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# nextprime

Next prime number

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```nextprime(m)
```

## Description

nextprime(m) returns the smallest prime number larger than or equal to m.

If the argument m is an integer, then nextprime returns the smallest prime number larger than or equal to m. A symbolic call of type "nextprime" is returned, if the argument is not of type Type::Numeric. An error occurs if the argument is a number that is not an integer.

The first prime number is 2.

## Examples

### Example 1

The first prime number is computed:

`nextprime(-13)`

If the argument of nextprime is a prime number, this number is returned:

`nextprime(11)`

We compute a large prime:

`nextprime(56475767478567)`

Symbolic arguments lead to a symbolic call:

`nextprime(x)`

 m

## Return Values

Prime number or a symbolic call to nextprime.

## Algorithms

nextprime uses a fast probabilistic prime number test (Miller-Rabin test) to decide if the computed result is a prime number. The result returned by nextprime is either a prime number or a strong pseudo-prime for 10 randomly chosen bases.

## References

Michael O. Rabin, Probabilistic algorithms, in J. F. Traub, ed., Algorithms and Complexity, Academic Press, New York, 1976, pp. 21-39.