On the primality of 𝑛!±1 and 2⋅3⋅5⋯𝑝±1

Caldwell, Chris K.

doi:10.1090/S0025-5718-1995-1284663-3

On the primality of $n!\pm 1$ and $2\cdot 3\cdot 5\cdots p\pm 1$
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by Chris K. Caldwell PDF

Math. Comp. 64 (1995), 889-890 Request permission

Abstract:

For each prime p let p# be the product of the primes less than or equal to p. Using a new type of microcomputer coprocessor, we have found five new primes of the form $n! - 1$, two new primes of the form $p\# + 1$, seven new primes of the form $p\# - 1$, and greatly extended the search bounds for primes of the form $n! \pm 1$ and $p\# \pm 1$.

References

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J. P. Buhler, R. E. Crandall, and M. A. Penk, Primes of the form $n!\pm 1$ and $2\cdot 3\cdot 5\cdots p\pm 1$, Math. Comp. 38 (1982), no. 158, 639–643. MR 645679, DOI 10.1090/S0025-5718-1982-0645679-1

New primality criteria and factorizations of

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Factorial and primorial primes

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A new primorial prime

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The development of a powerful low-cost computer for number theory applications

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Mark Templer, On the primality of $k!+1$ and $2\ast 3$ $\ast 5\ast \cdots \ast \,p+1$, Math. Comp. 34 (1980), no. 149, 303–304. MR 551306, DOI 10.1090/S0025-5718-1980-0551306-2