# User:Contribution/Minimal Prime Limit

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# Minimal prime limit

## Definition

A positive rational number q belongs to the pmin-min-prime-limit, called the **minimal prime limit**, for a given prime number pmin if and only if it can be factored into primes (with positive or negative integer exponents) of size more than or equal to pmin.

In other words, a positive rational number q belongs to the pmin-min-prime-limit if and only if all primes of its factorization into primes are left-bounded to pmin.

### Examples

- 2-min-prime-limit contains ℚ+\{0}

- 3-min-prime-limit contains the above excluding numbers with 2 in their factorization into primes. Also called no-twos just intonation, there is no octaves in this system. It is the bigger min-prime-limit containing the Bohlen-Pierce scale.

- 5-min-prime-limit contains the above excluding numbers with 3 in their factorization into primes. There is neither octaves nor fifths in this system.