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On certain subsets of prime numbers which are consecutive and close. Prime twins $p$ and $p+2$, as well as $p-2, p, p+4$, are constellations. Also related are admissible sets in number theory, which are sets $A$ of integers $a_i$ such that there may be an integer $t$ with many or all of $t+a_i$ being prime. This has ties to prime gaps and additive number theory
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Can exist a positive integer number $x$ such that $a_1=x$ and $a_n=2a_{n-1}+1$ are not prime...
Using my computer, I found that the most of positive integer number $x$ such that $a_1=x$ and $a_n=2a_{n-1}+1$ is prime number after a few iterations. But exist some positive integer numbers, my comp …