# Documentation

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# `numlib`::`checkPrimalityCertificate`

Test the primality certificate

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## Syntax

```numlib::checkPrimalityCertificate(`certificate`)
```

## Description

`numlib::checkPrimalityCertificate` tests the certificate of primality returned by `numlib::proveprime`. For large prime numbers, the `numlib::proveprime` function generates certificates that provide all data you need for proving primality of a number by the Atkin-Goldwasser-Kilian-Morain algorithm. See Example 1.

For small prime numbers, `numlib::proveprime` does not return a certificate of primality. Instead, it returns `TRUE`. For nonprime numbers `numlib::proveprime` returns `FALSE`. In both cases, you do not need to use `numlib::checkPrimalityCertificate`.

## Examples

### Example 1

Use the `numlib::proveprime` function to check the primality of the number 1299709. The function returns the following sequence of lists. This sequence is the certificate of primality:

`certificate := numlib::proveprime(1299709)`

The certificate provides all data that you need for proving primality of 1299709 by the Atkin-Goldwasser-Kilian-Morain algorithm. You can substitute the numbers into the algorithm and verify the primality of the number. Alternatively, you can verify the certificate by using the `numlib::checkPrimalityCertificate` function:

`numlib::checkPrimalityCertificate(certificate)`

## Parameters

 `certificate` A list or a sequence of lists returned by `numlib::proveprime`