# `prevprime`

Next smaller prime

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## Syntax

```prevprime(`a`)
```

## Description

`prevprime(a)` returns the greatest prime number less or equal than a. If a < 2, then `prevprime(a)` returns `FAIL`.

`prevprime` returns the function call with evaluated argument if the argument is not an integer.

`prevprime` returns an error if the argument evaluates to zero or a negative integer.

## Examples

### Example 1

Computing the largest prime p ≤ 15485865:

`prevprime(15485865)`

### Example 2

There are no primes smaller than 2:

`prevprime(1)`

## Parameters

 `a` A positive integer

## Return Values

`prevprime(a)` returns either a natural number or `FAIL`.

## Algorithms

`prevprime` uses the probabilistic prime test `isprime` and may therefore return false results with small probability.