and 1 contributors

# NAME

Math::NumSeq::Primes -- prime numbers

# SYNOPSIS

`````` use Math::NumSeq::Primes;
my \$seq = Math::NumSeq::Primes->new;
my (\$i, \$value) = \$seq->next;``````

# DESCRIPTION

The prime numbers, not divisible by anything except themselves and 1.

``````    2, 3, 5, 7, 11, 13, 17, 19, ...
starting i=1``````

Currently this is implemented with `Math::Prime::XS` generating blocks of primes with a sieve of Eratosthenes. The result is reasonably progressive. On a 32-bit system there's a hard limit at 2^31 (though even approaching that takes a long time to calculate).

# FUNCTIONS

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

`\$seq = Math::NumSeq::Primes->new ()`

Create and return a new sequence object.

`\$bool = \$seq->pred(\$value)`

Return true if `\$value` is a prime.

In the current code a hard limit of 2**32 is placed on the `\$value` to be checked, in the interests of not going into a near-infinite loop.

`\$i = \$seq->value_to_i_estimate(\$value)`

Return an estimate of the i corresponding to `\$value`. `\$value` can be any size, it's not limited as in `pred()`. See "Value to i Estimate" below.

# FORMULAS

## Value to i Estimate

In the current code the number of count of primes up to value is estimated by the well-known asymptotic

``    i ~= value/log(value)``

# HOME PAGE

http://user42.tuxfamily.org/math-numseq/index.html

# LICENSE

Copyright 2010, 2011, 2012, 2013 Kevin Ryde

Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.