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## 8.29 Prime Numbers

### 8.29.1 Routines

#### 8.29.1.1 calc_primes

include std/primes.e namespace primes public function calc_primes(integer approx_limit, atom time_limit_p = 10)

Returns all the prime numbers below a threshold, with a cap on computation time.

##### Parameters:

`approx_limit`: an integer, This is not the upper limit but the last prime returned is the**next**prime after or on this value.`time_out_p`: an atom, the maximum number of seconds that this function can run for. The default is 10 (ten) seconds.

##### Returns:

A **sequence**, made of prime numbers in increasing order. The last value is the next prime number that falls on or **after** the value of `approx_limit`.

##### Comments:

- The
`approx_limit`argument**does not**represent the largest value to return. The largest value returned will be the next prime number on or after - The returned sequence contains all the prime numbers less than its last element.

- If the function times out, it may not hold all primes below
`approx_limit`, but only the largest ones will be absent. If the last element returned is less than`approx_limit`then the function timed out.

- To disable the timeout, simply give it a negative value.

##### Example 1:

? calc_primes(1000, 5) -- On a very slow computer, you may only get all primes up to say 719. -- On a faster computer, the last element printed out will be 1009. -- This call will never take longer than 5 seconds.

##### See Also:

#### 8.29.1.2 next_prime

include std/primes.e namespace primes public function next_prime(integer n, object fail_signal_p = - 1, atom time_out_p = 1)

Return the next prime number on or after the supplied number

##### Parameters:

`n`: an integer, the starting point for the search`fail_signal_p`: an integer, used to signal error. Defaults to -1.

##### Returns:

An **integer**, which is prime only if it took less than 1 second to determine the next prime greater or equal to `n`.

##### Comments:

The default value of -1 will alert you about an invalid returned value, since a prime not less than `n` is expected. However, you can pass another value for this parameter.

##### Example 1:

? next_prime(997) -- On a very slow computer, you might get -997, but 1009 is expected.

##### See Also:

#### 8.29.1.3 prime_list

include std/primes.e namespace primes public function prime_list(integer top_prime_p = 0)

Returns a list of prime numbers.

##### Parameters:

`top_prime_p`: The list will end with the prime less than or equal to this value. If`top_prime_p`is zero, the current list of calculated primes is returned.

##### Returns:

An **sequence**, a list of prime numbers from 2 to <= `top_prime_p`

##### Example 1:

sequence pList = prime_list(1000) -- pList will now contain all the primes from 2 up to the largest less than or -- equal to 1000, which is 997.

##### See Also: