### Abstract

Bertrand's postulate is an early result on the distribution of prime numbers: For every positive integer n, there exists a prime number that lies strictly between n and 2n. The proof is ported from John Harrison's formalisation in HOL Light. It proceeds by first showing that the property is true for all n greater than or equal to 600 and then showing that it also holds for all n below 600 by case distinction.

### License

BSD License

### Topics

- Mathematics/Number theory

### Session Bertrands_Postulate

- Bertrand

### Depends on

- Pratt’s Primality Certificates

### Used by

- Formalization of Randomized Approximation Algorithms for Frequency Moments
- Dirichlet L-Functions and Dirichlet’s Theorem

### Auto-related entries

- Pick’s Theorem
- Zeckendorf’s Theorem
- Basic Geometric Properties of Triangles
- Fourier Series
- Probabilistic Primality Testing

## Cite

×

Bertrands_Postulate-AFP

    @article{Bertrands_Postulate-AFP,
      author  = {Julian Biendarra and Manuel Eberl},
      title   = {Bertrand's postulate},
      journal = {Archive of Formal Proofs},
      month   = {January},
      year    = {2017},
      note    = {\url{https://isa-afp.org/entries/Bertrands_Postulate.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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