The number of primes is finite

Author:
Miodrag Zivkovic

Journal:
Math. Comp. **68** (1999), 403-409

MSC (1991):
Primary 11B83; Secondary 11K31

MathSciNet review:
1484905

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Abstract: For a positive integer let and let . The number of primes of the form is finite, because if , then is divisible by . The heuristic argument is given by which there exists a prime such that for all large ; a computer check however shows that this prime has to be greater than . The conjecture that the numbers are squarefree is not true because .

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Additional Information

**Miodrag Zivkovic**

Affiliation:
Matematički Fakultet, Beograd

Email:
ezivkovm@matf.bg.ac.yu

DOI:
https://doi.org/10.1090/S0025-5718-99-00990-4

Keywords:
Prime numbers,
left factorial,
divisibility

Received by editor(s):
July 19, 1996

Received by editor(s) in revised form:
January 23, 1997

Article copyright:
© Copyright 1999
American Mathematical Society