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Primorial primes are the primes that are of the form $p_n \# \pm 1$, where $p_n \#$ is the product of first $n$ primes.

My doubt is follows:

Is there any special name or study for the primes of the form $2p_1p_2p_3\cdots p_n + 1$,where $p_1, p_2 \cdots p_n$ are distinct odd primes but not necessarily the first $n$ primes?

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    $\begingroup$ You could call them "prime distinctorials". $\endgroup$ – Shalom Mar 22 '18 at 19:44
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    $\begingroup$ To help narrow things down before running an OEIS search, note that there are no primes of the form $4k + 1$ in your "distinctorials" $\mathcal P$ since $\mu(\mathcal P - 1) \neq 0$. $\endgroup$ – Robert Soupe Mar 23 '18 at 12:34

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