# Prime

There are 3 functions provided: `primeq`, `bigprimeq`
and `nextPrime`.

## Primality Test

### primeq

Primality test of an integer is a common tasks in number theory.
`primeq` is a rigorous primality test function.
It takes an integer argument *n*.

- service url:
`http://nzmath-json.appspot.com/prime/primeq/`*n*/

Returned value will be a boolean, *true* or *false*.

Note that this test may time-out.

## Probable Prime Test

### bigprimeq

Sometimes, it is sufficient to know probable primality of a number.
A probable primality test can be much faster than rigorous one.
`bigprimeq` is essentially a Miller-Rabin test function.
It takes an integer argument *n*.

- service url:
`http://nzmath-json.appspot.com/prime/bigprimeq/`*n*/

Returned value will be a boolean, *true* or *false*.
The error probability for false positive is less than 4^{-20}.

## Prime Generation

### nextPrime

What is the smallest prime more than 1 million?
Such a question can be answered by `nextPrime`.
It takes an integer argument *n*.

- service url:
`http://nzmath-json.appspot.com/prime/nextPrimeq/`*n*/

Returned value will be the smallest prime strictly bigger than the given *n*.
Note that this test may time-out as primeq.