Documentation

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)

Parameters

m

An arithmetical expression

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.

See Also

MuPAD Functions

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