## 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;
- Math. Comp.
**71**(2002), 441-448 - DOI: https://doi.org/10.1090/S0025-5718-01-01315-1
- Published electronically: May 11, 2001
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## 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.## References

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## Bibliographic Information

**Chris K. Caldwell**- Affiliation: Department of Mathematics and Computer Science, University of Tennessee at Martin, Martin, Tennessee 38238
- Email: caldwell@utm.edu
**Yves Gallot**- Affiliation: Department of Mathematics and Computer Science, University of Tennessee at Martin, Martin, Tennessee 38238
- Address at time of publication: 12 bis rue Perrey, 31400 Toulouse, France
- Email: galloty@wanadoo.fr
- Received by editor(s): March 21, 2000
- Published electronically: May 11, 2001
- Additional Notes: The first author would like to thank the fellow faculty members who allowed us to use their computers’ idle time over a period of months, especially David Ray and John Schommer.
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp.
**71**(2002), 441-448 - MSC (2000): Primary 11A41; Secondary 11N05, 11A51
- DOI: https://doi.org/10.1090/S0025-5718-01-01315-1
- MathSciNet review: 1863013