1$ should be a necessary condition.

Since $\gcd(4516,3)=1$ this condition is fulfilled.

Proth weight of coefficient $4517$ is $w \approx 0.98199 $ which may be considered to be high value.

I would like to know are there some other necessary conditions that this number has to satisfy , so that might be considered like candidate for prime number ?

1 Answers 1

2

Mathematica:

1: PrimeQ[$4517\cdot2^{332192811} + 1$]

2: False

I guess they use the Miller-Rabin primality test.

  • 1
    I think that there must be more similar conditions..2011-11-25