1Math::NumSeq::Primes(3)User Contributed Perl DocumentatioMnath::NumSeq::Primes(3)
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6 Math::NumSeq::Primes -- prime numbers
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9 use Math::NumSeq::Primes;
10 my $seq = Math::NumSeq::Primes->new;
11 my ($i, $value) = $seq->next;
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14 The prime numbers, not divisible by anything except themselves and 1.
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16 2, 3, 5, 7, 11, 13, 17, 19, ...
17 starting i=1
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19 Currently this is implemented with "Math::Prime::XS" generating blocks
20 of primes with a sieve of Eratosthenes. The result is reasonably
21 progressive. On a 32-bit system there's a hard limit at 2^31 (though
22 even approaching that takes a long time to calculate).
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25 See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
26 classes.
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28 "$seq = Math::NumSeq::Primes->new ()"
29 Create and return a new sequence object.
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31 "$bool = $seq->pred($value)"
32 Return true if $value is a prime.
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34 In the current code a hard limit of 2**32 is placed on the $value
35 to be checked, in the interests of not going into a near-infinite
36 loop.
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38 "$i = $seq->value_to_i_estimate($value)"
39 Return an estimate of the i corresponding to $value. $value can be
40 any size, it's not limited as in "pred()". See "Value to i
41 Estimate" below.
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44 Value to i Estimate
45 In the current code the number of count of primes up to value is
46 estimated by the well-known asymptotic
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48 i ~= value/log(value)
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51 Math::NumSeq, Math::NumSeq::TwinPrimes,
52 Math::NumSeq::SophieGermainPrimes, Math::NumSeq::Emirps
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54 Math::Prime::XS, Math::Prime::TiedArray, Math::Prime::FastSieve,
55 Math::Prime::Util
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58 <http://user42.tuxfamily.org/math-numseq/index.html>
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61 Copyright 2010, 2011, 2012, 2013, 2014, 2016 Kevin Ryde
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63 Math-NumSeq is free software; you can redistribute it and/or modify it
64 under the terms of the GNU General Public License as published by the
65 Free Software Foundation; either version 3, or (at your option) any
66 later version.
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68 Math-NumSeq is distributed in the hope that it will be useful, but
69 WITHOUT ANY WARRANTY; without even the implied warranty of
70 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
71 General Public License for more details.
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73 You should have received a copy of the GNU General Public License along
74 with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
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78perl v5.30.1 2020-01-30 Math::NumSeq::Primes(3)