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Here

https://primes.utm.edu/glossary/page.php?sort=PrimorialPrime

it can be seen that the largest known primorial prime of the form $p\#-1$ is far smaller than the largest known primorial prime of the form $p\#+1$. I do not see a reason why a plus-primorial number has a bigger probability to be prime.

Is this result pure chance, or is there a mathematical reason ?

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  • $\begingroup$ There is no such discrepance for the factorial primes : primes.utm.edu/glossary/xpage/FactorialPrime.html $\endgroup$ – Peter Sep 14 '15 at 16:09
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    $\begingroup$ I don't immediately see any reason that it's due to anything but chance. $\endgroup$ – Greg Martin Sep 14 '15 at 16:50
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    $\begingroup$ Does the question really make sense ? Your link doesn't suggest the $\pm $ primorial primes are not equidistributed $\endgroup$ – reuns Dec 7 '17 at 20:25

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