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Let us define following prime number :

Let $~S_p~$ be Sophie Germain Star prime number of the form :

$S_p=12\cdot p \cdot (2p+1)+1$

where $~p~$ is a Sophie Germain prime number .

Note that :

Since $~p \equiv 5 \pmod 6 \Rightarrow S_p \equiv 5 \pmod 8$ , So:

$S_p \nmid 2^p-1 ~~\text{and}~~ S_p \nmid 2^{2p+1}-1 \Rightarrow$

$ord_{S_p}(2) \neq p ~~\text{and}~~ ord_{S_p}(2) \neq 2p+1$

Heuristic results indicates that percentage of S.G. Star prime numbers whose primitive root is $2$ among all S.G. Star prime numbers up to arbitrary upper bound $n$ is approximately $66$ %

My question :

What would be expected number (percent) of composite numbers of the form :

$S_p=12\cdot p \cdot (2p+1)+1~$ such that :

$2^{S_p-1} \equiv 1 \pmod {S_p}$

up to some arbitrary upper bound $n$ ?

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