Documentation

# `ithprime`

I-th prime number

MuPAD® notebooks will be removed in a future release. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

## Syntax

```ithprime(`i`)
ithprime(<PrimeLimit>)
```

## Description

`ithprime(i)` returns the `i`-th prime number.

If the argument `i` is a positive integer, then `ithprime` returns the `i`-th prime number. An unevaluated call is returned, if the argument is not of type `Type::Numeric`. An error occurs if the argument is a number that is not a positive integer.

The first prime number `ithprime(1)` is 2.

If the `i`-th prime number is contained in the system's internal prime number table (see the help page for `ifactor`), then it is returned by a fast kernel function. Otherwise, MuPAD® iteratively calls `nextprime`, using some suitable pre-computed value of `ithprime` as starting point. This is still reasonably fast for i ≤ 1000000. If `i` exceeds this value, however, then the run time grows exponentially with the number of digits of `i`.

## Examples

### Example 1

The first 10 prime numbers:

`ithprime(i) \$ i = 1..10`
` `

A larger prime:

`ithprime(123456)`
` `

Symbolic arguments lead to an unevaluated call:

`ithprime(i)`
` `

## Parameters

 `i`

## Options

 `PrimeLimit` Return the number of primes in the internal prime table `ithprime(PrimeLimit)` returns an integer, namely the number of primes in the internal prime number table. The table contains all primes below some bound which can be obtained by calling `ifactor``(PrimeLimit)`. On UNIX® platforms, the size of this table can be changed via the MuPAD command line flag `-L`.

## Return Values

Prime number or an unevaluated call to `ithprime`

#### Mathematical Modeling with Symbolic Math Toolbox

Get examples and videos