Romeo Meštrović

Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132

Volume 20, 2014, Number 4, Pages 33–36

**Full paper (PDF, 140 Kb)**

## Details

### Authors and affiliations

Romeo Meštrović

*Maritime Faculty, University of Montenegro
Dobrota 36, 85330 Kotor, Montenegro
*

### Abstract

If we suppose that *S* = {*p*_{1}, *p*_{2}, …, *p _{k}*} is a set of all primes, then taking

*x*=

*p*

_{1}

*p*

_{2}…

*p*+ 1 into a formula due to E. Meissel in 1854 gives

_{k}(

*p*

_{1}− 1)(

*p*

_{2}− 1)…(

*p*− 1) = 0.

_{k}This obvious contradiction yields the infinitude of primes.

### Keywords

- Euclid’s theorem
- Infinitude of primes
- Euclid’s proof
- Euler’s proof(s)
- Möbius inversion formula
- Meissel formula

### AMS Classification

- Primary: 11A41
- Secondary: 11A51, 11A25

### References

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## Cite this paper

Meštrović, R. (2014). Euler–Euclid’s type proof of the infinitude of primes involving Möbius function Notes on Number Theory and Discrete Mathematics, 20(4), 33-36.