On the primality of 𝑛!±1 and 2×3×5×\dotsm×𝑝±1

Caldwell, Chris; Gallot, Yves

doi:10.1090/S0025-5718-01-01315-1

On the primality of $n! \pm 1$ and $2 \times 3 \times 5 \times \dotsm \times p \pm 1$
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by Chris K. Caldwell and Yves Gallot PDF

Math. Comp. 71 (2002), 441-448 Request permission

Abstract:

For each prime $p$, let $p\#$ be the product of the primes less than or equal to $p$. We have greatly extended the range for which the primality of $n! \pm 1$ and $p\# \pm 1$ are known and have found two new primes of the first form ($6380!+1, 6917!-1$) and one of the second ($42209\#+1$). We supply heuristic estimates on the expected number of such primes and compare these estimates to the number actually found.

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